# Hydraulic Fracturing

Parr I
Introduction ............................................................... 1 Damage Around the Wellbore ............................................ 1 Low Formation Permeability ............................................. 2 Non-Homogeneous Formations ........................................... 2 Hydraulic Fracturing Definitions .......................................... 2

Parr 2 

### History of Fracturing ....................................................... 3 Early Work ............................................................ 3 Fracturing Today ....................................................... 3

Parr 3 Mechanics of Hydraulic Fracturing

........................................... 5 Fracture Initiation ...................................................... 5 Fracture Extension ...................................................... 6

Parr 4 Fracture Geometry ......................................................... 8 Fluid Injection into the Fracture .......................................... 8 Fluid Flow Along the Fracture Length ..................................... 9 Fluid Leak-Off ......................................................... 9

Parr _5 Particle Transport ......................................................... 10 Proppant Movement ................................................... 11 Proppant Settling ...................................................... 12 Proppant Bed ......................................................... 14 Tail-In Using Thin Fluids ............................................... 16 Suspended Proppants ...................................................16

Parr 6 Laboratory Tests for Selection of Base Fluids ................................ 17 Types of Base Fluids ................................................... 17 Structural and Chemical Analysis of Formation Samples ..................... 18 Evaluation of Fluid-Rock Interactions ..................................... 19 Evaluation of Fluid Properties ........................................... 20

Parr 7 Factors Influencing Hydrocarbon Production ................................. 21 Matrix Permeability .................................................... 21 Fracture Conductivity .................................................. 22 Summary ............................................................. 23



### HESI303125Part 8

Properties of Chemicals and Fracturing Fluids ................................ 23 Common Fracturing Chemicals .......................................... 23 Fracturing Polymers .................................................... 23 Crosslinking Agents .................................................... 28 pH Conu’ol Chemicals .................................................. 29 Gel Breakers .......................................................... 29 Surfactants ........................................................... 29 Clay Stabilizers ........................................................ Alcohol .............................................................. 32 Biocides .............................................................. 32 Fluid Loss Additives ................................................... 32 Summary ............................................................. 32



### Part 9 Proppants and Fracture Conductivity ........................................ 33 Types of Proppants .................................................... 33 Calculations for Production Rate ......................................... 34 Damage to Proppant Bed ............................................... 35 Selection of the Propping Agent .......................................... 38 Laboratory Tests for Conductivity ........................................ 38 Fracture Closure Stress ................................................. 40

Part 10 Production Increase ....................................................... 40 Calculations for Vertical Production Increase ............................... 41 Computer Simulations .................................................. 45

Part I I Hydraulic Fracturing Equipment ............................................ 47 Fluid Storage ......................................................... 47 Proppant Storage ...................................................... 47 Blending Equipment ...............................................  ̄ .... 48 High Pressure Pumping Equipment ....................................... 49 Control Center ........................................................ 49 Surface Lines and Manifolding .......................................... 50

Part 12 Practical Design of Fracturing Treatments .................................... 50 Fracture Design Variables ............................................... 50 Selection of Design Variables ............................................ 51

Part 13 Monitoring a Frac Treatment During Pumping ................................ 56 Analysis of Bottomhole Treating Pressure .................................. 56 Real-Time Treating Pressure Analysis in Field Operations .................... 57 Minifrac Process ....................................................... 58

Revised 6YH



### HESI303126

### Part i4

Post-Frac Analysis ......................................................... 60 Inadequate Initial Response ............................................. 60 Rapid Production Decline ............................................... 61 Refrac Treatments ..................................................... 62

References ............................................................... 63

Appendix A .............................................................. 67

Appendix B .............................................................. 74

Appendix C .............................................................. 80

Revised 6YH iii



### HESI303127

### HESI303128hydraulic fracturmR 1



## INTRODUCTION

Part 1 After an oil or gas well has been drilled, thewellbore pressure is reduced (lower than the reservoir pressure) which forces fluid to flow into thewellbore. The oil an~or gas will be displaced toward the wellbore by methods such as fluid expansion, natural or artificial fluid displacement, gravity drainage, capillary expulsion, etc. These processes may work together or independently to drive the hydrocarbon into the wellbore through the permeability of the reservoir rock or, in some wells, through a network of natural fractures. In many instances, production of the well maybe commercially insufficient. Assuming the reservoir does contain commercial quantifies of producible hydrocarbons, then at least one of the following conditions probably exists:

 ̄ damage around the wellbore  ̄ low formation permeability  ̄ non-homogeneous formation.



### Damage Around the Wellbore

In this situation, the natural flow channels within the reservoir (formation permeability or natural fracture system) are sufficient to allowcommercial production rates, but these flow channels are severely plugged in the near-wellbore region. This plugging may have been caused by the drilling fluid or 

### completion fluids 

### (i.e., cement filtrate, perforating fluids, etc.). In some cases, the damage may be a result of the formation reaction with one or more of these fluids. The swelling of formation clays, scale build-up and precipitation of iron oxides are a few such possibilities. The production problem then becomes one of treating the reservoir in some manner which will increase the flow of fluid into the wellbore (Fig. 1.1). This may be a simple acid wash or acidbreakdown of the perforations to remove or bypass the damage (restriction to flow) within theformation. However, it is often necessary to overcome the effect of the damage through hydraulic fracturing.

FILTRATE

Revised 6YH



### HESI303129hydraulic fracmrm~s



### Low Formation Permeability

Most of the fracturing treatments being applied today are the result of low permeability of the reservoir rock. We must keep in mind that themost valid definition of "low permeability" is related to the economics of each individual well.In many reservoirs, the original drilling proposal will include plans for a hydraulic fracturingtreatment as part of the completion program. Often, many details of the drilling or completion program will be dictated by factors which will help enhance the effects of the hydraulic fracturing treatment. Pre-planning for a fracturing treatment can be the deciding factor in the success or failure of obtaining commercial production rates.



### Non-Homogeneous Formations

This category is probably the one where theresult of a fracturing treatment is the most unpredictable. Two of the more common examples ofthe use of hydraulic fracturing in nonhomogeneous reservoirs are discontinuous lenticular sands and formations that produce primarily through natural fracture systems. These reservoirsare difficult to model. Often, the purpose of a fracturing treatment in a non-homogeneous formation is to communicate with parts of the reservoir that may have no hydraulic link to the wellbore.



### Hydraulic Fracturing Def’mitions

Hydraulic fracturing may be defined as the process in which fluid pressure is applied to the exposed reservoir rock until failure or fracturing occurs. After failure of the rock, generally referred to as formation breakdown, a sustained application of fluid pressure extends the fracture outward from the point of failure. This fracture creates anew and larger flow channel; it may connect existing natural fractures as well as provide additional drainage area from the reservoir. The fluid used to transmit the hydraulic pressure to the reservoir rock is called the fracturing fluid. At fracturing pressures, fluid will continue penetrating the zone (Fig. 1.2) causing continued fracturing of the formation rock, thus extending the crack (fracture) farther into the formation. The first fracturing fluid to enter the fracture is the padvolume. It creates the fracture and begins to control fluid loss into the formation porosity along the formation surfaces, which are the "walls" of the fracture. To help prevent the fracture from closing when pumping is stopped, propping agents (Fig. 1.3) are added to the fracturing fluid. Proppants act as supports to hold the fracture open after the treatment and to provide an improved ability ofthe fracture to conduct oil or gas through the fracture to the wellbore.

UPPER LAYER

LOWER LAYER

Fig. 1.2 - Schematic of Hydraulic Fracturing

A. 20/40 Mesh Ottawa Sand lB. 20/40 Mesh Intermediate

Strength Bauxite Proppant

Fig. 1.3 - Typical Propping Agents (enlarged)

Revised 6YH



### HESI303130hydraulic fracturing 3

Since the beginning of hydraulic fracturing, many different types of materials have been used as propping agents: sand, walnut hulls, aluminum pellets, plastic beads, steel shot, man-made glassbeads and sintered bauxite beads. Today’s propping agents are available in different size distributions and are used in varying quantities. Part 9 of this text is an extensive review of propping agents and their applications in hydraulic fracturing. The ability of the fracture to conduct fluids tothe wellbore affects the ability of the well to produce. The fracture conductivity as well as the length and the height of the fracture that is propped open are all very important. High fractureconductivity combined with a long propped fracture length may result in good increased production in old or new wells and may make a producer from a noncommercial well. In Part 10 of this text, we will discuss these production increases. The effect of fracture conductivity, propped length and propped height as they influence the stimulated producing rates will be studied in detail.



## HISTORY OF FRACTURING

Part 2

In 1948, Stanolind Oil & Gas Company (later Pan American Petroleum Corporation and nowAMOCO) received a patent for its hydraulic fracturing process to stimulate well productivity. Theannouncement culminated several years of extensive laboratory and field study. In March 1949, Halliburton Oil Well Cementing Company (now Halliburton Services), operating as an exclusivelicensee, performed the first two commercial fracturing treatments on the same day; one in Archer County, Texas, and the other in Stephens County,Oklahoma. Thus began one of the most outstanding well stimulation procedures that the petroleum industry has ever known. What has hydraulic fracturing meant to the oil industry? Conservative estimates indicate that three of every four wells fractured have resulted in profitable production increases that in turn have raised potential reserves tremendously.Today, many fields exist because of these techniques. Without hydraulic fracturing, several producing horizons would have been bypassed as either barren or commercially nonproductive. The famous Spraberry formation of West Texas was one of the first such zones. It was passed up in several wells as not productive. Then fracturing treatments indicated otherwise, and since that timeevery well completed in that interval has been fractured.


### Early Work

As in many new developments, changes in hydraulic fracturing were destined to take place. Early treatments were conservative. Volumes of200 .to 400 gallons of fluid with 1/2-1b sand per gallon injected at rates of 2 to 4 bbl/min were considered average treatments. Twice that quantity was considered a large job.OccasionaLly some brave operator would perform a 1,500 to 2,000 gallon treatment which was looked upon with critical speculation. In so doing,more pumps were usually used, resulting in increased injection rates. These larger, higherinjection-rate type jobs began to show higher, more sustained production increases. Gradually the job sizes and injection rates began to increase. Higher injection rates led to the belief that perhaps highly viscous fluids were not necessary, as previously had been believed. Experiments were conducted with less expensive fluids of lower viscosity with good results.In the latter part of 1952, use of ref’med petroleum residuals and heavier crude oils became popular in addition to the gelled hydrocarbons. This permitted greater volume per dollar cost;and, from that time on, aqueous base fluids became more popular and the treatment size increased steadily, as shown in Figures 2.1 and 2.2.Figure 2.3 shows other historical trends of fracturing treatments. By 1982, the average job had increased to more than 60,000 gallons.


### Fracturing Today

Present fracturing treatments are a far cry from those performed over 30 years ago. Although a great number of relatively small volume

### jobs are still completed each day, it is now common to see service equipment valued at several million dollars surrounding a well (Fig. 2.4) and pumping 200,000 to 500,000 gallons of fracturing fluid and 500,000 to 2,000,000 pounds of proppant. Part 11of this text discusses the fracturing field equipment presently in use.

Revised 6YH



### HESI303131Fig. 2.1 100 9O

8O
7O
60 5O
40
30 20
10 TREND OF FRACTURING BASE FLUIDS

AQUEOUS BASE FLUID_

49 ’53 ’57 ’61 OIL BASE FLUID



# I I"-1"1

’65 ,69 ’73 ’77 ~81 ’85 ’89 YEAR

TREND OF AVERAGE ~FRACTURE TREATMENTS

IN THE UNITED STATES 32.0 100 ]100

-~ 1.6 80 (n-o~ 80 z ~ m, I 0 1.4 70’z-0 ~ 

### ~ 1.2 6o ~--: s~ /
~ 1.0 50 ~o.8 4ogtl Ik /’/ ""

lso ~ ~ rFLUIDiTREATMENT 30 

## go.6 ao ~ 0.4 2o ~ ~ I I 2o

10

’49 ’53 ’57 ’61 ’65 ’69 ’73 ’77 ’81 ’85 ’89

YEAR

Fig. 2.2 IO00I

!500I

0001 EVOLUTION OF FRACTURING TECHNIQUES

INJECTION f ’-" ’-- RATE / J 

# /

-- .-~  ̄ HHPIJOB

’49 ’53 ’57 ’61 ’65 ’69 ’73 ’77 ’81 ’85 ’89

YEAR Fig. 2.3

Revised 6YH Fig. 2.4 - Massive HydrAulic Fracturing Treatment



### HESI303132hydraulicfracturing 5



# MECHANICS OF HYDRAULIC FRACTURING

Part 3

Since the hydraulic fractures of our interest are created in reservoir rock, a discussion of themechanical behavior of rocks would be appropriate. Essentially all reservoir rock will have some degree of elasticity and deformability. They will vary from highly elastic, well cemented sandstones to soft, weakly consolidated formations with very little elasticity that will deform under pressure. A very detailed theoretical discussion on rockmechanics and the mechanics of hydraulic fracturing is given in Appendix A at the end of this text.A brief overview of fracture mechanics will be provided here.

Fracture Initiation

In hydraulic fracturing we apply a 

### force against the reservoir rock. This is accomplished by 

### pumping a fluid into a wellbore that is in communication with the reservoir we wish 

### to fracture. The 

### anticipated reaction is 

### to overcome the tensile strength of the rock and the minimum in situ stress to create a tensile fracture in the formation. Initiation of the fracture is commonly referred to as "breakdown" of the formation. In an open hole completion, the breakdownpressure may be only slightly higher than the pressure needed to extend fracture growth. However, in a perforated completion the breakdown pressure may be significantly higher. This fact is related to how efficiently the fluid is able to communicate its hydraulic pressure to the reservoir rock. If there is a very large number of clean, open perforations and the fluid can easily penetrate the formation matrix, then the perforated wellbore will be similarto an open hole. But if only limited pressure communication exists, then breakdown pressure will be higher. Once breakdown occurs and the fracture has been initiated, the effect of rock tensile strength will essentially disappear. Unless they cause a severe restriction to fluid flow, the effect of the perforations will also become negligible. The fracture’s orientation and azimuth (i.e., compass orientation) will be dictated by the stresses that exist in the rock. These stresses are caused by the weight of the overburden and by 

### tectonic forces. As discussed in Appendix A, the system of 

### stresses can be represented mathematically 

### by an equivalent set of in situ principal stresses. In practical applications, one of these three stresses will be the smallest; this fact will dictate the orientation of the created hydraulicfracture. Because the overburden stress (represented in Fig. 3.1 by "o’,") is very seldom thesmallest, nearly all hydraulic fractures in hydrocarbon reservoirs will be essentially vertical in orientation. In a normally pressured reservoir, the least principal stress will be in the range of 0.6 to 0.9 psi per foot of depth. The least principal stress canbe measured in field practice by obtaining an "instant shut-in" measurement during a hydraulic fracturing treatment. However, the magnitude ofthe other two stresses cannot be determined accurately with current technology. Other methods of determining the least in situ stress, as well as discussion on its importance, are given in Part 12 of this text.

Lowest (least likely)

PRINCIPAL STRESS AND FRACTURE ORIENTAr]ON

Fig. 3.1 L~Lowest 2



### HESI303133

## 6 ~r~ulic fracturing

The azimuth of the fracture is not easily determined. However, extensive work is being done using both laboratory tests and various field study methods. Pierce, et. al. ~ discusses pulse testing as one of the more reliable methods; however, this method requires both the existence of and control over several adjacent wells. Lacy2 gives the result of a major operating company’s extensive fieldinvestigation of five other techniques for determining the orientation of hydraulic fractures. He concludes that all five methods gave reliable results. Figures 3.2 and 3.3 (taken from Lacy) are simple but very accurately illustrate the value of knowing the fracture orientation in both primary recovery and when using secondary recovery techniques for fractured wells.

Good Drainage

Incomplete Drainage

Fig. 3.2 Good Areal Sweep

Inject

Produce

Inefficient Areal Sweep

Produce

Inject

Produce 0

II C

II

II 0

Fig. 3.3



### Fracture Extension

Continuing to inject fluid into the fractureafter breakdown will result in extension of the fracture in the plane that is perpendicular to the least in situ principal stress?" The fracture is simply following the path of least resistance. In cased boreholes, the location of the perforations may affect the near-wellbore direction of fracture growth, but probably only for a few feet. Both laboratory and field observations have shown that the presence of small natural fractures will not alter the general direction of fracture growth. However, the presence of multiple (parallel)fracture strands were recently reported by WarpinskP in a mineback experiment.on a hydraulically fractured sandstone. He observed that these multiple fracture strands, which were in addition to the primary hydraulic fracture, usually extendedonly a few feet. In a mineback experiment involving a shallow, naturally fractured coal seam (that had been hydraulically fractured) only a very few multiple fracture strands were observed.’

Revised 6YH



### HESI303134As the fracture extends from the wellbore the

growth will be in a radial pattern as long as there are no significant changes in the magnitude of the in situ stress or in rock properties. However, in actual practice, the fracture will usually encounter changing stresses and rock properties as it grows in vertical height. In recent years, several investigators have shown that the minimum in situ stress in the various rock layers is the dominating feature.7-8 Earlier theories that higher elastic moduli alone will stop fracture growth at an interface have now largely been discounted7s9 unless there is a very distinct interface between the zones’°.

Boundary Rock

Pay Zone

U- - -B~u-ndary R-~ck

~r~Boundary Rock

F~YZOne 

# ./]__

~J’~oundary Rock

Fig. 3.4 If the fracture grows vertically into the zonewith higher stress, this will arrest (or at least retard) the vertical growth and force most of the fracture growth to be in length and/or width (Fig. 3.4). In some formations, such as massive chalks, the rock properties are very uniform and the stresses change so little that the hydraulic fracture will continue to grow radially. In many formations, the fracture may encounter a higher stress in onlyone direction. That is, only the zone above or below the pay zone will have sufficient stress difference to inhibit fracture growth (Fig. 3.5).

¢, = 2500 psi

-L- ~ = 2000 psi

_ ---- o’2 = 2000 psi

..... )

OR

2000 psi

Fig. 3.5

ReUsed



### HESI303135

## 8 hydraulic fracturing

Unfortunately, there are also instances where either the upper or lower boundary zone has a lower in situ stress and most of the created fracture is outside the pay zone (Fig. 3.6). When this situationexists, it will be very difficult to achieve commercially successful stimulation with hydraulic fracturing, unless very short propped fracture lengths are acceptable. If the vertical fracture growth is into awater bearing zone, the well may not be economical or, at best, will result in increased well costsdue to handling and disposal of the produced water. The high commercial success ratio of hydraulic fracturing applications suggests the limited height growth case (Fig. 3.4) is probably the most typical result.

., [ ~r. = 2500 psi

~ 1800 psi~

OR

Fig. 3.6 

# FRACTURE GEOMETRY

Part 4 

### The economic success or failure of a hydraulicfracturing treatment usually depends on the geometry of the created fracture. For horizontal fractures, this includes its width (separation of the two fracture faces) and radius. For vertical fractures this means its width, length (lateral dimension) and height (vertical dimension). Fracture shape was discussed in Part 3 of this text. The geometry of a hydraulic fracture depends on many factors interrelated in a complex manner.The physical events that simultaneously occur during fracture extension are:

 ̄ fluid injection into the fracture  ̄ flow of fluid along the fracture length  ̄ fluid leak-off into the fracture walls.These factors must all be considered no matter what fracture shape, orientation or azimuth isused in a calculation. For the purpose of simplifying the discussion in this part of the text, we have assumed a vertical fracture that is either radial orrectangular in shape. In field applications, horizontal fractures are uncommon. A more theoreticaland detailed discussion of fracture geometry calculation is given in Appendix B at the end of this
text.



### Fluid Injection Into The Fracture

The volume of fluid injected into the fracture (Vt) is the product of the injection rate (q) of the surface pumps and pumping time (t):
V,= qt
The value of V, is one of the few numbers accurately known during a fracturing treatment. Of this volume, part stays inside the hydraulic fracture (Vf) and part is lost to the formation as leak-off (V~). Therefore:
V, = Vf + V~

### The volume efficiency (El) of a hydraulic fracture is defined as: (4-1)

Ef = V¢ / Vt

or El= 1-Vt/Vf (4-2) ((

Revised 6YH



### HESI303136The parameter Ef defines the fraction of the

injected volume which forms the actual fracture volume. Thus, it is desirable to increase El, which is usually done by decreasing V,.In addition to the treatment volume, it is necessary to know the engineering properties of the fluid itself. Laboratory experiments indicate that most presently used treatment fluids have complex behavior that cannot be precisely described bysimple models. Therefore, for mathematical simplicity, treatment fluids are either assumed to be Newtonian, to behave like a power-law model, or possibly tO behave like a Bingham Plastic, as someauthors have proposed for foam fluids. The powerlaw model is the most commonly used. For apower law fluid, the engineering constants describing the treatment fluid behavior are its flow behavior index (n’) and absolute consistency (K’), which are measured in the laboratory.



### Fluid Flow Along the Fracture Length

The fluid being pumped is forced out of the wellbore and into the fracture being extended. The frictional losses due to fluid flow along the fracture create a pressure drop between the fracture tip and borehole, denoted by Ap~. The magnitude of thispressure drop plays an important role in the computation of fracture geometry. Kristianovich and Zheltov3 first pointed out that the treatment fluid does not occupy the entire length of the hydraulic fracture. The tip of the fracture has a cusp shape and does not contain the treatment fluid. According to Daneshy4, if x~ is the wetted length of a vertical fracture, and q(x) andw(x) denote the flow rate and fracture width respectively at a point along the fracture length, then:

Apo = 2(2n’+l/n’-~-~-/ × K’f° [6q(x)]n’ dx -’xo w(x)’"’÷’ (4-3)

Assuming that ~ry is the least in dtu principal stress (Fig. 4.1), then the treatment pressure of a hydraulic fracture (pf) can be calculated from:
p~ = (r~. + Ape (4-4) In common oilfield terminology this pressure (p~) is called the bottomhole treating pressure (BHTP). X= -L P, = ,ry + ..Xp(x) x= L--/

~llbore

~g. 4.1 - Overhead View of a Vertical Fracture

If the frictional losses due to flow in the wellbore are denoted as A Ppi~ , frictional losses through the perforations are A p~, and the hydrostatic pressure induced by the weight of the treatment fluid column down to the fracture depth is then the wellhead pressure pw can be expressed as: p, = pf + Ap~ + App~ - Ap~ (4-5) The value of Ape as given by equation 4-3does not include the influence of adding a propping agent to the treatment fluid. The Ape for a fluid containing a propping agent can be computed by replacing n’ and K’ of the fluid by that of the slurry, if such data are available.



### Fluid Leak-Off

As mentioned previously, part of the fluid in contact with the fracture faces penetrates into theformation pores and is lost as leak-off. This reduces the amount of fracture volume created per unit volume of fluid injected. To decrease the rate of leak-off, fluid-loss additives usually are added to the treatment fluid to form a filter cake on the fracture wall.Figure 4.2 shows the results of a typical fluidloss test conducted in the laboratory using coreplugs from formation cores. The curve in this figure can be divided into two parts. In Part I, a f’fltercake is in the process of forming. This fluid leakoff is mainly governed by the fracturing fluid viscosity, the formation fluid viscosity, pore pressure, formation compressibility, the formation porosity and permeability, etc. Fluid leak-off during this time is called "spurt loss."



### HESI3031370 hydraulic fracturmg~

PURT VOLUME m =2C,,, 

# b’-’"/ °>a ..

v’TIME

Fig. 4.2 - Plotted Data from Laboratory Fluid Loss Test

Point A in Figure 4.2 is identified by its ordinate, called spurt volume. This value is determined experimentally in the laboratory. The spurt volume measured in the fluid-loss test is usually dependent on the concentration and type of the fluid-loss additives and the formation permeability. It is quite common to measure a zero spurt loss on low permeability formation cores, especially with high viscosity fluids. The slope of the line in Part I of the curve isdenoted by 2Cvo. The term C,o is a combined fluidloss coefficient where the leak-off rate is controlled by fluid viscosity and compressibility but a filtercake has not yet formed. This is explained by WilliamsY Since the Cv, value in an actual off or gasreservoir may vary significantly from the laboratory test conditions, the C,, from the laboratory test is seldom determined or used. In Part II of the curve, a filter cake has now been formed and is controlling fluid leak-off. This part of the curve is identified by its slope, denoted by m = 2Cw. The Cw is the fluid-loss coefficient where the leak-off rate is controlled by the wall building properties of the fluid and/or fluid loss additives. The fluid-loss test is usually run to determine two parameters: the spurt volume and the fluid loss coefficient. The magnitude of C,, is computed from the reservoir as well as the treatment fluid properties. With spurt volume and C,o known, one can compute a spurt time. The rate of fluid leak-off at any point in the fracture depends on the time that the point has been exposed to fracturing fluid. If this time is lessthan the spurt time, then Part I of the curve determines the leak-off rate. For exposure times greater than the spurt time, the rate of fluid leak-off is measured from Part II of the curve. As long as the fracture is extending through permeable rock, some portion of the fracture will be in Part I, while most of the exposed area will be in Part II. Fluid leak-off has important effects on the geometry of the created fracture. First, it decreases the fracture volume, and consequently the size of the fracture dimensions. It also affects the rate of fluid flow down the fracture, q(x), which as shown by equation 4-3, changes the fluid pressure inside it.



# PARTICLE TRANSPORT

Part 5 The effectiveness of any fracturing treatment is strongly influenced by the conductivity of theresultant propped fracture. Conductivity will depend on the size and strength of the propping agent used, and the distribution of the proppant in the fracture. In the early days of fracturing, a common assumption was that the proppant traveled with the fluid with which it was mixed. This led to the assumptions that the proppant’s distribution was always the same as the fluid’s, and the fracture was propped over 100 percent of its area. These assumptions were not unrealistic whenthe jobs were very small and the fluid was kerosene gelled with napalm. This was a very highviscosity gel that could suspend the proppant partides during the treatment. However, as fracturing fluid development moved toward lower viscosities with such materials as water thickened with guar gums or cellulose gels, or even ungelled water or oil, the suspended proppant assumption becameless reasonable. Also, the treatment volumes increased significantly.It is usually assumed that any part of the fracture surfaces that are not separated by proppant particles will close back into their original position under the influence of the in situ stresses. Thus, only the propped portions of the fracture will be available for fluid flow and will contribute to the long term beneficial effects of the stimulationtreatment. The completeness of this fracture "healRevised 6YH



### HESI303138ing" has been argued for many years. It is generally believed that shallow, low stress wells may not heal as completely as deeper wells where in stresses are high. It would seem reasonable that a fracture in aproducing formation would result in a higher producing rate if a large part of the fractured surfacewere exposed than if only a small part of the fracture remained open. Therefore, the prediction ofthe final distribution of the proppant is an important part of the design of fracturing treatments. Present day fracturing fluids range across the entire spectrum of physical properties. Viscosities vary from that of water to materials that behave like rubbery semi-solids. Densities may range from that of gas-liquid foams ( = 1.6 lb/gal) to saturatedbrines (= 12 Ib/gal). Thus, the proppantsuspending properties of fluids vary widely. Therehas even been some recent application of compressed nitrogen gas using very low proppant concentrations (no liquid phase present).



### Proppant Movement

Several steps are involved in the transport of proppant particles in hydraulic fracturing: 1. Transport through the surface equipment (pumps, etc.) 2. Transport down the wellbore tubulars 3. Movement and change of direction through the perforation 4. Transport in the fracture itself and additional settling that may occur while the fracture is closing. The fracture may be of two major forms:

 ̄ Horizontal fracture - a slot radiating away fromthe wellbore in all directions in a plane perpendicular to the wellbore

 ̄ Vertical fracture - a slot extending in two directions from the wellbore. These forms are illustrated in Figure 5.1. As part B of this figure shows, the vertical fracture may be radial or more nearly rectangular in shape. The rectangular shape vertical fracture is usually expected to be the most common form of hydraulicfractures. Radial (either horizontal or vertical) fractures usually occur in a few select geographic areas. A. Horizontal Fracture

B. Vertical Fractures

Fig. 5.1

The shape of a vertical fracture created might be visualized to be elliptical in both the horizontal and vertical planes. Thus, each of the two fracture wings might have a shape like Figure 5.2, which shows only the right wing of the fracture. Of course, the illustration in Figure 5.2 is distorted. If the drawing were to a realistic scale, the length to height ratio would be much greater and the width would only appear to be a thin solid line.

Fig. 5.2

Predicting the movement of proppant particles in the fracture mainly concerns determining thefluid viscosities and velocities throughout the system."43 The fracture shown in Figure 5.2 has a different cross-sectional area down its length (L) and, hence, a different velocity for each position

Revised 6YH



### HES1303139

### 2 hydraulic ,"rac!urmg

along its length. The real shape of any given fracture is unknown. To simplify velocity calculations, a rectangular fracture such as one of the three cases shown in Figure 5.3 usually is assumed for a mathematical model. Which shape is selected is a function of how accurate and sophisticated the model will be.

Case 1 ~

Caseh~2

~ ~

Rg. 5.3

This type of a fracture model would have a constant height and, except in the most simple models, a width that changes all along its length. The most accurate model will be elliptical with the most width variation occurring near the tips, as in Case 3. Also, it usually is assumed that the entire height is open to fluid entry and that the proppant enters the fracture uniformly through its width at the wellbore. These simplifications help greatly insolving the mathematics of the proppant movement. 

### The movement of the proppant particles is " affected by such parameters as:

 ̄ fluid velocity

 ̄ fluid viscosity

 ̄ fluid leak-off

 ̄ fluid density

 ̄ proppant size

 ̄ proppant density

 ̄ proppant shape

 ̄ proppant concentration.



### Proppant Settling

The horizontal particle velocity and settlingrate (vertical velocity) will determine the distribution of particles in the fracture. When a proppant particle enters the fracture with the moving stream of fluid, the drag exerted on the particle will causeit to move horizontally along the fracture. Assuming the particle did not contact the fracture walls or other particles, it should travel horizontally with the same velocity as the fluid. If the fluid were of very low viscosity (a gas, for example) or the fluid~ particle density ratio is very great, there might be slippage and the particle could lag behind the fluid.Simultaneously, the particle would be accelerated downward in the vertical direction by the force of gravity. A particle settling in a static fluid would reach a terminal velocity at which the force due to gravity would balance the drag due to the particle moving through the fluid. Assuming a spherical particle, laminar flow, and Newtonian fluid, the following equation would express the settling velocity:

where: = [ 4gdp(pp - p)~0.,

(12) 3pCD ]

v = setting velocity, ft/sec d~ = particle diameter, in.
pp = particle density, lb/cu ft
p = fluid density, lb/cu ft CD = drag coefficient g = acceleration due to gravity, 32.2 ft/sec2 

### (5-1)

Revised 6YH



### HESI303140If the particle were very small or the viscosity

large enough that the Reynolds number (N~) is less than 0.3 (Stokes Law region), the drag coefficient would be:

24 

## cD -- ~ (5-2)

N~ denotes the Reynolds number and is defreed as:

where: ~ = fluid viscosity, cp From equations 5-1, 5-2 and 5-3: 18.486dp’(p~- p).

In the Stokes Law region, the vertical velocity reached by the fluid under these conditions would depend upon the particle diameter, fluid viscosity and the difference in density between the particle and the fluid.Figure 5.4 illustrates the vertical settling velocity for spherical particles falling in Newtonian fluids. This figure is calculated using the specific gravity of sand (2.65) and fluid density of water (1.0). (5-4)

SE13"LING VELOCITY vs SAND DIAMETER
0.1

0.01. 0.001 0.01 0.1 Free Sand Settling Velocity, O, Ft/Sec 8112 Mesh

12/20 Mesh

20140 Mesh

40/60 Mesh

1.0

Fig. 5.4 - Particle Settling Velocities


### The horizontal fluid velocity depends upon the fracture width and injection rate (assuming a constant height). As the treatment progresses, more fluid is pumped, and the fracture grows in length and width. The relationship between the fracture length, width and volume is logarithmic and is illustrated in Figures 5.5 and 5.6. Thus, the width is slowly increasing as the length increases. LOG w

LOG VOLUME

Fig. 5.5

LOG L

LOG VOLUME

Fig. 5.6

If a constant input rate to the system is maintained, the velocity at any point along the fracture length is slowly decreasing with time, due to the increasing width. However, the velocity is greater closer to the tip of the fracture, because the width decreases .towards the tip. In addition, all points on the fracture surface are experiencing fluid loss to some degree. This is caused by the high fluid pressure in the fracture. The loss of fluid reduces the fluid velocity and hence affects the particle velocity. Another factor to consider is that fluid loss increases the proppant concentration. This can affect settling rates, which will be discussed later as "hindered settling." A study of movement of a single particle in avertical fracture t-filed with a thin fluid is illustrated in Figure 5.7. If a particle M is introducedinto the frac.:ure from the wellbore, it will be accelerated to the bulk average fluid velocity .~ vertically. The resultant movement is the path MM’. The distance along the fracture length the particle travels before it reaches the bottom of the



### HESI3031414 hydraulic f~cturing

fracture will depend upon the magnitude of the fluid velocity, the settling velocity v, and position along the fracture height where the particle has entered the fracture.

M

Fig. 5.7

The fluid velocity depends on the injection rate, and the width and height of the fracture at the time, and position along the fracture length that is considered. The vertical settling velocitywill depend upon the fluid viscosity, particle diameter, particle shape, and the difference in density between the particle and the fluid.

Proppant Bed

If a large number of particles carried in a thinfluid is considered, such as in a fracturing treatment, the same situation exists as with a single particle. As illustrated in Figure 5.8, the particlesentering the mouth of the fracture all begin to settie. The lower particles do not have as far to fall and therefore reach the bottom of the fracture sooner than those starting from the top. After a longer period of time, more particles settle on topof the previously introduced ones. A bed of particles begins to form on the bottom of the fracture as more and more particles have time to reach the particles resting on the bottom (Fig. 5.9). Model studies conducted by Babcock" indicated that once the particles reached the bottom of the fracture they did not tend to move farther into the fracture but formed a stable bed of proppant at the bottom. Most fracturing treatments use a fluid that hasa significant viscosity. The thicker fluids will decrease the rate of proppant settling. Thus, there will be only a small bed of settled proppant and most of the fracture will contain a proppant slurry (see Fig. 5.10). If the pumping time is long enough, all the proppant in the leading edge of theslurry may reach the bottom before the job is completed. This distance is often called the "carry distance," based on the specific job conditions. This is essentially the greatest distance along the length that proppant can travel under these conditions.

~g. 5.8

--g. 5,9

Fig. 5.10

Revised 6YH



### HESI303142After the carry distance is reached, the growth of

the bed is only in the vertical direction because the particles entering the fracture at the wellbore willsettle to the top of the bed before they reach beyond this point (Fig. 5.11).

Carry D~stance

Fig. 5.11

Throughout the pumping time of the job a number of factors are changing simultaneously, each one of which affects the growth rate of the bed:

 ̄ The fracture width is increasing; which tends to decrease the fluid velocity, and thus to decrease the distance the particles travel horizontally.

 ̄ The temperature of the proppant laden fluid may be increasing as it moves down the fracture, possibly making the fluid less viscous.

 ̄ The walls of the fracture are being cooled, so the latter proppant stages are exposed to less heatand maintain higher viscosity than early proppant stages.

 ̄ The fluid loss is increasing the proppant concentration which results in greater particle interference and a decrease in settling velocity in thesame manner that increasing fluid viscosity decreases particle settling rate. This is called "hindered settling." Through the use of computer simulation of a fracturing treatment, we can calculate the growth of a hydraulic fracture. We can also model theproppant transport to estimate the degree of settling during the pumping operation, t3 When we doa computer simulation, we find that for most formation temperatures, gelled fluids will give an end-of-pumping proppant distribution similar toFigure 5.12. This figure is representative of a hydraulic fracturing treatment using a viscous fluid. In this example treatment, a specific volume of viscous fluid without proppant (pad fluid) was pumped first, followed by stages containing 1.0, 2.0, 3.0 and 4.0 pounds of proppant per gallon of fluid. A portion of the proppant has settled to the bottom during the pumping operation, but most of the proppant is still in a suspended slurry. Noticethat, due to fluid loss, the concentration of proppant in each stage has increased significantly. If thefluid loss were more severe, the proppant concentrations would be even higher.

II Slurry I 1.8ppg i ~ Slurry

Deposited Proppant Bed Pad

Rg. 5.12
Figure 5.13 illustrates the propped fracture ifthe suspended proppant could be trapped by fracture closure (healing) without any additional proppant settling having time to occur. Unfortunately, this condition will not necessarily be the actual result. The time needed for the fracture to close sufficiently to trap the proppant may be quite long. The settling velocity of the proppant will depend on the proppant type and size, as well as the fluid viscosity.

Unpropped Fracture

Fracture

Fig. 5.13

Figure 5.14 shows two other possibilities for the final propped fracture that may result from thetreatment represented in Figure 5.12. In most reservoirs, it can be assumed that the unpropped fracture area will essentially heal back to such a degree

Revised 6YH



### HES130314316 ,~vdraulic fracturing

that it will not significantly contribute to the stimulation of the well’s production. If a computer simulation of a fracture stimulation is to be valid, it will be necessary for the simulator to model thefracture closure and the additional proppant settling that will occur during the closure time.

Unpropped Fracture

Unpropped Fracture

Fig. 5.14

Tail-In Using Thin Fluids
III

Another circumstance to consider is what takes place when proppants of different sizes are run, such as 20/40 mesh sand tailed-in by 12/20mesh sand. The 12/20 sand will have a faster settling rate due to its larger grain size. If a low viscosity fracturing fluid is used, then where the 12/20 sand is deposited will depend upon where the 20/40 sand is and what its deposition history has been. If sufficient 20/40 sand were run toreach an equilibrium bed height, and a considerable amount of 12/20 pumped, it may be predominantly deposited on the leading edge of the 20/40 bed as in Figure 5.15. Although the 12/20 might be called tail-in, it really ended up at the leading edge of the bed. If only a small quantity of 12/20 sand were run, it might all be on top of the 20/40 bed with no extension of the carry distance. However, if the 20/40 sand had not been pumped long enough to reach equilibrium height, the 12/20 sand might be deposited as in Figure 5.16. In this case, the 12/20 sand only increased the bed height without increasing the length. If a very large quantity of 12/20 sand was pumped in this example, it might reach equilibrium height and then extend the carry distance. Note: These illustrations ignore any entrance effects at the wellbore.

Fig. 5,15

Fig. 5,16



### Suspended Proppants

The deposition of proppant will be somewhat different when fluids that have moderate to highviscosities are considered.13 If the fluid has an apparent viscosity greater than about 100 centipoise, there are several distributions that might occur. A condition that might exist is where only the first proppant remains in suspension in the fluid.If the fluid viscosity were high or the first proppant were small, the terminal settling velocity might be very slow and the particle settling would be insignificant during the time of treatment. If fluid of a few hundred centipoise viscosity were used to carry 20/40 sand, the settling ratemight be about 0.001 ft/sec (i.e., during a 100 minute treatment, the particles would settle only 6

Revised 6YH



### HES1303144hydraulic fracturing 

## 17

feet). If the fracture were 100 feet high, the deposited 20/40 sand bed would be very small and most of the particles would still be suspended at the end of the job. Tail-in of larger proppant introduced after the 20/40 could displace the 20/40 sand slurry and could form a bed configuration as in Figure 5.17.

Fig. 5.17 Suspenc~eO 12/20 ISuspended~ I 20/40 I I

-~x__. [~eposite~t 12/20 ~ Deposite6 20/40

If, after pumping ceases, the fracture remains open for a very long period of time, and/or the fluid viscosity thins enough for the proppant to settle, a final bed configuration like that shown in Figure 5.18 might result. a fracturing fluid with an apparent viscosity greater than 200 centipoise in the fracture probably will transport the proppant with little settling.

tad

Fig. 5.19

Obviously many possible situations 

### might be imagined, but the cases shown serve to illustrate some of the complexities of proppant distribution. The result of the consideration of proppant settling is that the propped length (xr) will be less than the created fracture length (L) and only partof the created height may be propped. The resulting production increase will depend upon both the propped length and the propped height, as will be discussed in Part 10.

Fig. 5.18

If the proppant is in suspension due to a highviscosity fluid and the fracture closed before settling takes place, a low concentration distribution may result (Fig. 5.19). This condition would not be uncommon with modern, complexed gelled fracturing fluids. The proppant distribution wouldbe at a much smaller concentration (lb/sq ft of surface area) than when a bed was formed. In general, 

# LABORATORY TESTS FOR SELECTION OF BASE FLUIDS

Part 6

Types of Base Fluids

Two basic types of fluids are used in hydraulic fracturing: hydrocarbon (or oil) base and aqueous (or water) base fluids. Hydrocarbon base fluids may be crude oils or refined liquid hydrocarbons. The advantages of this type of fluid are that they:

 ̄ are non-damaging to clays

 ̄ have low fluid-rock interfacial tension

 ̄ are generally compatible with most formations and formation fluids. The economics of hydrocarbon fluids may be advantageous, depending upon whether the fluid is

Revited



### HESI3031458 hT,~raulic fracturing~

recovered and either reused or sold. Of coursethere are disadvantages to the use of liquid hydrocarbons. The primary disadvantage is that they can be hazardous to handle under certain conditions. The use of water base fluids has continually increased. This type of fluid includes low strength salt solutions, water-alcohol mixtures and low strength acids using 3 to 5 percent hydrochloric acid as an aqueous base. Water from various sources may be used as a base fluid. The mostcommon sources are city and well water. Occasionally, water from streams, lakes or sea water is used as a base fracturing fluid. However, water from these sources should be checked for suspendedsolids or other contaminants which should be removed before the fluid is used. There are a number of advantages to water base fluids:

 ̄ these fluids are safe to handle  ̄ water sources are usually readily available  ̄ gelling agents and other chemicals can be batch mixed (premixing)

 ̄ chemicals can be mixed continuously as the fluid is being pumped into the wellbore ̄ it is possible to obtain much higher temperature stability than with oil base fluids. 

### The primary disadvantage is that water basefluids could have some detrimental effect on formations which tend to be water sensitive, i.e., those with clay minerals and/or fluid retention problems. There are several laboratory tests which can be conducted to determine the compatibility of the fracturing fluid with a given formation. These tests include petrographic analysis, X-ray diffraction analysis, and basic fluid-rock compatibility testing.Fluid-rock compatibility is evaluated through immersion tests, porosity and permeability testing, fluid flow tests through the core samples usingvarious potential base fracturing fluids, and regained gas permeability testing. Other tests can help predict potential emulsion problems and how to reduce them, the compatibility of formation oil with fracturing fluid oil (if an oil base fluid has been selected), how best to destroy the gellingagent which has been used in a fracturing treatment (gel break), fluid loss control, and fracture conductivity measurements. These tests will be discussed in more detail during the remainder of this section. 

### Structural and Chemical Analysis of Formation Samples

Selection of base fracturing fluid is one of themost important parameters in the successful application of hydraulic fracturing. Several laboratory tests can be conducted on formation samples to help us select the most appropriate base fracturing fluid. Petrographic Analysis Using thin sections and the scanning electron microscope (SEM), it is possible to determine thetype of formation with which we are dealing. Using thin sections, the type of minerals present and the general relationship between the formation matrix, the cementing materials and pore space can be observed. This gives an indication of the type of minerals that the fracturing fluid will contact whenfluid loss occurs. With knowledge of basic fluidrock interactions, thin section petrographic analysis gives some insight into potential compatibility problems. Another type of petrographic analysis uses the SEM

### to observe the pore space and pore configuration of formation samples. The effects of various fluids when placed on the core samples can also be observed.1~-1~ The use of the Energy Dispersive Xray (EDX) analysis with the SEM allows better identification of the samples being obse .ry~l-,~--~ ’ ..

 ̄  ̄ .~.¢J ’~£ ~L:r3’,.~ , X-Ray Diffraction Analysis ~

...... ;,, ; " This analysis is commonly use~l in bur indits--’"- try to determine the type of crystalline formation minerals present. X-ray diffraction, coupled with the petrographic analyses described earlier, allows us to determine the chemical and mineralogical make-up of the formation. The X-ray diffraction analysis is normally done in two steps. The bulk sample is ground and X-rayed to determine the non-clay fraction. The minerals normally detected in the non-clay fraction

are quartz, feldspar, calcite, dolomite, anhydrite, and other minerals in lesser quantities. The clay fraction is separated by mixing the ground bulksample with water. The smaller particles are suspended in the fluid and are poured off onto a glass slide. The water is allowed to evaporate, allowing settling and orientation of the small particles. AnX-ray diffraction analysis is then made of this sepRevi~ed 6YH



### HESI303146arated, small particle fraction of the bulk sample.

By separating the fine, small particles, the clays are concentrated and a better analysis is made. In the clay fraction, clays of the kaolinite, chlorite, illite, smectite and mixed-layer types may normally be detected.



### Evaluation of Fluid-Rock Interactions

Immersion TestsThese are basic and qualitative tests. However, immersion tests do allow a relative determination of the amount of fines which may be released from the reaction between a fluid and rock sample. By comparing the quantity of fines released from the rock samples when subjected to various fluids, relative compatibility is obtained. For the immersion test, formation core pieces are placed in various test fluids: fresh water, 2% calcium chloride water, 10% sodium chloride, 2% potassium chloride, various acid base fluids, and kerosene. The acid base fluids allow evaluation ofthe effects of low pH fluids. If the formation sample contains significant quantities of swelling clays (smectite, mixed-layer, etc.), release of f’mes may be partially controlled by the low pH or acidic basefluids. Previous work has shown that aqueous fluids with pH less than 7 are more compatible with clay containing formations than those with pHgreater than 7. ~16-~8 For this reason, ff at all possible, the aqueous base fracturing fluids are designed with pH less than 7. However, because of other fluid properties related to pH, a pH greater than 7 may be necessary in some cases to obtain the most desirable fracturing fluid properties. This subject will be discussed in more detail later in this text (Part 7). Porosity and Permeability Tests Tests on formation samples cannot always be made with the greatest degree of confidence. Whena core is removed from a well, it may be contaminated with drilling fluid. In addition, there is asignificant pressure change which could cause alteration of the physical condition of the clays. In many instances, the cores have not been preserved and are completely dry before any test is initiated. This condition can develop a strain in the clay packets which is rapidly released when the rock is rewet. The drying-wetting procedure is certainly one that would enhance the migration of clays, resulting in an indicated permeability damage more severe than would occur in the formation. On the other hand, permeabilities normally determined in the laboratory may be significandy greater than those that exist in the formation. Thomas and Ward’9 found that with cores that contained very little clay, an overburden pressureof 3,000 psi reduced surface gas permeability values by 62 to 90%. At 6,000 psi, permeability reduction was in the range of 73 to 99%. Thus, permeability damage determined in the laboratory with formation samples does not necessarily reflect the same degree of damage that could occur in the formation. Porosity and permeability testing help us to determine:  ̄ how much fluid might be lost to the formation under various conditions during a fracturing
treatment  ̄ the levels of porosity and permeability which may be related to potential fluid retention problems

 ̄ which core samples should be used in various types of laboratory testing.


### Fluid Flow TestsFluid flow tests are normally used in our industry to evaluate the effects of fluid which may be lost and forced to flow through the formation. Of concern here is the movement of f’me particles through the formation. Fluid flow tests are normally conducted onformation core samples having liquid permeabilities of at least 0.1 millidarcy. Lower permeabilities tend to yield results which are somewhat erratic due to low flow rates. Flow tests are conducted by obtaining an initial flow rate with some compatible fluid such as formation water, oil, etc. through a core plug. Then a second flow is normally made in the reverse direction through the core plug with a test fluid. Following the second flow, the final flow in the same flow direction as the original flow ismade with the original flowing fluid. By comparing the initial flow to the f’mal flow, it is possible to determine the effects of the test fluid on the core sample. There is an API standard test procedure, discussed in API RP 39, for conducting these tests; however, there are many variations of this basic procedure used in our industry.



### HESI303147Regained Gas Permeability Tests

In the case of extremely low permeability and where it would be anticipated that the produced hydrocarbon would be a gas, the concern is not so much from fluid flow through the formation as it is in fluid retention. Small amounts of fluid which are lost to the formation may be retained by the formation due to capillary effects. Regained gas permeability may be low or nonexistent. Several papers have dealt with the effects of damage along the fracture face.2°’2 Fluid retention in very low permeability formations can be aggravated by small capillaries, fluid-rock incompatibility, and low reservoir pressure. The laboratory testused to determine the relative fluid retention effects of various fluids on low permeability gas sands is a basic regained gas permeability test. The core samples are saturated with a test fluid to as near 100% saturation as possible. Then the core sample is contacted with a gas, normally methane or nitrogen, at a given pressure. The permeabilityto gas is then measured versus time. The time required to obtain some fraction of the original gas permeability, normally 70%, is recorded for some fluid. Various fluids are tested, and by comparing the relative times (T-l, T-2, etc.), it is possible to determine which fluids would allow faster regained gas permeability and well clean-up after fracturing (Fig. 6.1).When fluid retention or slow clean-up following fracturing is thought to be a problem, energized fracturing fluids may be advantageous. Nitrogen and carbon dioxide gases are often used for this purpose.

100%

Fluid 1



# ~ Fluid 2



# ~ Fluid 3

,.

T1 Time T2

Fig. 6.1 

### Evaluation of Fluid Properties

At least five other tests can be conducted inthe laboratory for information about fluid compatibilities.


### Emulsion Tests 

### Once a base fracturing fluid has been selectedwhich is compatible with the formation, it is important to select the right non-emulsifying agent tobe added to that fluid. The purpose of the nonemulsifying agent is to prevent down.hole emulsions from occurring if liquid hydrocarbons are present and aqueous base treating fluids are used.These tests are normally conducted in the laboratory by mixing equal volumes of the base fracturing fluid and the liquid hydrocarbon under agitation to see if an emulsion is formed. If so, through additional testing the proper quantity and type of non-emulsifying agent is determined.
Oil Compatibility Tests If the laboratory testing has indicated that an oil base fluid should be used in an oil producing formation, then it is important to determine if the two fluids (the fracturing fluid and the formation fluid) are compatible. This is normally done by mixing equal volumes of the two hydrocarbons and observing any formation of precipitates, sludge,

etc. Gel Break Tests Since viscosifiers (gelling agents) are used in the majority of fracturing fluids, it is important to incorporate the proper breakers to assure a gelbreak after the gelling agent has served its purpose. In many cases, standard gel break curves aregiven by the various service companies for the different gelling agents. If long pumping times, at possibly high bottom hole temperatures, are to be encountered, special gel break tests may have to beconducted to find out if the gelling agent will withstand the extreme conditions for the desired pumping time and break within the desired gel break time.


### Fluid Loss Tests Fluid loss tests are usually conducted with the base fracturing fluid that had been selected through previous tests. Fluid used in fluid loss

R¢,dsed 6YH



### HES1303148testing would normally contain gelling agents and

solid particulate or liquid fluid loss additives when necessary. 

### Fracture Conductivity Tests

If there is concern about the selected base fracturing fluid softening the formation face so that proppant embedment may become a problem, core samples can be subjected to the base fluid prior to fracture conductivity testing. Then the effects of the wetted core on fracture conductivity can be determined. The type of testing will be discussed further in Part 9 of this text.



## FACTORS INFLUENCING HYDROCARBON PRODUCTION
Part 7

Several factors can influence the results oftreating hydrocarbon reservoirs by hydraulic fracturing using proppants to maintain conductivity in the created fracture. These factors can be divided into two areas where the effects of fracturing fluids and additives are observed: ̄ matrix permeability in the vicinity of the fracture face

 ̄ fracture conductivity of the proppant bed.



### Matrix Permeability

Cementing Materials in Sandstones When dealing with the hydraulic fracturing of sandstone reservoirs, there are three basic types of sandstone to consider. These types are categorizedby their cementing material: silicate, clay, or carbonate. With silicate cemented sandstone, there is little concern about fluid reaction with the rock since the silicate is basically inert to any of the basefracturing fluids. The second type is a clay cemented sandstone in which clay is exposed at the pore space. Any fluid which leaks off to the porespace may contact a potentially very reactive material which can cause formation damage by swellingor dislodging the clays and/or fines so that migration can occur. In carbonate cemented sandstone, the cementing material in contact with the pore space is acid soluble. Here we can expect low pHor acidic fracturing fluids to react with the carbonate, which could have either advantageous or detrimental results. In may cases, there may be more than one cementing material in a given interval, and multiple reactions must be considered. There are also those formations which arealmost entirely carbonate (limestones and dolomites) which may respond to hydraulic fracturing using either propping agents or acids to generate fracture conductivity.



### Fluid Retention The result of fracturing fluid retention nearthe fracture face can decrease the rate of hydrocarbon production. Fluid retention is a commonproblem encountered in the fracturing of low permeability sandstone formations using aqueous base fluids. This problem can be minimized by using various chemicals such as surfactants and alcohols to reduce surface and/or interfacial tension, andenergizing gases such as nitrogen and carbon dioxide. 

### Iron Compounds Another common problem can be encountered in formations which have high concentrations of iron containing clays and minerals in the matrix rock. These iron compounds can result in matrix permeability reduction either as migrating fines or as precipitation of dissolved iron compounds. The precipitation of gelatinous iron compounds can beminimized by controlling pH below 3.5, preventing oxidation of ferrous to ferric iron, and/or using chelating agents to maintain the iron in a soluble form. 23

Fluid Residue 

### Other sources of potential reduction in matrix permeability near the fracture face are the solids introduced in the fracturing fluid. These solids canarise from gelling agent residue, fluid loss addifives, and impurities in the water used for the fracturing fluid.
Clays The presence of clays in the matrix can have amajor influence on the production of hydrocarRevised 6YH



### HESI303149bons. The problems presented by clays are complicated by the fact that clay composition and itslocation in the rock permeability can vary extensively. In reality, clays along any part of the drilled hole can present a variety of problems in all phases of the life of the well. There are shales that show a high degree of deterioration when contacted by the common types of water base drilling fluids. Fluid loss from cement slurries and certain water base stimulation fluids are other sources of potential damage to permeability. Clays may be found in almost all types ofrock. Some rocks may be defined as a "water sensitive" formation if a reduction in effective permeability is noted when a foreign water invades the formation. Normally, sandstone formations exhibit the greatest degree of water sensitivity. Clays mayalso be present in carbonate rocks, but are frequently encapsulated in the rock matrix. Thus, they are not in a position to be contacted by the invading fluids.In addition to the problems caused by swelling clays, permeability damage may be caused by migration of clays and other fines with fluid flow.Subsequent bridging of particles at flow restrictions in the rock flow channels causes a plugging action which results in a permeability reduction. This overall effect primarily occurs during the flow of water. (Clays are discussed further in Appendix 

### C.)

Fracture Conductivity.

Since one of the primary goals of a successfulstimulation treatment is to place a high permeability proppant bed in the created fracture, any factors which tend to reduce the conductivity should be minimized. Some of these factors are discussed below.


### Embedment Proppant embedment in the fracture face asclosure occurs will reduce the proppant bed conductivity. Fracturing fluids should be carefully selected to minimize softening of the formation due to incompatibility of the rock and fracturing fluid.As leak-off occurs during the fracturing treatment, the filter cake deposited by the various chemicals used can also lead to a potential source of conductivity reduction. This reduction can

RevVed 6YH 

### result due to embedment of proppant in the filter cake which forms along the fracture face. This problem would be most prevalent in formations with high rates of fluid leak-off.
F’mes in Fracture Several sources of potential flow restrictions in fracture proppant beds originate from the chemical additives in the fracturing fluids. Nondegradable fluid loss additives such as silica flour can lead to significant reductions in fracture conductivity if the material migrates into the proppant bed. Solidsoriginating from the gelling agents used in fracturing fluids are also a source of potential damage toproppant bed conductivity. As the polymers degrade, many leave an insoluble residue which can reduce flow through the proppant bed. Clays along the fracture face can contribute to conductivity reduction especially if the fracturing fluid is not selected carefully for compatibility with the formation rock. Fines can be released into the proppant system. These fines may drastically reduce the conductivity of the proppant bed.2’ As illustrated in Figure 7.1, greater than 65% reduction in fracture conductivity can result with as little as 5% fines (60 to 140 mesh) added to a 1.0 lb/ft2 sand proppant system. These fines can result from fluid-rock interaction along a fracture face.

FINES VS. FRACTURE CONDUCTIVI’~

5 10 15 20 25 % Rnes Added

Fig. 7.1

Fines associated with the propping agent canalso cause significant reduction in fracture conductivity. These f’mes can originate from impurities present in the propping agent or can be generated due to crushing of the proppant.



### HESI303150

### Solids in the proppant bed may arise from

drilling fluids that have been lost in the hydrocarbon bearing zone that is fractured. These drillingfluid solids can cause significant production problems as the fines migrate into the propped fracture.

Summary

The result of a successful fracturing treatment is a highly conductive fracture. Many factors have to be considered in selecting a fluid to minimize the fluid-rock and fluid-fluid interactions. Careful selection of the base fluid and additives will result in designing a hydraulic fracturing treatment with optimum results.



# PROPERTIES OF CHEMICALS AND FRACTURING FLUIDS

Part 8


### Many factors should be considered when selecting a base fluid for hydraulic fracturing. In addition to the formation properties discussed in Part 7, other conditions that influence the selection of base fluid include:

 ̄ fluid temperatures encountered

 ̄ treating pressures  ̄ well completion (tubing vs. casing)  ̄ economics

 ̄ safety. As noted earlier in this section (Fig. 2.1), the trend of base fluid selection has resulted in more than 90% of the current usage being water base fluids.



### Common Fractttdng Chemicals

There are a number of chemical additives being used in fracturing fluids. These chemicals give the fluids certain desired properties to assist in successful hydraulic fracturing treatments. The following general classes of chemicals and their properties are discussed in the remainder of this part of the discussion on hydraulic fracturing: 

###  ̄ polymers

 ̄ crosslinkers  ̄ pH control chemicals  ̄ gel breakers

 ̄ surfactants

 ̄ clay stabilizers

 ̄ alcohol

 ̄ biocides

 ̄ fluid loss additives

 ̄ friction reducers.

Fracturing Polymers

A polymer is defined as a substance composed of giant molecules that have been formed by a chemical combination of specific small molecules. The polymers used in fracturing are used primarilyas gelling agents to increase viscosity of the fracturing fluid for the development of fracture width and proppant transport. The gelling agent also gives some reduction in pipe friction from the basefluid while treating down the tubular goods. Polymers are also often used in low concentrations solely for the purpose of reduction in pipe friction. With oil base fluid., a polymer is formed i.ndtu in the oil through the formation of an "association polymer." An organic acid or organicphosphoric acid and a base are reacted in the liquid hydrocarbon to form association polymers (Figs. 8.1 and 8.2). Currently, the most common chemicals being used for the gelation of oils for fracturing fluids are the aluminum phosphate type products. In addition to the primary associationpolymer being formed, there have been recent developments which allow the addition of a solid aluminum phosphate to the pre-gelled oil. This solid material acts as a secondary gelling agentwhich yields viscosity downhole for better temperature stability than has been available in the past. ~ The use of polymers in aqueous base fluids is somewhat less complex and more controllable than those formed in oil base fluids. In aqueous base fluids, polymers as free flowing solids are normallyadded to the water and hydrate, yielding an increase in fluid viscosity. As illustrated in Figure 8.3, this tightly coiled, dry polymer uncoils as it reacts with water and hydrates to become more linear. This long chain, linear polymer occupies more volume as it hydrates and tends to reduce the

levied 6YH



### HESI3031514 hydraulic fracturing



### mobility of the water molecules. This’decreased mobility results in an increase in fluid viscosity. The base fluids, water and oil, usually exhibitNewtonian fluid behavior in viscosity characteristics. In any of the base fluids in which a polymer or an association polymer is formed, the shear rate - shear stress relationship is changed, and we are no longer dealing with a Newtonian fluid. As shown in Figure 8.4, in addition to Newtonianfluids, there can be several types of nonNewtonian fluids with different rheological properties. The Bingham plastic fluids are those which can be characterized by a straight line curve which as an intercept on a shear stress axis, have a yield stress value.

CHEMISTRY OF OIL GELS



### CHa(CH2)mCO2H Acid

+ 

### NaOH Base CHa 

# I

Association Polymer

F~g. 8.1



### ALUMINUM PHOSPHATE ASSOCIATION POLYMER

RN /R /R ON /O RNON /O



# ...o, ,. ::,,:::o. O "" "’" "" 0% p ok p

o/ NO o/ NO
H/ NR H/ NR

Fig. 8.2 COILED POLYMER (DRY) 

### WATER BASE

LINEAR POLYMER (HYDRATED)

Fig. 8.3



### The pseudo-plastic fluids are those which exhibit no yield stress value and are characteristicof most of the fracturing fluids used in our industry today. In Figure 8.4, a rectilinear plot of shear stress versus shear rate, these pseudo-plastic fluidsare represented by a curve. However, where a loglog plot of the same data is made, a straight line, Linear relationship with a slope between 0 and 1 is obtained. An empirical relationship known as the"power law" is widely used to describe these fluids. As shown in Figure 8.5, the slope of the straight line is denoted as n’ and the intercept at unity shear as K’. The n’, a measure of the degree of the non-Newtonian behavior of the fluid, is a constant. By knowing the n’ and K’ values for agiven non-Newtonian, power law fluid, the apparent viscosity can be calculated using the following equation:47,879 K’ P" - (SR) "°’
where: Ix. = apparent viscosity, cp K’ = consistency index, lbf (sec)*’
ft2 n’ = flow behavior index SR = shear rate, sec .1 Shear stress is expressed in units of lb/ft2. (8-1)

Revised 6YH



### HESI303152The shear rate in the fracture can be calculated with the following equation:
40.464 q SR - w~ h 

### (8-2)

where: q = injection rate, bpm w = fracture width, inches h = fracture height, feet There are many ways of reporting viscosity of the various fracturing fluids in our industry today.However, through the use of the power law concept, an apparent viscosity can be calculated at aspecified shear rate. The shear rate used in calculating the apparent viscosity should always be reported. As an example, a fluid having an an n’ of0.5 and K’ of 0.025 would have a calculated apparent viscosity of 53 cp at 511 sec-~ and 120 cp at 100

seC4

. There are several polymers used in aqueous base fracturing in our industry including:



###  ̄ guar

 ̄ refined guar

 ̄ hydroxypropyl guar (HPG)  ̄ carboxymethylhydroxypropyl guar (CMHPG)  ̄ hydroxyethyl cellulose (HEC)

 ̄ carboxymethyl cellulose (CMC)  ̄ carboxymethylhydroxyethyl cellulose (CMHEC)

 ̄ polyacrylamide (PAM)

 ̄ xanthan (XC).

Shear Stress, Pressure Drop, or Torque Laminar Flow

Shear Rate, Rate of Flow or Rpm

Fig. 8.4 NON-NEWTONIAN POWER LAW FLUIDS

47879 K’ IJ, a = (SR)I -n’ ,cp

Fig. 8.5 log SR, sec-1



### The requirements for fracturing fluids are quite variable. Because of the wide variation in requirements and applications of fracturing fluids, a large number of fracturing chemicals have been developed. The gelling agents for aqueous base fluids are polymeric, hydrophilic chemicals. ~z7 These chemicals are polymers, and as such are distinguished from non-polymers on the basis of their molecular size. This large molecular sizeleads to their ability to alter the viscosityrheological properties of the fluids. The structure for each repeating unit for the guar, guar derivative and cellulose derivative is shown in Figures 8.6, 8.7, and 8.8. All of the polymers possess quite different chemical characteristics, and each imparts different properties to a fracturing fluid. Polyacrylamidesand the xanthan polymers are used only occasionally as gelling agents. Guar and guar derivatives are most commonly used.

Guar 

### Guar is a naturally occurring polymer. Itcomes from the guar bean, which is grown primarily in India. The bean’s hull is removed and the inside portion (or endosperm) is ground into a fine powder giving us the basic guar polymer used as aviscosifier. This polymer is used in many industries, and several million pounds of guar are used in the hydraulic fracturing industry each year. The general properties of guar include:

 ̄ May be used in brines

 ̄ 8 - 10% residue

 ̄ Easy to crosslink

 ̄ 50 lb -- 48 cp ~ 511 sec~

 ̄ Cost factor -- 1.0



### HESI303153One of the concerns in the use of guar hasbeen the residue which remains upon its degradation following a fracturing treatment. Several studies have been conducted on the effect of inherent solids present in the guar and fracturing fluids.These studies indicate that damage can be expected from the solids in some cases. 28.~9 However, the solids associated with such fracturing fluids should not always be looked upon as detrimentalsince fluid loss to the formation is a very important fracturing treatment parameter. Fluid loss to the formation can be controlled in some cases with fracturing fluid viscosity, as discussed earlier. However, in many cases solid particles are required to control fluid loss. If a gelling agent contains solid particles, it obviously possesses better fluid loss properties than one which is solids free. For this reason, in selecting a gelling agent, potentialdamage from solids should be considered in con

### junction with the fluid loss and successful proppant 

### placement during the treatment.

REPEATING UNIT FOR GUAR

POLYMER n ~ 400-600

CH±OH

H N

Fig. 8.6

REPEATING UNIT FOR GUAR DERIVATIVE R = H OR HYDROXYALKYL GROUP

I n-’~o4o~ RO H

CH:OR REPEATING UNIT FOR CELLULOSE DERIVATIVE R = H, HYDROXYALKYL, OR CARBOXYMETHYL n 5 3000-4000

CH=OR

Fig. 8.8

The popularity of guar as a gelling agent for fracturing fluids is primarily due to its ability toproduce substantial viscosity per unit cost, compared with other gelling agents. A refined guar has been introduced recently that has a reduced amount of residue compared to guar, but similar properties otherwise.


### Guar Derivatives Derivatized guars, such as hydroxypropyl guar (HPG) and carboxymethylhydroxypropyl guar(CMHPG) have most of the advantages of the regular guar with the additional advantage of a reduction in residue after break. Current usage trendsshow that HPG is now being favored over the underivatized guar. It should be pointed out that not all hydroxypropyl guar polymers are the same.They can vary depending upon the degree of derivatization. For example, when there is a high degree of substitution with hydroxypropyl groupson the guar molecule, the HPG becomes more soluble in alcohol. Various HPGs are available for different applications. The general properties of HPG include:

 ̄ May be used in brines

 ̄ 1 - 2% residue

 ̄ Easy to crosslink

 ̄ 50 lb -- 51 cp @ 511 sec~

 ̄ Cost factor -- 1.4Another guar derivative, carboxymethylhydroxypropyl (CMHPG) has properties similar to HPG with additional versatility in crosslinking properties. Its properties include:

Fig. 8.7

Revised 6YH



### HESI303154

###  ̄ May be used in brines

 ̄ 1 - 2% residue

 ̄ Easy to crosslink

.1 

###  ̄ 50 lb-- 42 cp @ 511 sec

 ̄ Cost factor -- 1.4
Cellulose Derivatives

Cellulose derivatives have been used in ourindustry for several years. The most popular cellulose derivative used in hydraulic fracturing operations has been hydroxyethyl cellulose (HEC). The general properties of HEC include:

 ̄ May be used in brines

 ̄ Residue free

 ̄ Not usually crosslinked

 ̄ 50 lb -- 68 cp @ 5 I1 sec~

 ̄ Cost factor -- 1.7 

### One of the primary advantages of HEC is that it is residue free after degradation. If formation orproppant system damage from residue is anticipated, HEC is preferred. (See Figs. 8.9, 8.10, and 8.11 to compare amountS of residue from guar, guar derivatives and cellulose derivatives.) The HEC is not usually used as a crosslinked fluid for most fracturing applications. Carboxymethyl cellulose (CMC) is used as a residue-free polymer which can be crosslinked. One disadvantage of CMC is its limited use in brines due to its salt sensitivity; the higher the percentage of salt in an aqueous solution, the lessviscosity yield per pound. The maximum acceptable salt (NaC1 or KCI) content is normally 2% or less. It is extremely sensitive to calcium salts. CMC is being used in a number of areas to prepare acrosslinked, residue-free fracturing fluid. The general properties of CMC include:

 ̄ Limited use in brines

 ̄ Residue free

 ̄ Easy to crosslink

 ̄ 50 lb -- 43 cp @ 511 sec~

 ̄ Cost factor -- 1.6 More recently, a double derivatized cellulose, carboxymethyl-hydroxyethyl cellulose (CMHEC) is f’mding wide usage in a number of applications.CMHEC has the advantages, but not the disadvantages of HEC and CMC. Its properties include:

 ̄ May be used in brines

 ̄ Residue free

 ̄ Easy to crossllnk .!



###  ̄ 501b--55cp(~z 511sec

 ̄ Cost factor -- 1.7 Polyacrylamides As mentioned earlier, polyacrylamides (PAM) are very rarely used as a fracturing fluid gelling agent. Those polyacrylamides and copolymers thatare being used primarily function as friction reducers at concentrations in the dry form of 2 to 4 lbs per 1000 gallons fluid. They would normally beused in a prepad and/or flush volume of the fracturing treatment. PAM can be degraded, is residuefree and usually ionic in nature. Cationic and anionic (as well as nonionic) forms are available forvarious applications. The properties of polyacrylamide and copolymers include:

 ̄ Friction reduction

 ̄ Residue free

 ̄ Used in low concentrations

 ̄ Cost factor -- 1.8

Fig. 8.9

Fig. 8.10



### HESI303155Fig. 8.11



### Xanthan The xanthan polymer has been used for a number of years in the drilling industry. However, within the last few years it has been introduced into the fracturing fluid industry, and there are some areas which are using the xanthan gum as a viscosifier. Xanthan properties include:

 ̄ May be used in brines

 ̄ 3% residue (using hypochlorite, oxidizing breaker)

 ̄ Can crosslink

 ̄ 50 lb -- 28 cp @ 511 sec"1

 ̄ Cost factor 2.0 Although xanthan polymers do not yield as much viscosity per pound as other viscosifyingpolymers, they do have very good proppant transport characteristics. This has been one of their main advantages of use in hydraulic fracturing work. One of the primary disadvantages is the inability to obtain a controlled break of the gelled fluid.



### Crosslinking Agents

A large percentage of fracturing fluids are being crosslinked with chemical agents. Used in very small amounts, these agents can give very large increases in apparent viscosity of the base gel. The crosslinkers work by chemically linking the linear polymers in the fluid together, further restricting the ability of the water molecules to move as shown in Figure 8.12. Some common crossLinking agents are:



###  ̄ borates  ̄ aluminum  ̄ titanium  ̄ zirconium  ̄ antimony. The selection of the proper crosslinking agent is based upon the type of gelling agent being used,the pH of the gel system, predicted fluid temperatures, as well as other factors. In the case of borates, the pH of the base fluid needs to be in the range of 9 to 10 for crosslinking. With most of theother crosslinkers, metallic ions, the pH will usually be in the range of 2 to 8 depending on the polymer used. Of concern with these crosshnked fluids is the shear stability while pumping down the tubular goods and through the perforations. The shear stability can be evaluated in the laboratory by shearing the crosslinked gel with a gear pump or other shearing device and determining the timerequired for the crosslinked gel structure to reappear or reheal. This may be related to the fluid going through the surface pumping equipment, the tubular goods, and perforations. Following shear, the crosslinked fluids should reheal rapidly under downhole conditions so the propping agents will be transported and not dropped from the fluid insidethe fracture near the wellbore. This is an important consideration in the choice of any of the gelling agents and crosslinkers available.3°31



### CROSSLINKED POLYMERS

I~g. 8.12

Revised 6YH



### HESI303156The use of delayed reacting crosslinkers to

minimize the effect of shear in surface equipment and tubular goods is a recent development. The reaction of the crosslinker can be controlled so that crosslinking occurs near the perforations or after the fluid enters the fracture. The resulting fluid has considerably more viscosity in the fracture than a fluid that experiences high shear while crosslinking (Fig. 8.13).

CROSSLINKED FLUID VISCOSITY AS RELATED

TO CROSSLINK TIME

D+R

Temperature

Fig. 8.13 These chemicals may be preblended with thegelling agent or added separately as required during a hydraulic fracturing treatment.



### Gel Breakers

Gel breakers are important chemicals whichare used in most fracturing treatments. The breakers for oil gels work by interfering with association polymers. Normally an acid or a base is used for the oil systems. In water base fluids where a polymer has beenused, the breaker will chemically degrade the polymer into several short chains with reduced viscosity. This change from high to low viscosity is necessary to minimize flowback of any proppant from the fracture and to maximize the amount oftreatment fluid returning after the fracturing treatment. There are three classes of chemicals norreally used by the service industry as gel breakers in water base fluids: enzymes, oxidizers, and acids (see Fig. 8.14).



### pH Control Chemicals

The pH of the fracturing fluid has been mentioned several times throughout this discussion. The control of pH is very important to the total fracturing operation. The pH control chemicals allow buffering of aqueous base fracturing fluids inthe desired pH range. By proper pH control, polymer hydration rate, polymer temperature stability, crosslinking characteristics, gel break and clay control may be obtained. A pH less than 7 is preferred from a formation-fluid compatibility standpoint. However, because of the many factors involved, it may be necessary to override this to obtain other desired properties of the fracturing fluid. Common pH control chemicals used in our industry include:

 ̄ monosodium phosphate  ̄ sodium acetate (acetic acid)  ̄ fumaric acid

 ̄ citric acid

 ̄ formic acid

 ̄ sodium bicarbonate

 ̄ sodium carbonate

 ̄ magnesium oxide. GEL BREAKERS IN WATER BASE FLUIDS
Temperature pH
Enzymes 80 - 140°F 4 - 7.0 Oxidizers 140 - 260°F

- Acids 200°F <7.0
Fig. 8.14



### Surfactants

Most fracturing fluids include surfactants (surface active agents) for one purpose or another. Surfactants are used to reduce surface tension and capillary pressure in pore spaces. They are alsoused to form emulsions, to prevent or break emulsions, to create or break foam, or to alter wetting properties of capillary surfaces. (Surfactants arediscussed in more detail in Section 10 of this manual, Chemical Stimulation.) Surfactants are polar chemicals and can beadsorbed on all rock surfaces. Silicates (sand, feldspar, and clays) carry a negative charge and would naturally attract any organic chemical that carries a positive charge. In addition, relatively large anionic(negatively charged) and nonionic organic molecules are adsorbed by silicates through hydrogen

Revised 6YH



### HESI303157bonding and Van der Waal’s forces. The amount of chemical that will be adsorbed by a silicate surface is directly proportional to the available surface area. Dispersed smectite may have a surface area as great as 750 square meters per gram. However,where the clay crystals are in packets and not thoroughly dispersed, only a small portion of this area is available for adsorption. The adsorption of surfactants on clay would be significantly greater than on sand (150 to 200 square centimeters per gram). 

### Wetting PropertiesSurfactants are frequently used with stimulation fluids to help prevent emulsions and aid in the recovery of water from the rock. With smectite, it has been shown that up to 0.55 grams of some surfactants can be adsorbed by one gram of this clay.32 Cationic surfactants are very strongly adsorbed and are essentially impossible to remove with water. Nonionlc surfactants are also strongly adsorbed but can be partially removed by water. Anionic surfactants are adsorbed but are readily removed by water. The degree of surfactant ad- - sorption by illite and kaolinite is, on the average,about 5% of that adsorbed by smectite while adsorption by sand is even less. The wettability of the rock can be alteredfrom water wet to oil wet by the adsorption of cationic surfactants and by certain nonionic surfactants. This change in wettability can cause a severe decrease in the permeability of the rock to oil.Flow tests with cores having a wide range in permeability have indicated the greatest percentage decrease in flow due to oil wetting to occur where the original permeability was quite low.The use of cationic surfactant in water fracturing procedures can present problems in more than one area. Water lost to rock may becometrapped in the small flow channels due to oil wetring, thus limiting the production of hydrocarbons. It has also been reported that oil-wet sand used as the propping agent reduced fracture conductivity a significant amount." An oil-wetting surfactant had been used with water to fracture several wells in a certain area. Water recovery was almost nil, and the resulting oil production was very disappointing. A change to a water-wetting anionic surfactant resulted in a fastwater recovery and a good increase in oil production.

Reused 6YH 

### Some oil-base and invert emulsion muds contain surfactants that oil wet sandstone formations. The resulting permeability damage frequently masks the true potential of the well during initial testing. This condition can be, at best, partially remedied by treating the formation with a fluidcontaining a strong water-wetting surfactant. However, complete contact of all the damage area with this treatment cannot always be assured. In recent years, a new technique in treatingsandstone formations to enhance aqueous fracturing fluid recovery was introduced. ~’ A special surfactant leaves the sandstone matrix and proppant bed in a non-wet condition. The percent recoveryof the aqueous fracturing fluid following the fracturing treatment has been significantly improvedover conventional surfactants. The results of enhanced fluid recovery are shorter clean-up times and larger production increases.
Emulsions 

### Surfactants are used in the preparation of emulsions for use as fracturing fluids. The most common emulsion" contains approximately 33% water as the external phase and approximately 67% as the internal phase of the emulsion. Emulsifying surfactants are used at approximately 0.3 to 0.8% by volume of the water phase. The water phase is normally gelled with 20 to 50 lbs of gelling agent per 1,000 gallons. This emulsion fracturing fluid has several desirable properties. It has very good viscosity and fluid loss properties as well as good temperature stability and proppant transport. If the oil is recovered and sold or reused, the total cost of the emulsion per gallon is low. There is lesswater to contact the formation than in a 100% water base fluid treatment. A disadvantage of the emulsion is high pipe friction. However, in areas where it has been usedon a large scale, completion strings have been designed around the use of an emulsion as a fracturing fluid. As a result, the friction property disadvantage is overcome.

Foams 

### Surfactants are also used in the fracturing industry to prepare foam fracturing fluids. The surfactant concentration usually ranges from 0.5 to 1.0% (based upon volume of liquid). Normally, 20 to 40% water, acid or oil and 80 to 60% nitrogen or carbon dioxide gas is used.



### HESI303158Foams used as fracturing fluids are dispersions of carbon dioxide or nitrogen gas in a liquid with a small amount of surfactant. They have been proven to be very effective, particularly in low permeability, low pressure gas and oil zones. The external liquid phase may be water, alcohol, acid oroil. In most cases, the liquid phase is gelled to assist in transporting propping agents through the surface equipment and to add viscosity to the foam.The apparent viscosity of foam is directly related to the volumetric percentage of gas phase andliquid phase (Fig. 8.15). The volumetric gas percentage is referred to as the foam quality. For example, a 70 quality foam would consist of 70% by volume gas and 30% liquid under the temperatureand pressure conditions to which it is being subjected.

APPARENT VISCOSITY OF CO,WATER

TWO PHASE FLUID AS A FUNCTION OF 300 CO2 QUALITY

.

o io ~ ~ ~o

P~e:~et CO~

F~g. 8.15

A normal foam fracturing treatment wouldconsist of passing the gelled liquid phase containing a surfactant through a blender where it is mixed with propping agent and is then passed through a pressurizing pump. Gaseous nitrogen or liquid carbon dioxide is injected downstream from the pressuring pump. A foam is formed at the point of gas injection into the liquid-propping agent stream. In some cases, foam generators are used at the point of gas injection to assure a more homogeneous foam. A maior concern in early foamfracturing treatments using proppant was the relatively low concentration of proppant in the foam. Since propping agent is added only to the liquid portion of the foam, the proppant concentration is reduced when the foam is made. However, this potential disadvantage has been overcome through the use of proppant concentrators, changes in pumping equipment valves, etc., and proppant concentrations of 1 to 10 lbs per gallon of foam are now being used. The advantages of foam are:

 ̄ excellent fluid loss characteristics  ̄ good viscosity development

 ̄ sand carrying capability

 ̄ less liquid on formation

 ̄ rapid clean-up following treatment.

Fluid loss characteristics for foam have been evaluated and reported by Blauer~, KingsT, and Harris.3s These results indicate the fluid loss to the formation is very low and superior to conventional 

### treatment fluids.Foam viscosity has been described by Mitchell" as a Bingham plastic fluid, and by Reidenbach, et. al.~ as a yield pseudoplastic fluid. The foam viscosity is related to the foam quality and liquid phase viscosity. Sand carrying capability has been measured in static foams, which have been found to be verygood for. this purpose. Blauer reports that measured settling velocities in foams are much less than settling velocities in water or gelled water. Foam is sensitive to injection pressure since the internal phase is compressible. Higher pressure during a treatment would require more of the gas phase to maintain the volumetric ratio for a given quality foam. (For further information about the applications of nitrogen, see Section 15 in this 

### manual.) Computer programs are available~41 to calculate wellhead pressure, friction pressure, bottomhole treating pressure, etc. for foam frac treatments.. Computer programs are also available for frac design calculations where foam is being used.



### Clay Stabilizers
Clay migration can be effectively controlled by two processes. One uses the hydroxyaluminum ion which is strongly adsorbed by clay. Subsequent polymerization of this ion develops an inorganic coating on the clay surfaces which minimizes clay migration. Its use is well established in severaltypes of field applications. However, a treated formarion should not be acidized since this will remove the polymer from the clay.

RevVed 6YH



### HESI303159The other process uses a cationic organic polymer that is effectively adsorbed by clay. Again, the polymer coating minimizes the possibility of clay migration. Its use has been field proven in acidtreatments to help maintain a high level of production for a longer period of time and in preflushes in fracturing. In addition, the organic polymer coating appears to be stable to most hydrochloric acid solutions and other well fluids.

Alcohol

Alcohol, a common fracturing chemical, is used in two ways. In one use, alcohol is mixedwith water base fluid to make the fluid more compatible with the formation. With alcohol present in a water base fluid at normally 20 to 40%, lower surface and interracial tension between the fluid and the rock is anticipated. It will also increase the vapor pressure of the fluid. These factors will help in the clean-up following treatment. Alcohol has the disadvantage of being somewhat expensive and can be hazardous to handle on location. In other cases, alcohol is used in the range of 5 to 10% primarily to add temperature stability tothe gel system. In addition to alcohol for gel stabilization, other types of gel stabilizers are also used.



### Biocides

Biocides are used in many fracturing fluids toprotect the polymer from attack by bacteria. Bactericides, or biocides, are chemicals that destroybacteria or microorganisms and prevent their further growth. Two types of microorganisms may befound in water base fluids: aerobic (which consume water) and anaerobic. The anaerobic type are sulfate reducing microorganisms which destroy the polymer and produce hydrogen sulfide downhole. Bactericides such as formaldehyde, amines and amides are used to control growth of bacteria insolutions containing polymers. The cycle for polymer degradation by microorganisms is illustrated in Figure 8.16. 

### DEGRADATION OF POLYMER BY MICROORGANISMS

Rg, 8.16 

### Microorganism Polymer

~Sugar /



### Fluid Loss Additives

Fluid loss additives are a necessary part of many fracturing fluids to assist in the control of leak-off of the fracturing fluid to the formation during treatment. Commonly used fluid loss agents

 ̄ silica flour

 ̄ silica flour and polymer

 ̄ oil soluble resin  ̄ oil soluble resin and natural polymer  ̄ emulsions

 ̄ insoluble gases

 ̄ hydrocarbon phase.

Both oil base and water base fracturing fluids are being used in the fracturing industry. Water base, which includes alcohol-water mixtures andlow strength acids, make up the majority of treating fluids. The common chemicals added to these fluids are polymers for viscosity development, crosslinkers for viscosity enhancement, pH control chemicals, gel breakers for polymer degradationfollowing the treatment, surfactants, clay stabilizers, alcohol, bactericides, fluid loss additives and friction reducers. By using surfactants, emulsions and foams can be made.By proper analysis of the formation and treatment parameters, the proper chemicals may be selected.

Revised 6YH



### HES1303160

# PROPPANTS AND FRACTURE CONDUCTIVITY

Part 9

### A main factor affecting the outcome of a hydraulic fracturing treatment is obtaining an adequate propped fracture. The propping agent should provide and maintain a highly permeable path for fluid flow toward the wellbore. The need for a propping agent to help provide that path has been verified by numerous field experiments. When proppants are used, production is usually higher and the production decline rate is much slower. This suggests that an unpropped fracture is subjected to a combination of forces that tend to close the fracture which reduces its conductivity.Fracture conductivity (or fracture flow capacity) is the ability of the fracture to convey the reservoir fluid to the wellbore. It is generally expressed as the product of fracture permeability and the fracture width. Proppant particles must support the closure stress to prevent fracture closure. In so doing,some of the particles may crush, or in a soft formation, embed into the rock. The degree of crushing or embedment depends on:

 ̄ proppant strength and size

 ̄ hardness of the formation being propped

 ̄ closure stress being applied to the proppant bed. If the particle either crushes or embeds, the fracture conductivity will decrease markedly. If severe crushing or embedment occurs, the fracture conductivity may decrease so low that not enough contrast exists between the conductivity of the proppant bed and the permeability of the reservoirrock. If this were to happen, results from the fracturing treatment may not be satisfactory because of the loss of fracture conductivity.’2’ ~,.,~ ~ ,3



### Types of Proppants

One of the ~st propping agents used in fracturing treatments was screened river sand. However, such angular, poorly screened sand containedsome particles that were too large to enter the fracture. Also, bridges sometimes would form in thewellbore, on subsurface tools, or within the fracture itself. If the proppant is too large or if bridg

### hag occurs, then a "screen out" will result and the treatment will have to be ended prematurely. This may result in a smaller propped fracture than had been designed and addltionai expense for cleaning out the proppant in the wellbore. Sands and other types of selected propping agents now employed are less angular and more uniformly graded ha size than the early sands. There is a long list of materials that have been tested as potential propping agents. Many have been tried in various types of formations but most have been rejected from excessive cost or failure tosignificantly outperform sand. Plastic beads, aluminum pellets, rounded walnut hulls and glass beads of various sieve size ranges are found in the "graveyard" of experimental propping agents. High strength glass beads experienced possibly the longest life of the earlier proppants.Six proppants are commonly used in fracturhag today:

 ̄ sand

 ̄ high strength sintered bauxite

 ̄ intermediate strength sintered bauxite (or other aluminum oxide ceramics)  ̄ calcined bauxite  ̄ resin coated sand  ̄ zirconium oxide.Today, graded silica sand (SiO2) is the predominant propping agent used in hydraulic fracturing operations. It is the most economical proppant to use. However, it may be somewhatlimited in its effectiveness because of lower resistance to crushing. In deep formations with highstresses, a higher strength proppant is usually substituted for sand. In the late 1970’s sintered bauxite particles were introduced which were able to maintain high conductivity to very high closure stressesJ5 "" In the 1980’s, we have seen a proliferation of intermediate strength and high strength proppants intended for closure stress applications above 6000 psi.’5~Figure 9.1 gives the specific gravities and absolute volumes of sand and other types of proppants.The shape of a proppant particle is a significant factor in its ability to provide conductivity. Particles should be smooth and spherical so they will pack with large pore spaces. In some select cases, angularity may be advantageous because the proppant will tend to bridge in the fracture and be



### HESI3031614 hydraulic fracturing

less likely to flow back into the wellbore. This is especially true in a formation where the fracture is very slow to close back completely. The range of the mesh sizes recognized by the API’748 is provided in Figure 9.2. This figure alsogives the maximum and average proppant diameters for each of the sizes.

Specific Absolute Volume Proppant Gravity gaFlb

Sand 2.65 0.0453 Super Prop~R’ 3.55 - 3.73 0.0338 - 0.0322 Resin Coated Sand 2.57 - 2.61 0.0467- 0.0460 Z-Prop 126’ 3.1 70.0379 ISB~ 3.1 - 3.2 0.0387 - 0.0375 ISC’ 2.7 ~ 2.8 0.0445 - 0.0429

High strength sintered bauxite proppant Zircorfium oxide proppant Intermediate strength sintered bauxite proppant Intermediate strength cera~c proppant
Fig. 9.1

Proppant Maximum Average Proppant Size Diameter Diameter (PD) --mesh --in. --in.

4/8 0.187 0.173 6/12"* 0.132 0.099 8/12 0.093 0.087 8/16"* 0.093 0.082 10/20 0.079 0.061 10/30 0.079 0.056 12/20" 0.067 0.054 16/20"* 0.047 0.041 16/30"* 0.047 0.039 18/20"* 0.039 0.036 18"35 0.039 0.032 20/40" 0.0336 0.0272 20/50 0.0336 0.0218 30/50"* 0.0237 0.0185 30/60 0.0237 0.0180 40/60 0.0168 0.014 40/70" 0.016 0.013 70/140"* 0.0084 0.0099 (100 mesh) * Recognized by API as a primary proppant size ** Recognized by API as a alternate proppant size NOTE: Average proppant diameters shown are based on typical size distribution from screen analysis data, not the average of large and small sieve openings.

Fig. 9.2

Revised 6YH Sand is available in both round and sub-round shapes. Based on the API guidelines, at least 90%by weight of the proppant’s grains should fall between the range of screen sizes specified. Generally, the larger sizes of sand are more angular thanthose available in 20/40 mesh or smaller sizes. Figure 9.3 is a photograph of a round 20/40 mesh sand and a typical 20/40 mesh sintered bauxite proppant.

20/40 Mesh 20/40 Mesh Sand Sintered Bauxite

Fig. 9.3



### Calculations for Production Rate
From Darcy’s law, the production rate for radial flow may be calculated from this formula:
2 w(kh) Ap q - I~ In (rdr,,) (9-1)

where: 

### q = production rate (kh) = formation flow capacity Ap = pressure drop ~ = fluid viscosityIn r,/r. = ratio of drainage radius to wellbore radius
This equation shows that the production rate is a direct function of the formation flow capacityif you assume a constant pressure drop, fluid viscosity, and ratio of drainage radius to wellboreradius. Figure 9.4 illustrates a formation of thickness h~ feet, having an average permeability of k millidarcies. The formation conductivity is k times hi or (kh) millidarcy-feet.



### HESI303162If a vertical fracture is created in the formation and propped open, it will have an ability toconduct fluid measured by the fracture conductivity of the proppant bed within the fracture. This is expressed as the product of fracture permeability and the fracture width, (kw)f. The fracture conductivity is a property that is measurable in the laboratory. Rather than measure the fracture permeability (kf), the term (kw)f is used. If the width were measured, the kf could be determined. However, laboratory measurementsshow that, for most proppants, the fracture permeability (kf) will vary with width (wf) for very narrow bed widths. For example, k~ at a fracture width of 0.1 inch is not usually equal to kf at a fracture width of 0.25 inch. This phenomenon is mostly caused by "wall effects" since mostpropped fractures are relatively narrow. This behavior is also partly caused by particle size distribution, particle shape, embedment, and grainstrength of the proppant. If proppants were perfect spheres with a single grain size and neither crushing nor embedment were to occur, then we would be more likely to find k~ to be constant with varying widths, once the proppant pack thicknessexceeded three to four layers of proppant. Formnately, this problem of k~ varying with width can be overcome by conducting multiple laboratory tests with different proppant bed widths (w~) for each proppant used. Figure 9.4 shows a fracture that has been placed in a formation and is being held open bypropping agents to a width w. The fracture conductivity of this propped fracture is k~ times w or (kw)~. Consider a formation 20 feet thick with an average permeability (k) of 5 md. The original formation flow capacity is 100 md-ft. A fracture filled with a three layer pack of 20/40 mesh sand would have a width of about 0.082 inch (or 0.0068 feet) with a fracture conductivity of approximately 2000 rod-ft. This assumes insignificant crushing or embedding of particles. The fracture permeability would be 2000 md-ft divided by 0.0068 ft, whichis 294,000 md. In this example, the propped fracture has a flow capacity 20 times that of the formation and the permeability contrast (k/k) is a factor of 58,800. Therefore, it would appear that fracture conductivity is a significant factor in the successful application of hydraulic fracturing stimulation. The fracture must be able to easily conduct fluid delivered to it by the formation. (Part 10 of this text will discuss theoretical production increase.) For the purpose of calculation, consider a case where the fracture permeability is much higherthan that of the formation (k~>>k). The production increase created by the fracture can be approximated by replacing the fracture with a borehole.The radius of this borehole would be approximately haft the fracture lengthy Using Darcy’s Law to approximate the production increase:

k/q- ro kl r’\ 

# +

where: (9-2)

r’ = effective wellbore radius (1/2 fracture length) k~ = fracture permeability k = formation permeability In the previous illustration, if r. = 660 ft, L = 500 ft and r, = .5 ft, then r’ = 500/2 = 250 ft:



### ~/q =

In 2-~ + 294,000 In 

### The production increase is 7.40.

I 

### Damage to Proppant Bed IIIThe crushing or embedment of proppant particles may cause a fast decline in productivity because of the reduction in fracture conductivity.

Re~i~l 6YH



### HESI303163Figure 9.5 illustrates what may happen in a thxn,

multilayer system of rigid particles when there is significant embedment. The flow capacity may be partially or entirely lost because of the closure. In many cases, the closure may crush the formation instead of the proppant. The formation may then release debris that partially plugs the proppant bed. When you have a wide, multilayer proppantsystem, the effect of the plugging caused by formation fines is usually much more significant that the loss in fracture width caused by embedment.

Proppant Not Embedded

Proppant Partially Embedded

Fig. 9.5

Figure 9.6 illustrates severe crushing of rigid particles. Sand may be crushed by the action of the formation stresses in hard rocks; however, it does not usually crush to a very fine powder. Sand may shatter into smaller grains and, eventually, produce enough small particles to give some support. Theresult may be a propped fracture of a slightly narrower width and a poorer range of proppant sizes than expected. Therefore, the proppant bed would have less conductivity.

Proppant Not Crushed

Proppant Severely Crushed

Fig. 9.6 Silica sand (SiO:) has been employed as a proppant since commercial fracturing began. It is still the most economical and the most widely used proppant. However, it may be somewhat limited in its effectiveness because of lower resistance to crushing. In deep formations with high stresses, a higher strength proppant is usually substituted for sand. The conductivity of a propping agent will depend on, among other factors, the concentration of the proppant in the fracture. For low viscosity fluids (or for other conditions that develop a bed of proppant because of settling), the propped fracture width is equal to the pumping fracture width lesssome shrinkage caused by compaction, embedment, and crushing. You can use Figure 9.7 to estimate the proppant concentration if you know the propped width.

10000

5000

z

1000 0 PROPPANT CONCENTRATION

IN FRACTURE

vs FRACTURE WIDTH (w)



# /

0.05 0.1 10o 0.01 0.5 1.0

w in.

Fig. 9.7



### In the case of more viscous fluids which are capable of suspending the proppant, the slurry concentration can be used to estimate the proppant concentration in units of pounds per square foot of fracture area. Once you obtain the concentration, you can estimate the propped width using Figure9.7. Using sophisticated computer design simulators, a very detailed calculation of the final proppant bed can be modeled.



### HES1303164

### The fracture conductivity of a particular type

of proppant also will depend upon the characteristics of the rock being propped. Typical conductivity curves for 20/40 mesh sand and 8/12 mesh sand are shown in Figures 9.8 and 9.9, respectively. Figure 9.10 is a comparison of several different proppants under identical test conditions. Thesecurves were based on tests of proppant packs between steel plates for Figures 9.8 and 9.10, and between cores of Berea sandstone (with moderate hardness) for Figure 9.9.

3

2

lO’

z 0

5

3

2 FRACTURE CONDUCTIVITY VS. PROPPANT CONCENTRATION IN FRACTURE

20,’40 OTTAWA SAND STEEL PLATES

CLOSURE STRESS (PSI)

6000

101 0.1 0~ 0.3 0,4 0.5 1.0 2. 3. 4. S, 10

CONCENTRATION - LB/SQ. FT.

Fig. 9.8

A close examination of the data for low proppant concentrations in Figure 9.9 indicates some abnormal shapes in the curves. In this graph, theabnormalities begin to occur as the proppant concent.ration is decreasing from a full 2 + layer pack down to a monolayer (at 0.7 lbs/sq ft in Fig. 9.9). As the proppant concentration decreases below a 

### monolayer pack, the conductivity will increase if the particles can support the load without being severely crushed (see Fig. 9.10 at the lower stresses). However, if the grains are too weak to support the load in a partial monolayer system, then the conductivity will drop as shown in Figure 9.9 for the higher stresses.

FRACTURE CONDUCTIVITY

VS. SAND CONCENTRATION IN FRACTURE

~12 BRADY SAND ON BEREA SANDSTONE CORES

0.1 0.2 0.3 0.4 0.5 1.0 2.

CONCENTRATION - LB/SQ. FT.

Fig. 9.9

Fig. 9.10 FLOW CAPACITY DATA FOR VARIOUS PROPPANTS

2000 4~O0 6000 ~ 10000 12000 14000 1~000

CLOSURE STRESS (PSi)

Rcvi~d 6".£H



### HESI3031653 8 hydraulic fracmrm~g’

In a realistic application, it would be highly unlikely to obtain proppant beds of less than a 2- layer thickness in a vertical fracture. Many field studies in the past have attempted to use partial monolayers for various reasons, but very few were a commercial success. Some were such completefailures that many wells had to be refractured using higher proppant concentrations to increase production.



### Selection of the Propping Agent

One of the most important factors in the design of hydraulic fracturing treatments is the selection of a propping agent that can effectivelyprovide the fracture conductivity needed for stimulation of a well. Examination of Figures 9.9 and 9.10 shows a marked difference in the conductivities of 20/40mesh sand and 8/12 mesh sand. The tests for Figure 9.10 were conducted using a medium hardness sandstone outcrop (Berea) as the fracture faces. Only slight embedment (1/3 grain diameter or less) was observed even at the highest stress (6000 psi). Therefore, this data is not representative of soft formations where embedment could be a problem, nor is the data in Figures 9.8 or 9.10 which were measured on steel plates. Several interesting points should be noted during a comparison of Figures 9.8, 9.9, and 9.10:



###  ̄ The larger particles (8/12 mesh sand) have a much higher conductivity that the 20/40 sand for the same concentration at the lower closure
stresses.

 ̄ The 8/12 mesh sand is much more affected by changes in closure stress (i.e., it is more easily crushed).

 ̄ At stresses above 4500 psi and concentrations above 1 lb/sq ft, 20/40 mesh sand has more conductivity than 8/12 mesh sand.

 ̄ The data in Figure 9.10 shows that different proppants resist crushing to different degreesalthough all these are 20/40 mesh size proppants. Selecting the proper type and size of proppantto use in a particular formation requires the gathering of laboratory data such as the information provided in these figures. Three factors previously discussed may influence the conductivity resulting from a bed of proppant under load:



###  ̄ The particles may embed in the rock surfaceif they are stronger than the rock and the closure stress is sufficient to cause embedment.

 ̄ A large percentage of the grains may crush if the rock is strong and the stress is greater than the grains can withstand.

 ̄ The proppant bed may become plugged because of the invasion of formation fines. Of these three, only proppant crushing can easily be modeled in the laboratory.



### Laboratory Tests for Conductivity

One of the best methods for determining theapplicability of a proppant is the test for conductivity. This test was used to obtain the data listed in Figures 9.8, 9.9 and 9.10. Conductivity tests areroutinely performed by service company laboratories to aid in choosing the proper proppant for various formation conditions. Figure 9.11 shows two methods which use actual cores in the flow capacity test. The samples in the lower part of the figure show a core samplecast in a lead mold with a stainless steel screenwire molded in place to retain the particles on the core face. A second core is also mounted in lead with part of the core projecting above the lead.

Fig. 9.11

Revised 6YH



### HESI303166

### This part of the core is the "head" and will be inverted onto the proppant bed after the desired quantity of proppant has been placed inside the screen. The test cell shown in the upper part ofFigure 9.11 is a steel cell which uses thin core wafers to provide the same final type of test set-up (i.e., the proppant bed is "sandwiched" between core wafers). Figure 9.12 illustrates two of the metal cells being tested simultaneously in a loadingframe. The closure stress is increased and conductivity (fracture flow capacity) measurements can bemade at any stress level up to the limit of the loading frame.

Fig. 9.12

Typically, conductivity of the proppant pack being tested will be measured at different closure stress values. Test fluid flows through the centralweilbore and radially out through the bed of proppant. By knowing the flow rate, pressure drop, and the geometry of the system, you can calculate aconductivity value using Darcy’s Law at each closure stress:



### (kw)f =

where: 5.22 ql~ In

Ap (%3)

(kw)f 

### q

ro

rw 

### Ap = conductivity, md-ft = flow rate, cc/sec = outer radius, cm = weilbore radius, cm = pressure drop, arm = fluid viscosity, cp Conductivity tests are used to evaluate the relationship between the hardness of the actual formation rock and the strength of the proppant grains. The values from the conductivity tests are usually applied directly to design calculations thatuse production increase ratios. However, the crushing of proppant grains may not have the same influence on the results of the test as it might have in a full size fracture. The short flow path of the test may allow the fines produced by crushing to wash out of the bed and cause a conductivity value that is too high. Also, in actual downhole conditions, the proppant bed may have two or more fluid phases present during the producing life of thewell. Formation fines that may invade the proppant pack are also difficult to simulate in the laboratory. Because of these and many other factors, someof the more experienced design engineers will discount the conductivity data measured in the laboratory before they calculate production increase. Unfortunately, no single discount factor can be used because so many factors are involved in each separate case. The appropriate value may vary from 1 (no discount) to 0.1 or lower. Typically, values from 0.5 to 0.1 will be used?° In recent laboratory studies, McDaniel ~1.s, identified that much lower conductivities exist with extended test times and elevated temperatures. These tests used an API linear test ceil $3 like the drawing in Figure 9.13 and the photograph in Figure 9.14, where the ceil is inside a load frame.

LINEAR FLOW PROPPANT CONDUCTIVITY TEST CELL

Fig. 9.13

Re~sed6YH



### HESI30316740 hydrouS frat:turini’

Fig. 9.14

The calculation of effective fracture conductivity for an actual treatment depends upon theproppant distribution in the fracture. Computerized simulations of hydraulic fracturing are widely available to make. such calculations.



### Fracture Closure Stress

The fracture closure stress is the amount of stress the propping agent must withstand insidethe fracture. Closure stress affects treatment parameters such as the type and amount of proppant,the fracture conductivity, and the amount of production increase. The magnitude of the closure stress depends on the least in situ principal stress, the reservoir pressure and the flowing bottomhole pressure while the well is producing. The least in situ principle stress can be determined if an instant shut-in pressure is measured while fracturing a formation. If possible, record the magnitude of the instant shut-in pressure during the very early stages of the treatment, since the instant shut-in pressure at theend of a treatment may be falsely high due to "supercharge" of the reservoir caused by frac fluid leak-off. The closure stress applied to a proppant bed will vary with the producing condition of the well. When the fracture has first healed on the proppant bed, but prior to opening the well for cleanup andproduction, the closure stress will be at a minimum. This value for minimum closure stress can be calculated:

Revised 6YH 

### Minimum closure stress = P,si + APh - Po
where: (9-4)

= instant shut-in pressure at the wellhead, psi

= hydrostatic pressure of fluid in the wellbore, psi Po = static reservoir pressure (pore pressure), psi When the well is opened to flow (or is pumped), the closure stress on the proppant bed will increase. This is because the pore pressure in the proppant bed is now considerably lower than the formation pore pressure. Probably the best estimate of the closure stress for the producingwell is to substitute the bottomhole flowing pressure for the reservoir pressure in equation 9-4. Since this is often the value used in selecting a proppant for a treatment design, we will refertothis as the "design closure stress." It can be calculated as follows: Design closure stress = P,., + APh - P~,, (9-5)

where: P~o. = bottomhole flowing pressure from producing well, psiThe closure stress does not stay constant during the life of a fracture. The reservoir pressurewill decrease as fluid is withdrawn from the reservoir, and the Pnow usually decreases even faster..



# PRODUCTION INCREASE

Part 10 The use of hydraulic fracturing methods forproduction stimulation has become a common procedure in the oil and gas industry. Fracturing treatments are performed on wells of various potentials to help increase the production rate. Along with the desire for increased production is the need to predict what increase might be expected. Thisknowledge is useful in planning economical treatments that accomplish the desired production goals for the well. Production increase may be defined as theratio of production rate after fracturing to the production rate before fracturing at the same pressuredifferential (that is, the ratio of productivity indices).



### HESI303168

### Production increases from horizontal radial

fractures may be calculated in theory by using equations developed from mathematical analyses and electrical models.’3 Theoretical productionincreases due to vertical fractures may also be predicted using curves developed from electrical and mathematical models.’"" ~’~’ Early studies usually assumed that the vertical fracture height and the formation height were equalfl However, the final fracture height through which fluid is produced may not be equal to thecreated height because of the propped bed configuration. This is based on the study of proppant transport relationships in vertical fractures. ~2  ̄ ~ Modern fracture design simulators are capable of calculating the proppant suspension and settLing during pumping. Some of the more sophisticated simulators will also model the changes in proppant location during the time that the fracture is closing following shut-in.l~ If increased hydrocarbon flow occurs only through the propped portion of thefracture, it becomes essential to know how production increase varies with the ratio of propped fracture height to formation height. Future investigation may determine that the fracture does not heal completely and that a highly permeable channel exists over the deposited bed of proppant. The effect of such a channel is not considered in this discussion. We need to consider a number of variables when designing a fracturing stimulation treatment. The dimensions and conductivity of the fracture are affected by factors including:

 ̄ volume of the treatment  ̄ type of proppant

 ̄ size of proppant  ̄ concentration of proppant  ̄ treatment fluid properties  ̄ well conditions. 

### Production increase from a vertical fracture is affected by propped length, height, width, and theconductivity of the fracture for a given set of formarion conditions.



### Calculations for Vertical Fracture Production Increase

The parameters used in the calculation of production increase must be either measured or rea

### sonably estimated. For example, the conductivity of the fracture may be measured in the laboratory using layers of proppant placed between formation core surfaces as described previously in this section (Part 9). The reservoir pressure must be known, and the properties of the reservoir fluid must be measured or estimated. When such parameters are used to determine production increase ratios using analog models, some assumptions are usually made:

 ̄ The formation is a homogeneous, isotropic, porous medium.

 ̄ The reservoir fluid is incompressible.

 ̄ The fracture width is constant.

 ̄ The fracture is constant in height and extends equal distances in two opposite directions from the wellbore.

 ̄ The conditions that exist in the reservoir are steady state.

 ̄ The effects of gravity on the fluid may be ignored.

 ̄ The flow that exists is single phase. 

### One of the ftrst papers published concerning fracturing and its effect on production stimulation was by McGuire and Sikora.‘3 Their study was accomplished using an electrical model composed of a network of capacitors and resistors. The results of this work are shown in Figure 10.1. This work has several limitations that, in some cases, lessen its usefulness in particular field applications:

Fig. 10.1 14

12

4

2 ol x._!

.5 .4
.3
.2
.1

10s 10~ 10s 10s RELATIVE CONDUCTIVITY, (kw)~, ~ k " S

 ̄ Because of the way the reservoir was modeled,the resulting production increases are indicative of an unknown time. The curves do not

Reviled 6YH



### HESI303169

## 2 ,hydraulic frac:urmg



### apply to a steady-state production rate that would exist at later times. (However, in thecase of gas wells in fight formations, steadystate conditions may not apply until an appreciable period of the producing time haspassed.) The authors call the model a semisteady-state case. The data assume that the propped fracture extends throughout the entire vertical interval of the producing section. It does not consider the propped fracture height being different from the thickness of the interval. The data assume an incompressible fluid.
The resulting values may be too high for steady-state production increase ratios. They differ from work done by others in this field of study, including that by Prats,° Smith,s* and Tinsley, et. al?~ Wtfile the shapes of these curves agree, the magnitudes of the values do not.


### Calculations for Increase Ratio The paper by Prats may be used to obtain ameasure of the effectiveness of the vertical fracture. For values of (r=/xf) > 2, the improvement in production rate for infinite fracture conductivity is given by equation 10-1:



### where: qgq = increase ratio

ro = drainage radius, ft

x~ = fracture length, wellbore to tip, ft
r, = wellbore radius, ft r’,, = effective well radius - may be found from Figure 10.2 using a value for "a"

as follows: 

### (10-1)

k = formation permeability, md
(kw)f = fracture conductivity, md-in.

Prat’s work is valid for these conditions:  ̄ short fractures, xf < r)2  ̄ incompressible fluids

 ̄ single plane vertical fracture ̄ when a ~< 1; if a > 1, a well pressure correction should be made using Figure 10.3

 ̄ equal fracture and formation height. If the fracture conductivity is less than infinite, a correction for fracture pressure drop is introduced using Figure 10.3 and the value of a to Fred p.,o(a,r.D):

In r. 

### q~_ q In 77- -2

where: 

### (10-2)

pressure drop as a function of a dimensionless well radius r.t, =

r~/xf 

### Another method for estimating an effective wellbore radius (r’.) uses the skin factor and the following relationship:

’ (10-3) r ~ = r.e"

~ 1.0 ",-- 0.5

<w 0,7



## ~o.o~ WUJ

,uJ, 0.001 WELL RADIUS OF THE

FRACTURE AND L IS THE HALF LENGTH OF THE FRACTURE

0.01 0.1 1.0 10 100 1000 RELATIVE CAPACITY PARAMETER, a

Fig. 10.2 - Effective Well Radius

o. 0.8

z .,~ W

-- tr 0.4



### °8~ o.~ a = 100 

# 1⁄2 ’

~ a=10

la = 1 !

0.01 0.02 0.03 0.04 0.05 DIMENSIONLESS WELL RADIUS, r,.,/xf

Fig. 10.3 - Pressure Correction at Well


### In an unfractured formation, the productionrate is affected by the formation height. The production rate in a hydraulically fractured formation

Revised 6YH



### HESI303170is affected by the propped fracture height which

can be significantly less than the formation height.Therefore, the production increase ratio is a function of the ratio of propped fracture height to formarion height.For a truly meaningful prediction, the production increase should be affected by the degree to which the producing zone is propped. Assuming that the unpropped portion of the fracture closes, then the production increase ratio should be a function of the propped height to formation height ratio. In one study", an electrolytic model was used to study this relationship. Production increasewas related to the model parameters. In a subsequent paper$6, the mathematical analysis was corrected and modified to dimensionless form. It was also generalized to any r Jr, ratio. Examples of new graphs are presented in Figures 10.4 and 10.5. These plots are similar to the earlier work of McGulre and Sikora (Fig. 10.1), except the x-axis is dimensionless and the propped fracture height is considered as a variable. 

### Calculations for Dimensionless Fracture Capaco

The x-axes of Figures 10.4 and 10.5 represent "dimensionless capacity." This term is def’med as:
C,hf r(~._~ C - 2 K- in (10-4)

This term uses the C, definition of Cinco, et.



### (kw), (10-5) C, = ~kx,

where: (kw)~

k

h~

r,
r= = fracture conductivity, md-ft = propped fracture length, ft = formation permeability, md = propped fracture height, ff = formation thickness, ff = radius of drainage, ff = wellbore radius, ft
The curves for x]ro ratios of 0.9 and 1.0 are not included because the data were not considered to be applicable to field conditions. In the model that was used, a fracture that extends to or near the boundary of the model would have an infinite supply of fluid. In reMity, the boundary of the prototy.pe is not an infinite source of fluid and 

### would also be affected by surrounding wells. Examination of Figures 10.4 and 10.5 showsthe effect propped fracture height has on steadystate production increase. Lowering the proppant bed height decreases the C value, thus decreasing the JdJi term. In addition, lower h/h~- results in shifting to a different graph where the range of Jd Ji values is lower.

h!

--= 1.0

I 0.1 1 10 100

h~ C= [0.5C,~lnrdr~,]

Fig. 10.4 - Productivity Index Ratio (h/h=) = 1.0

0.25 Xtire
(~)f

0.1 1 10 100

C = 0.5 C, ~ In rdrw

Fig. 10.5 - Productivity Index Ratio (hCh3 = 0.25

For example, if C = 10 at hflni = 1, and x~rc = 0.6, the JdJi term - 4.6. If the bed height were lowered and h/hi = 0.25, C would become 2.5 and Jf,/Ji term - 3.0. This effect is quite significant if the C term is in the range of 1 to 10.

Revised ~YH



### HESI303171Note that the C~ term is inversely proportional to fracture length xf. This indicates that longer fractures require higher fracture conductivity to result in the same production increase. When an x~/ro curve approaches its asymptote (becomes horizontal), this implies that the fracture is conducting fluid as fast as the formation can deliver and that no improvement can be realized for C values above a certain point. If h~/h~ -- 1.0 and an 8 inch diameter well is drilled in an 80 acre pattern where k = 0.1 md, then for xf = 500 ft,the (kw)f term need be not greater than 3,820 mdft. That conductivity value would yield essentially an infinitely conductive fracture, having a C, value of 24. Cinco’s results imply that for C, > 100, there is almost no difference between finite and infinite conductivity fracture cases. His figures indicate very small differences above Cr -- 10. Figures 10.4 and 10.5 agree with his conclusion. An example of the effect of height ratio (h/hi) on the steady-state production increase is shown inFigure 10.6. The effect is pronounced for low values of h,dai. For practical purposes, a fracture height ratio > 0.5 is suitable.

1 O0

~ 80
~ 60



## " ~’~ 2o/

.1 .2

INFLUENCE OF h#hi ON Jfs/Ji

.3 .4 .5 .6 .7 .8 hjhi VALUE .9 1,0

Fqg. 10.6 - Height Ratio Effect



### Production increase ratio, JdJ,, assumes no wellbore damage. In practice, wellbore damage may be common and the effect of damage usually is eliminated by the fracturing operation. Prior to the treatment, production is restricted due to the damage around the wellbore. However, following the treatment the majority of the production is through the fracture and the damage around the wellbore offers no appreciable restriction.

Revised 6YH The damage, as calculated by drill stem testsor pressure build-up data, can express the restriction in production as a damage ratio or skin(s). The former is the ratio of theoretical production capacity with no damage to the present production (i.e., the inverse of flow efficiency). Therefore, if a well were making 10 BOPD with a damage ratio of 4.0, the production without damage should be 40 BOPD. If the well were to be fractured and the results of a design calculation indicate Jf,/Ji ratio of 3.0, the total expected steady state production ratio would be 10.0 x 4.0 (damage ratio) x 3.0 (Jf,/Ji) or 120 BOPD. As can be seen, the damage ratio is avery important consideration and cannot be ignored. Keep in mind that caution should be exercised in predicting exact production values fromproduction increase curves because of the assumptions inherent in the development of these curves.An important factor in the use of the production increase curves is the selection of values for well spacing and drainage radius. It should not beassumed that since wells are drilled on some assigned surface spacing that they are actually draining this area. It might be years before the effects of withdrawing fluid from the wellbore are felt at thespacing boundary. Well spacings used in frac design should be realistic values, not necessarily government specifications. The production increase curves in Figures 10.4 and 10.5 have limitations as mentioned, but are useful in fracture treatment design. Curves such as these represent a way that the treatment variables may be related to each other to compare their effect on the treatment results. A typical curve (for example, Fig. 10.4) showsthat there are only three variables under the control of the treatment designer. These are the parameters that may be modified by selection of fluids, proppant types, and treatment conditions:

 ̄ height ratio, h/hl  ̄ fracture conductivity, (kw)f  ̄ propped length, xf. An example of the use of curves would be the case in which a choice of a proppant in a particular permeability formation resulted in a low value of the C, term. If the proppant is in suspension in the fluid, a height ratio of 1.0 may be assumed. Thelow C, would also imply a low dimensionless capacity (C). At very low C values, the Jf,/Ji would be



### HESI303172affected very little by fracture length xf. One

would not consider increasing length as a means of increasing J,/J~ without making a corresponding increase in C, through a higher conductivity value, (kw)f. As x, is increased, its effect on Cr must be considered and the (kw)~ adjusted. ACr value of > 10 would be a suitable goal in most designs.



### Computer Simulations

All of the above discussions on production increase prediction methods assume essentiallysteady-state flow of incompressible fluids. Predictions become more involved ff transient flow prevails for the time in question or a compressible fluid is flowing. Usually this type of problem issimulated by using a computer to solve the differential equations describing the pressure behavior. These equations may not be solved analytically except for specific simplified cases, so the pressure must be approximated by numerical methods. Theuse of the steady-state methods is generally accepted for oil wells, but will be pessimistic in gasreservoirs in which the fluids are very compressible.


### Production Simulators The most recent method for predicting theincrease in production involves the use of a "production simulator" computer model. These modelsare based on predicting the transient pressure response of a reservoir. The modeling of oil or gas production from aradial flow (unfractured) reservoir has been available for a long timefl Later, methods for modeling flow through an infinitely conductive fracture in a reservoir were developed." However, it has only been since the late 1970’s that usable models havebecome available to simulate production of a hydraulically fractured reservoir where the fractureconductivity could be variedf143 Continued refinement of this technique has made production simulators an important tool for predicting theproduction increase resulting from hydraulic fracturing.~ When a solution of a model is plotted in a dimensionless form, it is usually called a type curve. Because of the generality of the type curve, it can be used for either analysis of well tests"*~or predicting future performancefl In the following few pages, the model for predicting production increase using type curves is presented. 

### Type Curve Analysis Method The "Fractured Reservoir" type curves are used to model production following a hydraulic fracturing treatment. The earliest type curves were based on infinite fracture conductivity and had limited practical applications. However, the morerecent development of type curves for finite conductivity fractures has resulted in production simulators that have definite practical application to help design hydraulic fracturing treatments. 

### Mathematical Model for Type CurvesThe mathematical model has several assumptions. The well is assumed to be vertically fractured in the center of a square reservoir and producing at a constant bottomhole pressure under unsteady state conditions. The formation has aconstant height. The outer boundaries of the reservoir are no-flow boundaries. The fracture extends an equal distance on each side of the wellbore. The fracture is propped and has a finite conductivity (wfkf). It completely penetrates the formation in height. Other assumptions are used in developing the model. Foremost among these are:

 ̄ The porous medium is homogeneous and isotropic.

 ̄ Gravitational effects are negligible and thereservoir is bounded above and below by impermeable strata. The problem is therefore two-dimensional.

 ̄ The working fluid is a single phase and compressible. Fluid density is described by the 

### equation:

p = po exp 

### [c(p- po)] (10-6)

 ̄ The flow in both the formation and the fracture is laminar and described 

### by Darcy’s Law. A finite element simulator may be used to solve the partial differential equations that describe the initial and boundary conditions. An example of this solution is shown in Figure 10.7. Series of these type curves have been developed. Each ofthese curves gives the dimensionless flow rate versus dimensionless time for various x,Jxf ratios. Each of these graphs represents a specific dimensionless fracture conductivity. These type curves can be

Revised



### HESI303173

## 6 hydraulic fracturing

used in analysis of drawdown tests by applying the conventional and frequently discussed type curve matching technique. If the graphs are to be used for that purpose, they should be applied for a well producing at a constant flowing pressure.

Fig. 10.7

The type curve can be used to:  ̄ predict flow decline with time  ̄ help design a fracture treatment  ̄ evaluate a fracturing treatment using a history match technique. To use the type curve for prediction or history match, curves are first stored into a computer.Because the original solution is obtained numerically, only data points were available. The data were stored as continuous functions rather than discrete points, eliminating the need for numerical interpolation. The data points of each curve werefitted by a polynomial of seventh order. The coefficient of these polynomials are stored in the computer memory. The deviation of the calculated points using these polynomials from the original data points was always less than 1% and in most points within 0.3%. Because of the nature of the inner boundary condition, wellbore storage would not affect thetype curves. However, a few aspects regarding actual well performance have to be considered to obtain a reliable prediction and/or history match. These aspects are:

 ̄ Change in flowing pressure - In historymatching, it is obvious that well flowing pressure does not remain constant for the long time considered in such a study. Thus, it is

Re~ed 6YH 

### important to consider the change in flowingpressure using superposition. EhlegEconomides and Ramey~’ discussed superposition for wells producing under constant pressure. Their equation for step pressure testing is used to accommodate the effect of changing flowing pressure.  ̄ Reduction in fracture conductivity - With increasing closure stress, there is a reduction in fracture conductivity. When a fractured well begins production, the pressure in the fracture is reduced significantly. The closurestress is approximated as the difference between bottom_hole treating pressure and the average pore pressure in the fracture. The fracture conductivity of the proppant bed will decrease as the closure stress increases. As a result, the fracture conductivity will decreasewith time. Laboratory data on fracture conductivity as a function of proppant concentration and fracture closure stress are available in the literature. Examples of these graphs were presented in Figures 9.8 through 9.10. Using these data, the effect of changing closure stress can be considered in calculating the predicted fracture conductivity. Because the type curves neglect the effect closure stresshas on fracture conductivity, this effect is considered in an approximate way. For a given time step, an average closure stress value for the fracture is estimated.  ̄ Turbulent flow - Using a numerical simulator (finite difference simulator) and calculating the fluid velocity inside a fracture, it has been found that the apparent fracture conductivity can be significantly affected by turbulent flow inside the fracture. This effect is especially pronounced in early time when the flow rate ishigh. The effect of turbulent flow is considered in a similar fashion to the closure stress effect. First, a turbulent factor ~ is calculated:

(10-7) ~ - kf - 2.97 x 10 ~°[3vl~

1 +This equation is based on work done by Forcheimer.67 Because the fluid velocity inside the fracture changes with time, this turbulent factorstarts at a low value and increases with time. Eventually this factor approaches one for laminar flow. This approach, which has been used before,62 ~’ ~ can be incorporated into a computer program that



### HESI303174

### uses the presented type curves with these discussed

features. The program can predict a well performance with an accuracy comparable to a numerical simulator but it has the advantage of taking much less computation time. ever, the rate of improvement declines. The increase in cumulative production after three years as the fracture length changes from 200 to 600 md-ft is only about 17%. This shows that for the longer fracture length, a fracture conductivity of 1000 md-ft may not be sufficient; the dimensionless fracture conductivity (Cr) for the 600 ft length is too low. As discussed earlier, experience has shown that a dimensionless fracture conductivity of about10 is usually desired to produce a particular formation efficiently.

Fig. 10.8 

## HYDRAULIC FRACTURING EQUIPMENT

Part 11
The equipment used to perform hydraulic fracturing treatments has evolved from simple modified cementing units to become some of the most powerful and specialized equipment in the service sector of the oilfield. A brief overview of the types of equipment currently used is provided in this part.

0.9


### The type curves may be used to estimate fracture parameters. This may be achieved by changing fracture length and conductivity and plotting the production as a function of time. Example well data were used to demonstrate this procedure. The fracture length was chosen at varying percentagesof the drainage radius, and the type curve simulator was run using fracture lengths of 200, 400, and600 ft. A formation permeability of 0.1 and a fracture conductivity of 1000 md-ft were assumed. Results of this simulation are shown in Figures 10.8 and 10.9. The well performance can be seento improve as the fracture length increases. How

### Fluid Storage

On very small jobs, fluid is frequently used directly from transport trucks of 50 to 150 bbl capacity. Portable lay down tanks (frac tanks) of about 500 bbl capacity are used on a majority of frac jobs. On some jobs using fresh water, lined earthen pits are used to store volumes of over a million gallons of water. 

### In offshore operations, the fluid may be stored in tanks on the rig or on a stimulation vessel. Sometimes, £fltered sea water may be used without any storage.



### Proppant Storage

On small to moderate size jobs, proppant is usually fed to the blending equipment directly from the trucks used to transport the proppant to location. Larger quantities of proppant or high concentrations at high rates are usually stored in portable field storage facilities (Fig. 11.1). This type of storage unit usually uses gravity feed onto a hydraulic driven conveyor belt system to supply the proppant to the blending equipment.



### HESI303175Fig. 11.1 - Proppant storage unit with integral unloading belt.

Capacity = 222,000 Ibs sand.



### Blending Equipment

The success of a fracturing treatment alsodepends on the reliability of pumping and blending equipment. A blender (or proportioner) transfers the fracturing fluid from the storage area (such as 500 barrel frac tanks) to the high pressure pumping equipment. As the fluid passes through the blender, a uniform mixture of chemicals and propping agent is added to the fluid. The blender must be capable of maintaining a uniform mixture regardless of injection rates and volumes. Fracturing fluids containing gelling agents to increase viscosity may be mixed either in a batch or in a continuous process; the choice depends on conditions at the well location. Regardless of the mixing process used, the fracturing fluid should besmooth and lump-free to obtain maximum efflFRACTURING SUPPLY PUMP

BASIC FLUID

-~

CHEMICAL METERING PUMP A -- 

### ciency from a particular chemical.Mechanical mixers that provide excellent mixing have been developed and are used extensively in field operations. Fast hydrating chemicals canbe used which provide better yield at lower concentrations and make continuous application moreefficient. Dry chemical proportioners permit accurate addition of fluid loss agents, propping agents, and~or other additives. A typical blender (Fig. 11.2) may consist ofone or more chemical metering pumps and proppant proportioners, all metering materials at various ratios into the fluid. The fluid is pulled into the blender by a centrifugal pump and goes into the agitator tank (blender tub). After addition of the chemicals and propping agent, the pressurizerpump moves the sand-fluid mixture to high pressure pumping equipment. Present proportioning equipment can alter the concentration of eitherchemicals or propping agent during the job as dictated by treatment conditions. It may be desirable to increase or decrease the concentration of gelling agents, fluid loss additives, or breakers during the treatment or in the flush at the end of the job. Theconcentration of propping agent in the fluid normally is started at 0.5 to 1.0 pound per gallon and increased, as the job progresses, to as high as 20 + pounds per gallon in some cases. However, should excessive pressure or reduced rate be encountered during the treatment, the blender must be able to immediately stop adding the propping agent.

DRY CHEMICAL PROPORTIONER


# ySAND PROPORTIONING CONTROL

~ SAND BULK OR SACK

CHEMICAL METERING PUMP B AGITATOR TANK OR TUB

STABILIZER

PRESSURIZER P~ 

# S FLOWMETER

~ SAND-FLUID MIXTURE TO PUMP TRUCK

Fig. 11.2 - Schematic diagram of sand proportioner which permits (a) continuous operation (b) maintenance of constant ratio of materials

within narrow limits regardless of injection rates (c) instantaneous variation of the sand to fluid ratio
Re~$¢,~ 6¥H



### HESI303176Use of an accurate, flexible and continuous

type of blender (Fig. 11.3) has been shown to be the most efficient method of mixing and metering fluid and additives. Development of this type equipment has made it possible to conduct the large volume, high iniection rate treatments now being performed. Intensifier pumps (Fig. 11.5) use either conventional pumps or special dedicated primary pumps as their power source. Intensifier pumps provide more reliable pumping at high pressuresand high proppant concentrations for long pumphag times due to their long stroke (typically about 5 feet) and high volume per stroke.

Fig. 11.3 - Trailer mounted 100 barrel per minute blender



### High Pressure Pumping Equipment

The primary high pressure pumps used in fracturing are truck mounted (or air transportable skid mounted), predominantly diesel powered, crankshaft driven plunger pumps (Fig. 11.4). The size and weight limitations imposed to comply with state load 1Lrnits have resulted in a total delivered hydraulic horsepower of 1,000 to 1,500 hydraulic horsepower (HHp) per truck, whether delivered by one pump or two. Recent advances in engine, transmission, and pump design should result in an increase in maximum HHp per truck unit to 2,000 HHp by the late 1980’s.

Fig. 11.4 - Body load truck mounted high pressure pumps. The

two pumps can deliver a total of 1200 hydraulic horsepower. Fig. 11.5 - Intensifier pump with 5-foot stroke. Rated at 15 BPM to 15,000 psi or I0 BPM to 20,000 psi.

Control Center


### The operational control center for a frac job isgenerally mounted on its own van or truck. It conrains the readouts and recording devices for theinstruments used to monitor the job and the necessary communications equipment to control the job. Pressure transducers usually monitor pressure in the treating line near the wellhead. If the job isthrough tubing, the annulus pressure is also monitored. Flow meters (usually turbine type) are usedto monitor fluid flow rates while radioactive densometers are frequently used to measure fluid density, from which proppant concentration is calculated. Computers have recently been introduced as part of the control center equipment. This resultsin improved recording and data handling capabilities and can provide "real-time" calculation of information such as a calculated bottom-hole treating pressure and, on foam jobs, a calculated foamquality both at the surface and at bottom-hole conditions. For foam treatments using N~ and CO~ gas, special flow meters that use both temperature and pressure inputs are required to obtain accurate gas flow rates.

HES1303177

### Surface Lines and Manifolding

Low pressure and high pressure flow lines used in fracturing have been developed and adapted from other uses to allow rapid and reliableassembly and disassembly in a wide variety of configurations. Low pressure manifolding will usually use multiple flexible hoses coupled to large (8 to 12 inch) diameter steel lines used for long runs. The high pressure discharge lines use either a WECO® type hammer union or a GRAYLOC® type clamp union. In normal operations, the high pressure discharge line will be rated at working pressures up to 10,000 psi. However, discharge lines rated to 15,000 psi are common, and 20,000 psi rated lines are available in most areas where they might be needed. On offshore stimulation vessels, a reel of steel jacketed flexible hose (rated to 15,000 psi) is normally used to make connections from the pumps on the boat to the wellhead on a platform (Fig. 11.6).

Fig. 11.6 - Flexible steel-jack hose which provides connection

between stimulation vessel and jack-up rig Wellhead isolation tools are available that isolate the wellhead tree from fracturing treating pressure by inserting a mandrel through the tree andsealing it into the top of the tubing. This will isolate the wellhead from both pressure and proppant during the treatment.



# PRACTICAL DESIGN OF FRACTURING TREATMENTS

Part 12The practical application of hydraulic fracturing to oil and gas wells incorporates the use of many "technological tools" such as:

 ̄ electric logs

 ̄ pre-frac and post-frac wellbore surveys

 ̄ laboratory studies on formation samples, fluid theology, propping agents, etc.

 ̄ reservoir transient pressure analysis

 ̄ computerized reservoir production simulators ̄ computerized hydraulic fracturing design simulators

 ̄ "microfrac" tests and analyses

 ̄ "mini£rac" tests and analyses. Long term post-frac production analysis of a well will also influence the type of stimulation treatments used on other wells in the same field. This will be discussed in Part 14 of this text.



### Fracture Design Variables

There are many parameters that can be varied in designing a hydraulic fracturing treatment. The type of fluid used could be water based, oil based, an emulsion, or a foam. The fluid viscosity can be adjusted by using various types of gel systems.Typically, the volume to be pumped will be specified as part of the design, and the injection rate is also predetermined for most treatments. The type of proppant and the sieve size must be selected. The proppant addition schedule will usually be specified and the specified volume of proppant willbe on location before the job starts. In most applications, the sequence will be:

 ̄ pre-pad volume

 ̄ pad volume  ̄ proppant-laden volume  ̄ displacement volume.

Revised 6YH



### HESI303178

### The "pre-pad fluid" is ungelled or lighdy gelled fluid that is pumped prior to starting the gelled fluid. If using an ungelled frac fluid, then this stage is not considered. Many treatments start the pumping with the viscous frac fluid. However, if the wellbore tubulars contain fluid when the job starts, this would be considered as pre-pad. A small volume of hydrochloric acid is occasionally used as a "spearhead" to remove scale or otherwiseimprove the perforation tunnels to promote adequate fluid penetration and lower breakdown pressure.The "pad" is the viscous fluid pumped prior to starting the proppant. If the fracture width is too small, then the proppant grains will bridge instead of moving down the fracture as a slurry. After the specified proppant schedule has been completed, a calculated volume of displacement is pumped before the pumping is terminated. This removes essentially all of the proppant slurry from the wellbore tubulars. The variables that must be considered in a specific fracturing treatment design are:

 ̄ base fluid type

 ̄ fluid viscosity, fluid loss properties and pipe friction  ̄ fluid volume  ̄ injection rate  ̄ proppant type

 ̄ proppant concentration  ̄ physical properties of the formation  ̄ fluid temperature in the fracture.

Fluid Loss~ WIDTH

~-~ ’nj~c, ttie°n 4 ....

In Situ Stress’

Young’s of Elasticit,~ Fluid Viscosity

Treatment Volume 

# ~ Fluid Loss

In Situ Stress

Young’s Modulus i of Elasticity

F]g. 12.1 - Factors Affecting Fracture Width 

### The limitations on many of the above factors are related to the crack width. In simplified terms, Figure 12.1 illustrates the effect of these factors on creating width. A more detailed discussion of this effect on crack width was presented in Part 4 and Appendix B of tiffs text.

Selection of Design Variables
Like nearly all facets of the oilfield, experience is the best teacher when it comes to designing a fracturing treatment for a specific well. However, none of us gets to start with experience, and even the very experienced are often faced with reservoirand well-site conditions that are drastically different than any previously encountered. For thesereasons, we will outline a step-by-step decisionmaking process that will help select the fluid, injection rate, proppant, and pumping schedule touse in a hydraulic fracturing treatment. The sequence given here is only a suggested order; the sequence will often be altered by various surface or reservoir conditions or possibly for economic’~ or political reasons.Step 1 - Selection of Acceptable Fracturing Fluids It is not necessary to choose the exact fluid composition and volume during this first phase. This step should be used to narrow the choice to no more than three possibilities. Appropriate fluid volumes will be determined later. The fluid selection process is usually based on three considerations, or some combination of the

 ̄ availability

 ̄ cost



###  ̄ technical superiority.
For the purpose of our discussion, we willassume any desired fluid would be available, although in many situations this is not true. The logistics of some wells may limit the types of fluids available. This is especially true in underdeveloped regions and offshore operations. For example, theuse of nitrogen and CO2 requires pressurized transport and storage as well as the specialized equipment that may not be be available without advanced planning and]or additional mobilization or set-up charges.



### HESI303179The relative cost of two different fracturingtreatments .will vary with the type and concentration of gelling agents and their chemical additives. The volume of the fluid used, the type and volumeof propping agent and the service company equipment pumping charges are also variables. In some cases, process license fees must also be added to the cost of a treatment. Most of these costs are relatively consistent from coast to coast in the United States. However, international prices will vary drastically due to transportation costs, import fees, and the local availability of some products. Pumping and equipment costs will also vary widely throughout the world. To compare costs betweentwo proposed fracturing designs, it will be necessary to obtain estimates from a service company that operates in the geographical area of the well(s). The technical superiority of one fluid versus another is related to the specific conditions of the well under consideration. In some instances, it may be that the least sophisticated and lowest cost frac fluid best fulfills the technical requirements. Unfortunately, this is usually not the case. The purposes of the fracturing fluid can be identified

as: ̄ to transmit hydraulic pressure into the fracture

 ̄ to extend the fracture penetration into the producing formation

 ̄ to create sufficient width for the fracture to accept the size and concentration of proppant used  ̄ to transport the proppant into the fracture and control proppant deposition. The selection of fluid type may be dependent on compatibility with the reservoir fluids or the rock itseff. The fluid loss properties and the fluid viscosity (as a function of temperature and time) are also factors to be considered. (Part 6 of this text presented extensive discussion of these topics.) For specific fluid systems being considered, the service companies will have extensive data on the fluids they offer. In a later step, this data will be used with a computer frac design simulator for more specific comparisons. Step 2 - Selection of Propped Length(s) There are basically three values that describe a propped fracture:  ̄ propped length  ̄ propped height  ̄ fracture conductivity. Unfortunately, it is nearly impossible to pro° pose a step-by-step design procedure where youcan make all the comparisons desired without specifying one of the above three values as a "target." It will later be necessary to loop back to this stepand choose another "target" for comparative purposes. The most commonly used "target" in current design technology is the propped fracture length,4s so that is what will be used here. 

### Step 3 - Selection of Created Fracture Height The design procedure common for many years has been to assume the created height will be the same as the perforated interval or the productivepay interval. This can be a major flaw in the design process. Prior to the 1980’s, only a few in the industry recognized the importance of accurate fracture height predictions,ss Previously, most computer simulators would only indicate shorterpropped lengths when excess height growth occurred. Very few could accurately model proppant transport and even fewer would model fracture closure. The industry now realizes that the loss of length is not the only concern.’s ~ a The most important question is "Do we prop the pay interval?"or "Does most of the proppant go to some nonproductive zone above or below the pay interval?" It has always been obvious when an operator would frac into a water zone, but for some reason this was the only situation where fracture heightgrowth was a major concern. Before using a computer design simulator, we need some understanding of possible fracture height growth. The major factors that affect height growth are listed here in their approximate order of importance:

 ̄ in situ stress variations

 ̄ pressure in the fracture

 ̄ size of perforated interval

 ̄ variations in elastic modulus. For many years, the only valid analysis for height was to use post-frac surveys. Using these surveys (which are sometimes difficult to interpret)

Revised 6YH



### HESI303180

### in conjunction with standard electric logs, an engineer may find an apparent correlation between logged features that would help predict what type of rock may impede fracture height growth and when excessive growth was Likely. As a result of extensive research work in many laboratory andfield studies in recent years, the industry has accepted the concept that fracture height is primarily controlled by the in siru stress variations in the reservoir. "" ,0. ,  ̄ 70There are now a number of pseudo-threedimensional (3-D) fracture simulators throughout the industry that use in situ stress variations to. predict fracture growth in all three dimensions. Figure 12.2 shows illustrations of optimistic andconservative two-dimensional (2-D) model predictions for created length (Case 1). In addition, Figure 12.2 shows 3-D simulations for good stresscontrast of400 psi (Case 2) and a low stress contrast of only 50 psi (Case 3). It is apparent that the2-D simulator could easily model the Case 2 situation. If a valid fracture height was used in the 2-D

Case 1 : 2-Dimensional fracture simulator prediction

Model

; Stress = 4300 ., .:.;,,:;’. ~

Stress = 4700 psi Case 2: High stress contrast 3-D simulation

~..,~/--- 3-D Model

Stressy

Case 3: Low stress contrast 3-D simulation

Fig. 12.2 - Comparison of 2-D Design with 3-D Simulator where

Pay Zone has Lowest Stress 

### simulator, Case 3 could also be approximated with a 2-D model. Figure 12.3 gives a better comparison of Case 2 and Case 3 with the 2-D examples. Case 3 shows that frac lengths will be considerably shorter when the stress contrast is low. Also, if the proppant is not well suspended, the fracture within the pay zone may not be adequately propped open.

:~:: .’.:: ":.’t2.: .": ....." :.:::: ::~ .":  ̄ ". :" .": .’..’.;:.’..:~: :.’. ".’...::. "..:’.".~.

Case 2

Case 3

Fig. !2.3 - Comparison of 3-D Simulations for Case 2 and Case 3

with 2oD Predictions

If a lower in situ stress exists in the reservoir immediately above the pay zone, the Case 4 result will occur (Fig. 12.4). The resultant length will bemuch less than desired. There should be no problem in being sure proppant remains in the fractured portion of the pay zone. However, the fracture width in the low stress zone will be greater than down in the pay interval, and the fracture will close first in the higher stressed portion at the completion of the job. A larger treatment size will have only a limited effect on obtaining more length within the pay zone. Case 5 in Figure 12.5 illustrates the result of a lower in situ stress existing in the reservoir immediately below the productive interval. This is usually the worst situation which could occur.Fracture length in the productive zone will be limited and proppant settling must be avoided during the pumping operation as well as during fractureclosure. The fracture will close fast in the productive interval, since it has the higher stress.



### HESI303181Model

= 4300 psi .~,

Stress = 4300 psi

Case 4: Lower stress above pay zone

Fig. 12.4 - Compare these with the 2-D simulations - note upward

growth. Stress = 4300 psi

Stress = 4150 psi 4300 psi

3-D Model

Case 5: Lower stress below pay zone

Fig. 12.5 - Fracture grows downward to lower stress, quite different

than 2-D simulations

The determination of in situ stress in the productive zone and adjacent rock is critical for the valid modelling of a treatment design. Even if onlya 2-D simulator is used, the accuracy of the prediction is dependent on the validity of the assumed fracture height. The in situ stress data are required input for using most of the pseudo-3-D simulation models. The only accurate way to measure these stress values is by creating a hydraulic fracture,then taking an instant shut-in pressure measurement. The created fracture should have a verylimited height, since the pressure response observed will be for the lowest stress value within the created fracture. A process called "microfracing" has been developed where very small volumes (typically 20 to 100 gallons of fluid) are used in a small fracturing operation to measure in situ stress. Fracture heights will be small with these volumes. Microfracs can be performed during the drilling orafter the well has been cased. Cased hole microfracs may required squeeze cementing, since stress measurements are often needed for zones that anoperator does not want perforated during the stimulation treatment.

Revised 6YH In the mid-1980’s, a logging technique was introduced to estimate in situ stresses in the reservoir using a long spaced acoustic tool which gives a more accurate value for the At of the shear wave.71 The tool itself was first developed in the mid 1960’s. There was little demand for the data, andcomputer technology at that time required significant "hand analysis" to separate the second shear wave response. The logging service itself is only asophisticated mechanical properties log and a fracture toughness log. The data is digitized and thelogging service company makes several assumptions including linear elasticity, isotrophy and homogeneous composition to predict in situ stressvalues throughout the logged interval. Some companies also link this data into a pseudo-3-D frac design simulator to present the results in a very simple, neat format as a "fracture height log." Many operators have used this service prior to a frac treatment and followed with conventional post-frac survey methods for comparison. Theagreement has varied from excellent to poor. However, within a single field, the results have been more consistent (good or poor agreement within



### HESI303182

### the field). Comparison of in siru stress predictions

of the fracture height log and by microfrac measurements have also shown inconsistent results. Step 4 - Selection of Range of Injection Rates At this point, it is necessary to consider the pump rate for the fracturing treatment. In most instances, this step is actually used to determine the range of injection rates to be considered. Here are four important factors to consider: 

###  ̄ maximum allowable treating pressure  ̄ equipment limitations

 ̄ proppant placement

 ̄ created fracture height. After the maximum treating pressure has beendetermined for the subject well, the predicted friction pressure of the fracturing fluid system(s) will usually establish an upper limit on the possible rate. In some instances, a certain fluid system may be chosen because it has the lowest friction loss of the fluids being considered. Other times, all fluids being considered will allow more rate than desired. There are several equipment limitations thatcould exist. The most obvious would be the horsepower availability of the service companies. In some instances, deliverability of the fluid (or one component of the fluid system) or of the proppant may set the minimum or maximum injection rate. Erosional effects of the proppant on the surfaceiron or the tree on the wellhead may dictate a maximum rate. The effect of injection rate on the ability tosuccessfully place the desired proppant is a difficult analogy. In fact, until there is some previous experience in the reservoir with the selected fluid system and specific proppant to be used, it may benecessary to ignore this consideration until experience indicates problems with proppant placement.Experience with the selected fluid system in similar reservoirs is helpful. Proppant size, proppant density, proppant concentration, fluid viscosity, and injection rate all are factors in the transport of the proppant. The width of the fracture, proppant size, and proppant concentration are all factors inwhether bridging of the proppant occurs somewhere inside the fracture. There are instances when the "proppant placement" problem is in the weLlbore, slowly filling the wellbore with proppant as the job progresses. The factors involved are the size of the casing, the length of the perforated interval, the number of perforations accepting fluid, fluid viscosity (in the wellbore) and the injection
rate. One of the most important effects of injection rate is its influence on fracture height. Numerous field studies related to excess height growth haveshown injection rate to be the most important single factor that can be controlled (in situ stress variations are the major factor). Conversely, when attempting to treat large perforated intervals, it isimportant to use the maximum injection rate feasible. Decreasing the rate to avoid excess height willlengthen the job time and increase proppant placement problems. Step 5 - Selection of Proppant Type(s), Size(s) and Concentration(s) In many fields, previous experience may have identified a suitable proppant type, size, andpumping schedule. However, even in these instances it is wise to re-examine the "status quo" forimprovements. Since the whole purpose of a hydraulic fracturing treatment is to place the proppant, this step should not be slighted. In most applications, cost considerations limit the proppant type to the common quartz sands being marketedas proppants. Frac sand and manufactured proppants are available in many different sieve sizes. (Part 9 of this text discussed proppants in detail.) The size and density of the proppant will affect proppant settling and also the maximum proppantconcentration that can be placed without a screenout from bridging of the proppants in the narrowcrack. Field experience usually shows higher concentrations will give better production results.n73 .In some instances, this is judged to be the effect of higher fracture conductivity, while other times theimprovement is attributed to more propped fracture height. Step 6 - Use of Fracture Design Simulator Now it is time to put all the parameters into afracture design simulator. Hopefully, a computerized simulator is available, since several "iterations" will usually be required to make comparisons between designs. There are hundreds of computer frac design simulators in existence,from very simple 2-D single-viscosity models without proppant transport correlations to the most



### HESI303183sophisticated pseudo-3-D models which calculatethe varying fluid viscosities as a function of temperature and time. Most 2-D simulators are basedon one of the two classical geometry theories described in Appendix B as Group 1 or Group 2. However, even when two different simulators werewritten using the same geometry theory, the resultant design calculations can vary significantly. Three other important factors in a simulator are the fluid loss model, the fluid viscosity model, and the proppant transport model. If there is more than one simulator available to an operator for designing treatments, the most practical approach is to determine which of the simulators has the features most important to the field application and use that simulator exclusivelyfor designing fracturing treatments. If, for example, the primary design criteria is propped length,then three different simulators may give conflicting calculations for fluid and/or proppant volumesrequired for a specific propped length. If the operator is considering propped lengths of 500, 800, and 1000 feet for a specific well, then the resultsfor 500 feet on simulator "A" should not be compared to results for 800 feet on simulator "B;’ etc. It is best to compare simulator "A" and "B" on their technical merits, then use only the selectedsimulator for comparisons of job designs for a specific well.

### Step 7 - Post-Treatment Check of Simulator Calculations
It is very difficult to accurately predict all the data input to the simulator. When field results vary significantly from the simulator prediction, the most likely problem is inaccurate data given to the simulator. Erroneous data for fluid viscosity or an incorrect fluid loss coefficient will force the design simulator to make poor predictions. In some cases, the simulator may use models that are too simple. This will be the case for a graphicalhand-calculated solution, as well as for some computerized models. Highly sophisticated 3-D models will also give unreliable results when much of the input data was "assumed." This is especially true for the in situ stress values. If field results appear to differ significantly from design simulator predictions, the first step is to validate the input data to the simulator. If this is not successful, the operator should try to obtain the use of a better simulator. 

# MONITORING A FRAC TREATMENT DURING PUMPING

Part 13



### Analysis of Bottomhole Treating Pressure

During the late 1970’s, an Amoco Researchproject gathered detailed pressure data during hydraulic fracturing treatments in several reservoirs.In 1979, using part of this data base, Nolte introduced a new method for analysis of treating pressures observed during fracturing propagation.7’-7~The pressure data was obtained by using an openended tubing/annulus configuration that enabled the real-time measurement of bottomhole treating pressure. This work predicted new relationships between the observed pressure response and thecorresponding fracture growth behavior. The researchers observed that a large number of the wells that were monitored followed one (or more) of four identifiable modes of pressure behavior (Fig. 13.1). The log of the net pressure (y-axis) versus the log of the pump time (x-axis) was plotted. The type of formation pressure response that may result was later expanded by Conway, et.al?6 The net pressure was defined as the pressure acting to open and propagate the fracture. Nolte and Smith presented a separate work which detailed methods for obtaining accurate values of the fracture closure
pressure.~7 This method will be detailed later in the "minifrac" discussion.

Mode I Mode II Mode III

~,~ Mode IV

Log (Pump Time)

 ̄ Fracture closure pressure as determined by mini-frac and pressure decline

Fig. 131 - Plot of Treating Pressure vs. Time

Revised 6YH



### HES1303184To explain their observations, Nolte and

Smith used the fracture model of Perkins and Kern" to describe the fluid pressure required to extend a fracture with time. Nolte’s assumptions lead to the conclusion that the fluid pressure would slowly increase with time if the fracture height is relatively constant. This concept predicts that for a Newtonian fluid extending a confined height fracture at constant injection rate, the wellbore pressure will increase proportionally to time raised to a power: p(t) = k * t% I/s < e < 1/5 (13-1) The larger value is for the assumption of arelatively small fluid loss rate (relative to the injection rate) while the smaller value of the exponent is for a relatively large fluid loss rate. The bounds ofthe time exponent of equation 13-1 are for a Newtonian fluid. To be applicable for non-Newtonian fluids, Nolte and Smith generalized that for a power law fluid (with a power law exponent n’), the bounds would be as follows: 1/(4n’ + 4) < e < 1/(2n’ + 3) (13-2) For n’ values typical of actual fracturing fluids used in the industry, this exponent normally falls between 0.18 and 0.33. From this work, it wasconcluded that the constantly increasing net pressure in this range is that of a relatively containedfracture within the zone of interest and most fracture growth is length extension in the reservoir.To explain the other pressure modes, the continuity equation was solved as follows:

ch = ch + LpCh + + +--~- (13-3)

where:

ch = injection rate ch = leakoff rate L = fracture length
p = net pressure C = average width to net pressure ratio def’med by Nolte as *h/2E h = fracture height E = Young’s modulus For a constant injection rate, the right side of 

### the equation is a constant and places a restriction on the permissible changes in the variables withrespect to each other. As a r,esult, any large positive change in height or fluid loss would result in a decLine in the rate of pressure change. With this reasoning, Nolte and Smith interpreted a constant net pressure (Mode II) as either sLightly accelerated height growth over Mode I or accelerated fluid loss. In addition, they interpreted a significant pressure decline (Mode IV) as unrestricted height growth. Nolte’s interpretation of an increasing net pressure which follows a unit slope (Mode III) is similar. Since there is no plausible basis, under theconditions of increasing pressure, for height, compLicance, or fluid loss to decrease significantly, it follows that the rate of length extension must have decreased significantly relative to Mode I. Theimplication of this is that the only variable changing significantly during the unit slope model is the pressure. Also, since length extension has beenreduced significantly, relatively little fluid is reaching the fracture tip (e.g., the fracture screened out with proppant at some point in the fracture). As a result, the fluid being pumped into the fracture essentially is being stored by increasing width and increasing pressure. Summarizing the interpretations of the four pressure modes as referenced in Figure 13.1:

 ̄ Mode I is a gradual pressure increase that, ingeneral, means that the fracture is being relatively contained and most movement is length extension into the reservoir.

 ̄ Mode II is a constant pressure in which accelerated height growth or fluid loss is causing less efficient length extension.

 ̄ Mode III is a unit slope pressure increase in which the fracture has screened out and nofurther length extension takes place. The pressure increase rate of the screenout is inversely proportional to the distance from the wellbore the treatment screened out.

 ̄ Mode IV is a gradual pressure decline inwhich uncontrolled height growth is occurring, resulting in narrow fracture width and poor fracture length propagation.



### Real.Time Treating Pressure Analysis in Field Operations

Since Nolte and Smith’s introduction of bottornhole treating pressure (BHTP) analysis and interpretation for hydraulic fracturing in 1979,



### HESI3031858 ,hydraulic fracturing,

service companies have developed a large fleet of computerized vans for the recording and analysis of fracturing pressure. However, most fracturingapplications do not permit the use of tubing without a packer to directly record BHTP from thesurface while fracturing. This wellbore configuration is not generally used because it may not be operationally possible, it may add significantly to the cost, or it may reduce the desirable injection rate. Consequently, attempts have been made to predict the BHTP from surface recordings of theinjection pressure. This prediction requires calculations of the change in hydrostatic head due to proppant, the friction pressure for the fluid, and a correction to the friction pressure due to proppant. From densometer recordings, the concentration ofproppant in the fluid can be accurately determined, and hence the change in hydrostatic head. The primary deficiency in predicting BHTP from surface measurements is the calculation offriction due to fluid flow within the wellbore tubulars.79 This calculation must include the coupling of the complex flow behavior of the viscoelasticfluids generally used, and the effect of large volume fractions of proppant on this flow behavior. Current methods of calculations are either based on empirical correlations, models for simple fluid behavior or correlations derived from matching acutal field data. Some of these current methods can produce errors that are significantly greater than the changes in BHTP required for an accurate interpretation.One additional flaw in the application of realtime pressure analysis is the failure to measure thevalue for the fracture closure pressure. An assumed value for closure pressure may be severalhundred psi in error, which can influence the decisions of when to continue pumping or to abort a job. When a valid closure pressure value is used and an accurate calculation of BHTP is achieved, it is possible to detect the onset of the large pressure increase which occurs when a treatment is in theprocess of a "screen-out." For this condition, realtime calculation of BHTP provides a significant advantage over surface pressure alone in predictingtiffs condition, and consequently permits the proppant slurry to be displaced to the bottom before pumping must be terminated. The displacement ofthe proppant into the fracture, compared to reacting too late and leaving the wellbore filled with

Revised 6YH proppant, provides significant enough cost savings that many operators require the computerized vans on most treatments. Because of the uncertainties of some fluid friction calculation models, the full potential of BHTP interpretations and analyses are not always available to the operator, even though a computerized van is on site during the treatment.As better friction calculation models are developed, the accurate prediction of BHTP can be achieved for most cases with a computerized vanon location. This can result in a significant increase in the effectiveness of hydraulic fracturing
treatments.



### Minifrac Process

A "minifrac" is a series of tests on a smallfracture performed on a well to determine thefracture extension pressure, closure pressure, the fluid loss coefficient, and fluid efficiency3~*’ 80-8~ Included in minffracturing are:

 ̄ the step rate test  ̄ the pump-in/flow-back test  ̄ the pump-in/shut-in test. 

### Step Rate Test The step rate test is performed after a fracture has already been created. The step rate is begun by injecting fluid into the well at a low matrix flow rate, usually on the order of .3 to .5 barrels perminute with any fluid. The injection rate is increased at increments of .3 to 1.0 barrels per minute until the pressure stabilizes or for 4 - 5 minutes. The pressure is monitored throughout the test. The maximum pressure at each flow rate is plotted versus the corresponding flow rate. Two straight lines are drawn through the plotted points " which define two slopes. The intersection of the two lines yields the fracture extension pressure(Fig. 13.2). The slope of the data beyond the fracture extension pressure can be valuable in predicting maximum desired injection rates when fracture height growth is a problem. 

### Pump-in/Flow-Back Test The pump-in flow-back test, when performed by itself, is begun by injecting into the well with any non-damaging fluid at a rate that will extend the fracture. The total volume pumped should be approximately 50 to 100 barrels. The well is then



### HESI303186shut in (get instantaneous shut-in pressure ISIP)

and flowed back at a low, constant rate, usually .25to 1.5 barrels per minute. The pressure is monitored as shown in Figure 13.3 and an inflection point should be observed. The inflection point from Figure 13.3 is the fracture closure pressure.This test can be repeated as necessary with different flowback rates to develop confidence in the measure value of fracture closure pressure.The inflection point (closure pressure) is interpreted according to different preferences, but for the most part the differences are negligible. For purposes of comparison, the same method should be used when interpreting closure pressures. The dominant opinion is that the closure pressure exists at the intersection of two straight lines defined by the pressure vs. time curve as shown in Figure 13.3. A second method uses the straight line in the upper fracture flow portion of the flow-back curve. The point on the line where the curve begins to become "concave down" is the inflection point. Pump-In/Shut-In Test The pump-in/shut-in test is performed by injecting 50 to 300 barrels of the actual treatment fluid at the expected fracturing treatment rate and then shutting the well in. Upon shutting in the well, the ISIP should be noted. The pressure should be allowed to decline for a time period of at least twice the pumping time (see Fig. 13.4) inorder to obtain enough data to calculate the effective fluid loss coefficient. Normally, a computer program will be used, since curve fitting of the data is necessary. It is very important to only take data during the decline that is above the fracture closure pressure.

 ̄ FCP - Frecture Closure Pressure as detm’mlned by mini-free and pressure decline



## /

1.0 ~0 3.0 4.0 S.O 6.0 7.0 8.0 9~ 10.0

Fl~w Rate (bbl/mln)

Fig. 13.2 - Example Step Rate Test 154) 160

F~g. 13.3 - Example Pump-in/Flow-back Test

3900

~ ’ PREVK~ISLY DETERMINED CLOSURE PRI~JRE

TI min

Fig. 13.4 - Example Pump-in/Shut-in Data for Pressure Decline

Analysis 

### The data required for a minifrac analysis are:

 ̄ Young’s modulus

 ̄ gross height

 ̄ net height

 ̄ flow behavior index

 ̄ gel degradation factor

 ̄ pump rate and injection time

 ̄ ISIP time and pressure

 ̄ closure pressure

 ̄ pressure/time data during the decline period. 

### The computer calculation (or manual analysis) yields the match pressure (symbolized by P’) which in turn yields the fluid loss coefficient, the fluid efficiency, the fracture width and length, and the closure time. P" is determined using theory developed by Nolte. The essence of the analysis is to obtain the match pressure through one or more of these methods:

 ̄ curve matching method

 ̄ graphical method

 ̄ mathematical computer simulation method.

Revised 6YH



### HESI303187Nolte and Smith use the Perkins and Kern geometry which generally predicts a long narrow fracture;77 it shows the width to be proportional tofracture height (H). More recently, Lee has modeled the treating pressure analysis problem using Kristianovich and Zheltov and ".Penny" shaped geometries?° The Kristianovich and Zheltov geometry generally predicts a short, wide fracture, where width is proportional to length (L). Lee alsohas presented a more valid analysis of the ellipsoidal shaped geometry model for the case where a fracture propagates in an unbounded zone or across botmdariesY The effects of compressibilityand of temperature change on the analysis of minifrac data have been published recently by Solimarl.



# POST-FRAC ANALYSIS

Part 14

The final result we seek to obtain with a hydraulic fracturing treatment is increased production. However, in most cases, a treatment isconsidered successful only if the resultant production rates meet or exceed the operator’s pre-frac expectations. When the increased production rate is still considerably below expectations, this means one of two things: pre-frac expectations werefalsely optimistic, or there needs to be some improvements made in the design or implementation of the fracturing treatment. An operator should not ignore the possibility of the former, but the discussion in this text will only relate to possible changes in the application of hydraulic fracturing. Disappointing production results can be broadly classified as one of two possible types: inadequate initial response, or rapid production decline.



### Inadequate Initial Response

Sometimes within days of (or at least a few weeks after) a frac job, it may become obvious that the production capability of the well is inadequate.A check list of possibilities that should be considered would include:

 ̄ inadequate k, +, and/or reservoir pressure

 ̄ fracturing out of zone  ̄ insufficient propped fracture length  ̄ inadequate fracture conductivity

 ̄ fluid-rock incompatibilities. It is always possible that it is a poor well. The effective reservoir permeability may be lower than was originally believed or the porosity may be much lower than was estimated from the logs. The reservoir may be much smaller than anticipated due to faults, pinch-outs, etc. If the well is in anexploratory area, or is a large step-out in an existing field, there possibilities are much greater than if the well is a f’fll-in or development well in an older field.If the fracture does not stay within the reservoir "pay zone" due to upward and/or downwardmigration, the production results can be disappointing. As has been discussed earlier in this text, the fracture will prefer to grow where the lowest in situ stress is encountered. Post-frac surveys (e.g.,temperature, radioactive, etc.) are usually necessary to identify where the fracture has grown out of zone. In a well with very low reservoir permeability,it is very important to achieve a long propped fracture. If excessive height growth occurs, as mentioned above, the propped fracture length will be much shorter than if the fracture height is well contained. If post-frac surveys indicate excessive height, then it it obvious that the resultant propped length is shorter. Post-frac build-up testsmay also allow an operator to determine if the effective propped length is significantly less than designed?7"~ For a hydraulic fracturing treatment to be successful, it is necessary that the propped fracture has adequate conductivity to allow high production rates without a significant pressure drop .down the fracture. Proppant crushing, plugging from gelresidue or produced formation fines and embedment of the proppant into a soft fracture face are the traditional concerns about losing conductivity in the fracture. One additional concern of great importance is the possibility that the proppant may have mostly settled into the bottom part of the fracture and, due to downward fracture growth, isnot propping open the fracture within the productive pay interval. The propped fracture may have excellent fracture conductivity, but if the propped fracture is in essentially a non-productive part of the reservoir, a post-frac pressure build-up analysis

Revised 6YH



### HESI303188hydraulic fracturing

# 61

will calculate very low fracture conductivity, whichis correct for the closed fracture up in the productive interval.The last consideration listed above is incompatibility between the treating fluid and the reservoir rock or possibly incompatibilities with the reservoir fluid(s). Water-based frac fluids reacting with formation clay minerals is the most commonly considered problem, but another possibility is thedissolving or weakening of the grain to grain cementation of a sandstone causing Frees to be released into the proppant bed. Another major problem is for the treating fluid to react with ironcompounds in either the rock or the reservoir water. This can cause severe plugging of both the reservoir permeability and the proppant bed due to the precipitation of iron oxides. Other potentialproblems include precipitation of paraff’m or asphaltenes and scale deposits. In many instances, a viscous emulsion may form and cause blockage.Sometimes emulsions that are stabilized by formation fines can be very viscous and difficult to break.



### Rapid Production Decline

In some instances, the earty time post-fracproduction rates may meet or exceed the anticipated levels, but follow an abnormally steep decline. It is important to accurately know the true "normal" decline for the well. In-depth modeling and simulation of reservoir production rates vs. time may show that rapid decline rates are to beexpected for many wells following hydraulic fracturing stimulation treatments. If an operator is certain that a well is experiencing an abnormal decline, major considerations to help identify the problem are:

 ̄ limited reservoir  ̄ loss of fracture conductivity with time  ̄ fracture closure at the wellbore

 ̄ insufficient propped fracture length. A reservoir that has a small volume may give excellent production rates immediately after a stimulation treatment and fall off rapidly as the reservoir pressure dissipates. Transient pressuretesting methods will identify near-wellbore boundaries assuming the test is conducted properly and for a sufficient length of time. In an established 

### field where the geology has been well defined, there is less possibility that abnormal declines are due to a limited reservoir. During exploratory drilling or early in a field development program, itis important to do adequate transient pressure testing before assuming a rapid decline rate is abnormal. During the producing life of a well, the propped fracture may suffer a significant loss of fracture conductivity. The conductivity loss may result from proppant crushing as the closure stresson the proppant increases or from gradual plugging of the proppant bed. The gradual plugging may be from formation fines. Some formations naturally produce fines, while in some instances the treating fluid may cause the release of f’mes. As the proppant grains imbed into the fracture wails,this can cause the breaking loose of small formation grains that can migrate into the proppant pack. Over a long time period, f’mes may migrate through the propped fracture toward the wellbore and a high degree of plugging may occur as the concentration of fines becomes very high. Other possible sources of fines would be precipitation products such as paraffin or scale deposits. In a retrograde condensate reservoir, the conductivity may drop significantly as the reservoir pressure decreases and the liquid saturation increases, oftenresulting in three phases being present in the proppant pack. Fracture closure in the near-wellbore area can result when this area is inadequately propped.Overdisplacement at the conclusion of the fracturing treatment can be one cause for this situation. However, some wells have a tendency to allow part of the proppant to be flowed back in the wellbore during cleanup and/or production. Flow back of proppant during cleanup may not be a problem if there is other movement of proppant toward the wellbore to replace the lost proppant. Also, the proppant that is carried back into the wellbore is not necessarily material that was adjacent to the wellbore. If there is significant proppant settling prior to fracture closure, there may an unpropped void area above the top of the proppant pack. Thefluid velocity through this open crack may be sufficient to pick up and transport proppant back intothe wellbore from significant distances. This phenomenon 

### is most plausible during post-frac cleanup or early in the well’s producing life. 

### With



### HESI303189

### time, the fracture will continue to close and hold the proppant in place. If the propped fracture penetration distance is insufficient, a rapid production decline may be evidenced even if the initial production rates were below expectations. See the previous discussionconcerning "inadequate initial response" for possible reasons that the propped length may be less than anticipated.



### Refrac Treatments

To design a successful refracturing treatment, it is necessary to identify the problem(s) with the original treatment,r2~83 Some refrac treatments are the result of a premature screen-out during the original attempt to stimulate the well. For this type of refrac design, refer to Part 12 of this section where treatment design is discussed. The primary discussion here relates to a refrac when the originaltreatment was successfully completed, but production results were disappointing or at least less than optimum. First, determine why the initial treatment was unsuccessful. Possible reasons for desiring to refrac a well include:

 ̄ inadequate producible reserves

 ̄ depleted drainage area

 ̄ insufficient fracture conductivity  ̄ insufficient propped fracture length  ̄ insufficient propped fracture height  ̄ formation damage. Next, determine the possible alterations in therefrac design from the original stimulation treatment. The potential design changes that may be needed include:



###  ̄ Change fracturing fluid.

- higher or lower viscosity

- more compatible with formation.

 ̄ Change proppant.

- different sieve size

- higher strength proppant

- curable resin-coated proppant

- significantly higher volume of proppant.

 ̄ Change design variables to alter propped length.

 ̄ Use multistage treatment.

 ̄ Alter injection rate.

 ̄ Use large pre-pad or pad to repressure formation. Each point in both of the lists above has been extensively discussed previously in this text.



### HESI303190

## References

1. Pierce, A. L.; Veda, S.; and Koonce, K. T.: "Determination of The Compass Orientation and Length of Hydraulic Fractures by Pulse Testing," J. Pet. Tech. (Dec. 1975) 1443.



### 2. Lacy, L. L.: "Comparison of Hydraulic Fracture Orientation Techniques," SPE 13225, 59th Annual SPE Tech. Conf., Houston (Sept. 1984).
3. Krisdanovich, S.A. and Zheltov, Yu P.: "Formarion of Vertical Fractures by Means of a Highly Viscous Fluid," Proc. Fourth World Pet. Cong. 2 (1955), 579-586. 4. Daneshy, A.A.: "On the Design of Vertical Hydraulic Fractures;’ J. Pet. Tech. (Jan. 1973) 83-98.


### 5. Warpinski, N. R.: "Measurement of Widthand Pressure in a Propagating Hydraulic Fracture," SPE ]. (Feb. 1985) 46.
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9. Daneshy, A. A.: "Hydraulic Fracture Propagation in Layered Formations;’ SPE y. (Feb. 1978) 33.
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11. Williams B.B.: "Fluid Loss from Hydraulically Induced Fractures;’ J. Pet. Tech. (July 1970) 882-888.


### 12. Babcock, R.E.; Prokop, C.L.; and Kehle, R.O.: "Distribution of Propping Agents in Vertical Fractures;’ API Meeting, Oklahoma City (March 1967). 13.

14.



### 15.

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### Lee, W.S., and Daneshy, A.A.: "Fracture Geometry and Proppant Transport Computationfor Multi-Fluid Treatments," SPE 14511, Eastern Regional Meeting of SPE, Morgantown, West Virginia (Nov. 1985). Simon, D.E.; McDaniel, B.W.; and Coon, R.M.; "Evaluation of Fluid pH Effects on Low-Permeability Sandstones," SPE 6010, 51st Annual Fall SPE Tech. Conf. and Exhibition, New Orleans (Oct. 3-6, 1976).Pittman, E.D. and Thomas, J.B.: "Some Applications of Scanning Electron Microscopy to the Study of Reservoir Rock," J. Pet. Tech. (Nov. 1979) 1375-1380.
Searle, Alfred B. and Grimshaw, R.W.: The Chemistry and Physics of Clays, Ernst Benn Ltd (1949) 425. 

### Mungan, Necmettin: "Permeability Reduction through Changes in pH and Salinity," J’. Pet. Tech. (Dec. 1965) 1449-1453. Coulter, G.R. and Hower, W.E: "The Effect of Fluid pH on Clays and Resulting Formation Permeability," Southwestern Petroleum Short Course, Dept. of Pet. Eng., Texas Tech Univ., Lubbock (April 1975). Thomas, R.D. and Ward, D.C.: "Effect of Overburden Pressure and Water Saturation on Gas Permeability of Tight Sandstone Cores;’ J. Per. Tech. (Feb. 1972) 120-124. Holditch, S.A.: "Factors Affecting Water Blocking and Gas Flow from Hydraulically Fractured Gas Wells," J. Pet. Tech. (Dec. 1979) 1515-1524.

### Van Poolen, H.K.: "Do Fracture Fluids Damage Productivity?" O//and Gas ]. (May 1957).Tannich, J.D.: "Liquid Removal from Hydraulically Fractured Gas Wells," J. Pet. Tech. (Nov. 1975) 1309-1317.Dill, Walter: "Iron Control in Fracturing Applications;’ Halliburton Services Technical Paper F3233, Duncan, Oklahoma (July 1985).



### HESI303191

## References (Continued)

24. Coulter, G.R. and Wells, R.D.: "The Advantages of High Proppant Concentration in Fracture Stimulation," J. Pet. Tech. (June 1972) 643-650.

25. Burnham, J.W.; Harris, L.E., and McDaniel, B.W.: "Developments in Hydrocarbon Fluids for High-Temperature Fracturing," ]. Pet. Tech. (Feb. 1980) 217-220. 

### 26. Tiner, R.: "Polymers and Their Use in theOilfield," presented at the Southwestern Petroleum Short Course, Dept. of Pet. Eng., Texas Tech Univ., Lubbock (April, 1976). 27. Chatterji, J. and Borhardt, J.D.: "Application of Water-Soluble Polymers in the Oilfield;’ SPE 9288, 55th Annual Fall SPE Tech. Conf. and Exhibition, Dallas (Sept. 1980).

28. Cooke, C.E., Jr.: "Effect of Fracturing Fluids on Fracture Conductivity," .L Pet. Tech. (Oct. 1975) 1273-1282.29. Pye, D.S. and Smith, W.A.: "Fluid Loss Additive Seriously Reduces Fracture Conductivityand Formation Permeability;’ SPE 4680, SPEAIME 48th Annual Fall Meeting, Las Vegas (Oct. 1-3, 1973). 30. Conway, M.W.; Almond, S.W.; Briscoe, J.E.; and Harris, L.E.: "Chemical Model for theRheological Behavior of Crosslinked Fluid Systems," SPE 9334, 55th Annual Fall SPE Tech. Conf. and Exhibition, Dallas (Sept. 21-24, 1980). 

### 31. Conway, M.W.; Pauls, R.W.; and Harris,L.E.: "Evaluation of Procedures and Instrumentation Available for Time-Temperature Stability Studies of Crosslinked Fluids," SPE 9333, 55th Annual SPE Fall Tech. Conf. and Exhibition, Dallas (Sept. 21-24, 1980).

32. Hower, W.F.: "Adsorption of Surfactants by Montmorillonite," Clays and Clay Minerals (1970) V. 18, 97-105. 33. Graham, J.W.; Monaghan, EH.; and Osoba, J.S.: "Influence of Propping Sand Wettability on Productivity of Hydraulically Fractured Oil Wells," J. Pet. Tech. (Nov. 1959) 324-329. 34.

35.

36.

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38.

39.

0.

41. Penny, G.S.; Soliman, M.Y.; Conway, M.W.;and Briscoe, J.E.: "Enhanced Load Water Recovery Technique Improves Stimulation Results;’ SPE 12149, 58th Annual Fall SPE Tech. Conf. and Exhibition, San Francisco (Oct. 5-8, 1983). Sinclair A.R.; Terry, W.M.; and Kiel, O.M.: "Polymer Emulsion Fracturing," 1. Pet. Tech. (July 1974) 731.
Blauer, R.E., and Kohlass, C.A.: "FormationFracturing With Foam," SPE 5033, Fall Meeting AIME, Houston (Oct. 1974). King, G.E.: "Factors Affecting Dynamic Fluid Leak-off with Foam Fracturing Fluids," SPE 6817, SPE-AIME 52rid Annual Fall Tech. Conf. and Exhibition, Denver (Oct. 9-12, 1977).Harris, P.C.: "Dynamic Fluid-Loss Characteristics of Nitrogen Foam Fracturing Fluids," ]. Pet. Tech. (Oct. 1985) 1847.

### Mitchell, B.J.: "Viscosity of Foam," PhD Thesis, Univ. of Oklahoma, 1969.
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### 42. Van Poolen, H.K.; Tinsley, J.M.; and Saunders, C.D.: "Hydraulic Fracturing Flow Capacity vs. Well Productivity," Trans AIME (1958) 213. 43. McGuire, W.J. and Sikora, V.J.: "The Effect of Vertical Fractures on Well Productivity;’ Trans AIME, (1960) 401. Cooke, C.E., Jr.: "Hydraulic Fracturing with aHigh Stength Proppant;’ SPE 6213, Fall Meeting AIME, New Orleans (Oct. 1976).



### HESI303192

### 45. 

## References (Continued)

Veatch, R. W., Jr.: "Overview of Current Hy- 56. Soliman, M.Y.: "Modifications to Production draulic Fracturing Design and Treatment Increase Calculations for a Hydraulically FracTechnology - Part 1 and Part 2," J. Pet. Tech. (April and May 1983). 57. 46. Cutler, R.A.; Ennis, D.O.; Jones, A.H.; and Carroll, H.B.: "Comparison of the Fracture Conductivity of Commercially Available and Experimental Proppants at Intermediate and High Closure Stresses;’ SPEJ. (April 1985). 58. 47. Recommended Practices for Tesffng Sand Usedin Hydrauh’c Fracturing Operations, fin’st edition, API RP56, Dallas (March 1983).

48. Recommended Practices for Testing High 59.S~rength Proppanrs Used in Hydrauh’c Fracturing Operations, proposed 8th draft, API, Dal= las (May 1986).
49. Prats, M.: "Effect of Vertical Fractures on Reservoir Behavior -- Incompressible Fluid Case," 60. ]. Pet. Tech. (June 1961) I05.
50. Seccombe, J.C. and Anderson, G.E.: "Selection of a Fracture Proppant in a Tight Gas 61.Field, Bauxite vs. Sand, Wamsutter Area, Wyoming;’ SPE 10827, SPI/DOE Unconventional Gas Recovery Symposium, Pittsburgh (May 1982). 51. McDaniel, B.W.: "Conductivity Testing of 62. Proppants at High Temperature and Stress," SPE 15067, 56th California Regional SPE Meeting, Oakland CA (April 1986).
52. McDaniel, B.W.: "Realistic Fracture Conduc- 63. tivities of Proppants as a Function of Reservoir Temperature;’ SPE/DOE 16453 presented atthe SPE/DOE Symposium on Low Permeability Reservoirs, Denver, May 18-19, 1987.

53. American Petroleum Institute: "Tentative 64. Fourth Draft of Recommended Practices for Evaluating Proppant Conductivity," Sept. 1986.

54.



### 55. tured Well," J. Pet. Tech. (Jan. 1983) 170-172. Cinco, H.L.; Samaniego, E; and Dominquez, A.: "Transient Pressure Behavior for a Well with a Finite Conductivity Vertical Fracture;’ SPE 6014, Fall Meeting AIME, New Orleans (Oct. 1976). Coats, K.H.; Dempsey, J.R; and Henderson,J.H.: "A New Technique for Determining Reservoir Description from Field Performance Data;’ SPE J. (March 1970) 66-74. Solorzano, L.N. and Arredondo, S.E.; "Method for Automatic History Matching of Reservoir Simulation Models," SPE 4594, SPE 48th Annual Fall Meeting, Las Vegas (Sept. 30-Oct. 3, 1973).

### Barker, B.J.: "Transient Flow to Finite Conductivity Vertical Fracture;’ PhD Dissertation, Stanford University (May 1977). 

### Agarwal, R.G.; Carter, R.D.; and Pollock, C.B.: "Evaluation and Performance Prediction of Low Permeability Gas Wells Stimulated by Massive Hydraulic Fracturing,"J. Pet. Tech. (March 1979) 362-372.
Holditch, S.A. and Morris, R.A.: "The Effectsof Non-Darcy Flow on the Behavior of Hydraulically Fractured Gas Wells;’ .]’. Pet. Tech. (Oct. 1976) 1169-1179. 

### Soliman, M.Y.; Venditto, J.J.; and Slusher, G.L.: "Evaluating Fractured Well PerformanceUsing Type Curves," SPE 12598, Permian Basin Oil and Gas Recovery Conf., Midland, Texas (March 8-9, 1984). El-deg-Economides, C.A., and Ramey, H.J., Jr.: "Transient Rate Decline Analysis for Wells Produced at Constant Pressure;’ SPE J. (Feb. 1981) 98-104.
Smith, J.E.: "Design of Hydraulic Fracture Treatments;’ SPE 1286. Tinsley, J.M.; Williams, J.R.; Tiner, R.L. and Malone, W.T.: "Vertical Fracture Height -- Its Effect on Steady-State Production Increase;’ SPE 1900, J. Pet. Tech. (May 1969) 633. 

### 65. Agarwal, R.G.: "A New Method to Accounting for Producing Time Effects When Drawdown Type Curves are Used to Analyze Pressure Build-up and Other Test Data," SPE 9289, Annual Tech. Conf. and Exhibition, Dallas (Sept. 21-24, 1980).

Revised 6YH



### HESI303193

# 66 hydr.ulic ,tra¢’~uring~



## References (Continued)

66. Allam, A.M.; Crichlow, H.B.; and Soliman, 75. Nolte, K.G.: "Fracture Design Considerations "M.Y.: "Numerical Simulation of Heteroge- Based on Pressure Analysis," SPE 10911, preneous Fractured Gas Reservoir Systems with Turbulence and Closure Stress Effects," SPE10119, 56th Annual Fall Tech. Conf. and Exhibition SPE/AIME, San Antonio, TX (Oct. 5- 7,1981).67. Forchheimer, E: "Wasserbemegung durch Boden," Zeitz net Deutsch Ing. (1901) 45, 1731. 68. Veatch, R.W.: "Economics of Fracturing: Some Methods, Examples and Case Studies," SPE 15509, 61st Annual Fall Tech. Conf. and Exhibition of SPE, New Orleans, LA (Oct 5-8, 1986). 69. Simonson, E.R.; Abou-Sayed, A.S.; andJones, A.H.: "Containment of Massive Hydraulic Fractures, " SPE J. (Feb. 1978) Vol 14, 1, 27-32. 70. Voegle, M.D.; Abou-Sayed, A.S.; and Jones, A.H.: "Optimization of Stimulation Design Through Use of In Situ Stress Determination," SPE 10308, presented at the 56th Annual Tech. Conf. and Exhibition SPE/AIME, San Antonio, TX (Oct 5-7, 1981). 

### 71. Newberry, B.M.; Nelson, R.E; and Ahmed, U.: "Prediction of Vertical Hydraulic Fracture Migration Using Compressional and Shear Wave Slowness;’ SPE 13895, presented at the SPE/DOE Low Permeability Gas Reservoirs Symposium, Denver, CO (May 19-22, 1985). 72. Gregorcyk, W.A.; Pauls, R.; Holtmeyer, M.; Venditto, J.J.; and Chisholm, E: "High Frac Sand Concentrations Boost Production in Texas’ Olmos Formations," Oil and Gas f. (Sept. 17, 1984) 105-108. 73. Shah, S.N.: "Ultra High Sand Concentration in Hydraulic Fracturing - A Case History,"SPE 11578, presented at SPE Production Operations Symposium, Oklahoma City, OK, (Feb 27-Mar 1, 1983).74. Nolte, K.G.: "Determination of Fracture Parameters from Fracturing Pressure Decline;’ SPE 8341, presented at the SPE 54th Annual Fall Tech. Conf. and Exhibition, Las Vegas, NV (Sept 23-26, 1979). 76.

77.

78.

79. 

### sented at the SPE Cotton Valley Symposium, Tyler, TX (May 20, 1982). Conway, M.W.; McGowen, J.M.; Gunderson,D.W. and King, D.G.: "Prediction of Formation Response from Fracture Pressure Behavior," SPE 14263, presented at the 60th Annual Tech. Conf. and Exhibition SPE, Las Vegas, NV (Sept 22-25, 1985). Nolte, K.G.; and Smith, M.B.: "Interpretation of Fracturing Pressures,"f. Pet. Tech. (Sept 1981) 1767-1775. 

### Perkins, J.K.; and Kern, L.R.: "Widths of Hydraulic Fractures,"f. Pet. Tech. (Sept 1961), 937. Lord, D.L.; and McGowen, J.M.: "Real-TimeTreating Pressure Analysis Aided by New Correlation," SPE 15367, presented at the 61stAnnual Tech. Conf. and Exhibition, New Orleans, LA (Oct 5-8, 1985). 80. Lee, W.S.: "Pressure Decline Analysis with the Khristianovich and Zheltov and Penny-Shaped Geometry Model of Fracturing;’ SPE/DOE13872, presented at the SPE/DOE Low Permeability Gas Reservoirs Symposium, Denver, CO (May 19-22, 1985). 81. Lee, W.S.: "Mini-Frac Analysis Based onE1- lipsoidal Geometry;’ SPE 15369, presented at the 61st Annual Tech. Conf. and Exhibition, New Orleans, LA (Oct 5-8, 1985).

82.

83. 

### Solirnan, M.Y.: "Technique for Considering Fluid Compressibility and Temperature Changes in Minifrac Analysis;’ SPE 15370, presented at the 61st Annual Tech. Conf. and Exhibition, New Orleans, LA (Oct 5-8, 1985). Conway, M.W.; McMechan, D.E.; McGowen,J.M; Brown, D.; Chisholm, ET.; and Venditto, J.J.: "Expanding Recoverable Reserves Through Refracturing," SPE 14376, presentedat the 60th Annual Tech. Conf. and Exhibition, Las Vegas, NV (Sept 22-25, 1985).

Revis~l 6YH



### HESI303194

# APPENDIX A MECHANICS OF HYDRAULIC FRACTURING

Mechanical Behavior of Rocks
Like other engineering materials, rocks are deformable. Let S be a cylinder of rock with radius, r, to which a force, F, is applied in the manner shown in Fig. A. 1. The effect of F on S is the inducement of a stress, or, which is equal to the force divided by the base area of the cylinder; i.e.,



### F (A-l)

The direction of this stress is parallel to the axis, z, and therefore is called Crz. In the x or y directions there are no stresses; i.e., o-,~ = O’y = 0. Thus, although stresses in the solids are calculated by the same manner as pressures in the liquids (and have the same dimensions), there are important differences between the two. For example, pressures have the same magnitude in every direction but stresses do
not. The effect off on S is a compression of S. Therefore, o’z is called a compressive stress. If the force F had a direction opposite what is shown in Fig. A. 1, then the rock sample, S, would have been under tension (material particles would have been pulled apart from each other) and the stresses would have been tensile.

Z F
~-AL

Fig. A.1 

### Thus, by changing the magnitude or the direction of the force, F, compressive or tensile stresses of any magnitude can be created in the sample (assuming that it does not fail). In solid mechanics, the type of stress is usually identified by a sign. If a compressive stress is designated by a plus sign; i.e., + ~rz, then a tensile stress will be shown by a minus sign; i.e., - o’z. This means that stresses can theoretically have values anywhere between + ~ to- ~. This is another major difference between pressures and stresses. The lowest value a pressure can have is zero. It is never negative. One important aspect of stresses is that their magnitude and direction can change from point to point within a body. Indeed, the solution of the rock mechanics problems often reduces to obtaining equations that express the variations of the stresses in a given body. 

### The study of the mechanical behavior of rock is not limited to an investigation of the stresses induced in it by the external forces. It is necessary to know how the rock has deformed as a result of the stresses existing in it. This is usually done by a study of the strain. Suppose the cylinder in Fig. A. 1 had an original length, L. After the force, F, is applied to it, its length will change by an amount, denoted by AL. Its deformed length is L - AL. The strain, ~, is defined as the ratio orAL to L:

~ = (L - AL) - L = _ AL

L L


### and has no dimension. Like stresses, strains in a body may have different values and directions at different points. For example, the strain in the z direction in Fig. A. 1 is:

AL

L (A-2)

After the application of F, the radius of the cylinder changes from r to r + Ar:

( Ar
~x = ~y = ,r + _r~ -r =

r r (A-3)

Notice that ~x and ~y have a plus sign while ez has a minus sign. The reason is that ~z is associated with a decrease in length while ~,, and % represent increases in radius.



### HESI303195

### The relationship between the stresses and strains is usually obtained through the theory of elasticity (although other theories may also be used for this purpose). In an elastic material, the strains induced by stresses are linearly proportional to them:

~z = 1 Crz (A-4) E

The constant E is called the Young’s modulus of the material. In addition to this constant, to be completely defined, isotropic, homogeneous, elastic materials need another constant. This constant is called Poisson’s ratio. For the example used here, this constant is equal to the ratio Of~x to ~z:

(A-5)



### in which v is Poisson’s ratio. The Young’s modulus (E) has dimensions of pounds per square inch while Poisson’s ratio (v) is dimensionless. The solution of most rock mechanics problems begin with a mathematical treatment of the problem. Like all other branches of engineering, these solutions are generally based on certain assumptions. In rock mechanics, it is usually assumed that rocks are isotropic, homogeneous and elastic. The definition of these terms is as follows: Elasticity: If the deformations produced in a body by external forces completely disappear by the removal of the forces, the material is considered to be perfectly elastic. Homogeneity: A material is homogeneous if the smallest element of it has the same physical properties as the body itselL I sotropy: If the elastic properties of a body do not change with direction, the body is isotropic. Let us examine the reasons for, and the validity of, the above assumptions. 1. Elasticity: No rock is completely elastic. However, some rocks have an elastic behavior up to a certain value of stress. Theory of elasticity has yielded many reasonable and accurate solutions to rock mechanics problems. In cases in which the rocks do behave elastically up to a given stress the elastic solutions are correct as long as the stresses have not exeeded the elastic limit. In other cases, elasticity, in general, is the most workable theory and any deviations from it may make the problem immensely difficult to solve. Among the presently known theories, elasticity often yields the closest fit to the actual results. There are cases that require the use of non-elastic theories, such as studying the creep in rock salt. Such cases will have to be handled individually and are not considered here. Homogeneity: Strictly speaking, rocks are not homogeneous materials. A block of rock containsdifferent crystals of various kinds, macro- andmicro-fractures, etc. However, this assumption is quite reasonable if the dimensions of the body under consideration are large compared to the dimensions of the discontinuity. Isotropy: The assumption ofisotropy is necessary for mathematical simplification. In most problems, the amount of deformation that can be produced by the applied forces is of interest. For instance, the width of hydraulic fractures is the deformation caused by the fluid pressure existing inside the fracture. The assumption ofisotropy simplifies the mathematical relationship between the forces and the created deformations. The force-deformation equations for an isotropic, homogeneous, linearly elastic body contain only two constants: Young’s Modulus and Poisson’s ratio. If it is not assumed that the material is isotropic, then, in general, 21 independent coefficients are needed to identify the material mechanically. This explains the need for the assumption.



### Strength of Rocks

As in most other materials, rocks can bear a certain amount of force without failure. The magnitude of the force bearable by rocks depends on the type of force (compressive, tensile, shear, etc. ) and the type and size of rock. The compressive and tensile strengths of rock def’me the load per unit surface area needed for compression and tensile failure. The compressive and tensile strengths of rocks usually are measured in the laboratory (Fig. A.2). A cylindrical sample of rock is placed in a loading

Revised 6~’1"1



### HESI303196machine. A compressive or tensile load is applied to

the specimen and increased until failure occurs. The load at failure divided by sample surface area will yield the sample strength. Due to natural variations in rocks, their strength usually is measured several times on different samples and averaged to yield a representative value.

I~g. A.2

Laboratory experiments on most rocks will show that their compressive strength is anywhere from 10 to 100 times larger than their tensile strength. This means that rocks can be broken much easier in tension than in compression. The result of compressive failure of most rocks is a crushed material consisting of particles with irregular shapes and sizes. Tensile failure, on the other hand, yields a fracture. The specimen usually breaks into two pieces along the fracture plane.



### Fracture Initiation
Every point of an undergrotmd formation is under the actions of stresses caused by overburden and tectonic forces. Existence of these stresses can be proved by the presence of structural features such as faults, folds, overthrusts, etc. Any study of the mechanical response of a reservoir rock will require the knowledge of the magnitude and the direction of all the stresses present in it. It has been proven mathematically that any system of stresses acting at a point (regardless of the number or the directions) can always be replaced by three normal stresses called "the principal stresses." These three stresses are mutually perpendicular and equivalent to the initial system from which they have been derived. Furthermore, for any system of stresses, there exists only one set of principal stresses. Thus, the stresses present in a formation can always be replaced by their equivalent "in situ principal stresses." This permits investigation of the mechanical behavior of that formation. Obviously, if every individual component of stress acting at a point is not known the in situ principal stresses cannot be computed. But the problem can be solved for a general set of principal stresses. Then, how changes in the magnitude and direction of the principal stresses will affect the mechanical behavior of the material can be observed. If the only force acting in a formation were the weight of the overburden (which is a rare case), the magnitude of the three principal stresses in an isotropic, homogeneous and linearly elastic formation could be calculated by the following equations:

crz = pgh (A-6)

crx ---- cry ~ crz (A-7)

1 -v

in which density of the rock gravity acceleration depth of the point under consideration Poisson’s ratio of the formation

In this particular case, one principal stress, o’z, is vertical and the other two, crx and cry, are horizontal. Assume that the three principal stresses in the reservoir under consideration are O’x, Cry, crz; and that crz is vertical. (Actually the solution of the problem is available for any direction of cry, but here, for the sake of simplicity, it is restricted to vertical cry). These stresses exist at every point of the reservoir. However, around the borehole, the state of stress changes from the above simple form. To study the changes occurring around the borehole, consider a cylindrical borehole drilled in an isotropic, homogeneous, elastic formation. A cross-section of this borehole perpendicular to its axis of symmetry will look like Fig. A.3. First consider the deformation of this borehole under the influence of crx. Intuitively, it can be seen that crx will deform the circle into a shape similar to the dashed curve. (This point can also be proved mathematically). A careful observation of the deformation of the borehole shows that those material particles close to



### HESI3031970 hydr~uJi~

A and A’ are being stretched (tension) while around B and B’ they are squeezed together (compression). Mathematically, it can be proved that the tensile stress induced at A is equal to - Crx and has the direction shown in Fig. A.3, while the compressive stress at points B and B’ is equal to 3o’x.

B

Fig. A.3

Rocks are considerably weaker in tension than in compression. Therefore, if this borehole is to be fractured, it will start at points A and A’. Looking at the principal stresses, note that o’x has a positive value while cry has implicitly been assumed to be zero. The above analysis shows that maximum tensile stress is induced at points A and A’, which are perpendicular to the cry direction (least principal stress). By a similar argument, it can be shown that when Cry has a positive value and Cr,, is zero, the borehole will deform in a way similar to the dashed curve in Fig. A.4, and that at point B and B’ a tensile stress equal to - Cry and at A and A’ a compressive stress equal to 3cry are induced.

Fig. A.4 

### The general situation will look similar to Fig. A.5 in which o’x is assumed to be greater than cry. In this case, the stresses at each point can be calculated by adding the components induced due to o’x and cry. Thus at A and A’ a stress equal to 3O’y - 

### crx is present and at B and B’ a stress equal to 3crx - cry is present. Since Crx is assumed to be larger than cry, the stresses at A and A’ have smaller values than at B and B’ and therefore are more tensile. A hydraulic fracture in this borehole will initiate at points A and A’ which, as shown in Fig. A. 5, are perpendicular to the least compressive in-situ principal stress.

A ~A._’

Fig. A.5



### In order for a fracture to initiate, the maximum tensile stress induced around the borehole must exceed the tensile strength of the formation. Ifcrx and cry are such that 3o’y -- O’x 

### exceeds the tensile strength of the rock, a hydraulic fracture will initiate around the borehole. If3cry - cry, is not sufficient for the spontaneous initiation of the fracture, a tensile stress may be artificially induced around the borehole by applying a fluid pressure inside it. It is intuitively obvious (and can also be mathematically proved) that applying a fluid pressure inside the borehole will tend to expand it, or, in other words, induce a tensile stress around it. It has been theoretically proved that the effect of the fluid pressure (ignoring leak-off) is to induce a tensile stress that has a magnitude equal to the fluid pressure all around the borehole. Since this tensile stress has the same value everywhere at the wall of the borehole, it will not change the point at which the fracture will initiate. In the case under consideration (crx > Cry), the hydraulic fracture will initiate at points A and A’ whenever the tensile strength of the rock is exceeded.

Revi~ed 6YH



### HESI303198Mathematically, this condition is stated as:

-Pwh + 3Oy - crx = O’T



### in which: (A-8)

borehole fluid pressure tensile strength of the formation

Another influence of the borehole fluid pressure is that it induces stresses around the borehole as it leaks into the formation. The mathematical solution of this problem has been obtained and reported in the literature, i This solution shows that fluid leak-off generally decreases the breakdown pressure of a hydraulic fracture. As mentioned earlier, the problem of the initiation of hydraulic fractures has been solved mathematically, and complete solution of it is available in the literature. For the sake of completeness, a brief discussion of the theoretical aspects of the problem will be presented.



### Mathematical Solution of State of Stress Around a Borehole
Suppose a borehole of radius (a) is drilled in a formation with the axis of the borehole in the direction (Fig. A.6). The OXY coordinate axes are considered in the same direction as the two other principal stresses. The stresses induced around the borehole due to the presence oft.he regional stresses are given by:



### o’= = o’,, + o’~, (1- a2)+ (A-9)

,2 r~

o’x- % (1-3 a4)+ 2 rE

(4 a2) cos20

crO0 ~"

cry- cry (1+3a4) -cos2O

2 r4 cry

-- ~x (1 -- 3__ a4 ) + 2 r4

2 ( a2 ) sin2O 

### r2 (A-11)

inwhich

O’rr = radical stress* o’oo = tangential stress "r~o = shear stress

r = radial distance 0 = angles measured from the direction ofcr=

Rg. A.6

At the periphery of the borehole r = a (Fig. A.7) and equations A-9, A-10, and A-11 become:

crrr-- 0 croo = crx + cry - 2(cr= - Cry)cos 20 (A-12)

Fig. A.7

*In polar coordinate* the stresses sge ¢all~l radial, tangentitl tnd ~etr stresses.

Rc~d6YH



### HESI303199

### Stresses Induced Around a Borehole Due 

### to Internal Fluid Pressure Suppose a fluid is applying a pressure p on the walls of a cylindrical cavity of radius (a). The stresses induced around the cavity are:

a2

crrr = P- (A-13)

cr00 = P- (A-14)

Tr0 : 0
On the internal wall of the cavity:

crr~ = P (A-15)
O’0o = -- P (A-16)

Tr0 = 0



### Stresses Around A Pressurized Wellbore The stresses induced around an impermeable underground pressurized borehole are the sum of two items:
1. Stresses due to in-situ forces. 2. Stresses due to fluid pressure. Thus, on the wall of the borehole the stress components become:

or= = p (A-17)

cr0O ~-" O’x -[- cry -- 

### 2(cry, - cry) (A-18) 

### cos 20 - p



### Mathematical Basis of Fracture Initiation
As mentioned earlier, the tensile strength of rocks is much smaller than their compressive strength. Thus, rocks will fail much easier under tension. Let crT denote the tensile strength of the formation. Whenever cr~ or cr00 equals err, failure will start. If~r00 In’st reaches this value, a vertical fracture will initiate. Suppose Cry is smaller than Crx. It can be shown that Cr00 will have a minimum at 0 = 0 and ~" equal to:

~roo = 3Cry-Crx-p 

### Thus, the fracture initiates perpendicular to the least compressive stress (in this example Cry) and:

cr00 = CrT = 3O’y - crx - P p = 

### 3 cry -- Crx -- CrT (A-19)

In the above analysis, no allowance was made for any fluid leak-off. Under certain assumptions, Haimson has shown that with leak-off the pressure will be:

p = 3 Cry - crx - CrT + Po



### 1 - 2v 2 

### 1 -v (A-20)



### in which a is a dimensionless porous rock constant and P0 is the formation reservoir pressure.



### Fracture Extension
Injection of fluid after fracture initiation results in extension of the fracture. In the course of its propagation, the hydraulic fracture follows the path of least resistance, which (under the assumptions of isotropy, homogeneity, and elasticity) is perpendicular to the least compressive in situ principal stress. Depending on whether the least in situ principal stress is horizontal, vertical or inclined, the hydraulic fracture will extend as vertical, horizontal or inclined, respectively. Most of the original experimental research in the area of fracture extension was limited to the observation of fracture orientation in the laboratory size specimen. Fig. A.8 shows the results of one such experiment. It shows a hydraulic fracture propagating in one plane and perpendicular to the least principal stress. The same results have been observed for fractures extending from perforated cased holes. Figs. A.9 and A. 10 show the direction of hydraulic fracture to be influenced more by the principal stresses than presence of the perforations. Similar laboratory results have been observed in fracturing of anisotropic, naturally fractured rocks.2’3 Fig. A. 11 shows a hydraulic fracture extending perpendicular to the least principal stress and unaffected by the rock anisotropy or the presence of the large natural fracture that has been intersected. (

ReUsed 6YH



### HESI303200Perforations have shown a significant effect only

in the area very near the wellbore. As mentioned in Part 4 of this section, the perforations can influence the breakdown pressure, but the near wellbore effect of perforation orientation will not affect the general fracture orientation or azimuth.

Fig. A.8

Fig. A.9 Fig. A.IO



### References For Appendix A

Halmson, Bezalel and Fairhurst, Charles: "Initiation and Extension of Hydraulic Fractures in Rocks," SPEJoumal(Sept. 1967) 310-318.



### 2. Personal observation ofB.W. McDaniel of fractured coal Seam; Sesser, IL (May 30, 1974).

Warpinski, N.R.; Schmidt, R.A.; and Northrop, D.A.: "In-Situ Stresses: The Predominant Influence on Hydraulic Fracture Containment," J. Pet. Tech. (Feb. 1978) 27.



### HESI3032014 laydraulic fracturing



# APPENDIX B FRACTURE GEOMETRY CALCULATIONS

The computation of fracture geometry consists of incorporating fracture mechanics theories with the considerations of fluid injection, fluid flow down the fracture, and fluid loss into the fracture faces. The computed geometry of hydraulic fractures is essentially an approximation. Several factors are responsible. First of all, the formation material is assumed to be isotropic, homogeneous and linearly elastic; conditions seldom satisfied in reality. The treatment fluid is assumed to behave according to a mathematical model, which it often does not. All design methods assume fracture height to be constant and equal to an estimated number. This poses the biggest restriction on the accuracy of the computed geometries. These and other simplifying assumptions make the computed geometries an approximation of the true values. The accuracy of the various design methods should be judged on the basis of their assumptions, keeping in mind that all the various methods yield "reasonable" results, and none of them has an unquestionably proven advantage over the others. The logic behind all design procedures is basically the same. The injected column is divided into two parts, one lost as leak-off and the other occupying the created fracture. The leak-off volume is a function of the fracture face surface area, formation properties, fluid properties and time. Fracture volume depends on its height, length, and the variations of width with length. The fracture width is a function of fracture length and frictional losses due to fluid flow in the fracture, the latter in turn being a function of fluid and formation properties. These physical observations, when translated into a mathematical language, yield a number of relationships between fracturing parameters, the solution of which yields the fracture geometry. The difference between the various design methods is mainly in the assumed equations used for the different physical events. Group 1 Methods-- Introduction The various methods of designing hydraulic fractures can be divided into two main groups, according to the particular form of the width equation used in arriving at the solutions. Group 1, consisting of methods derived by Perkins and Kern~ and Nordgren2, assumes that the fracture width is proportional to its height andhas the form

w = 4(1

- 1)2) Ape (h)

E

inwhich:



### w = maximum fracture width at the wellbore h = fracture height

An examination of this equation shows that since E and v are formation constants, and h is assumed to be constant, the only way the fracture width can increase during the treatment is for Ape to increase. Thus, since the fracture width is accepted to increase during the treatment, recording the fluid pressure at the bottom of the wellbore during the treatment (so it does not include friction due to flow in the pipes) should show an ever increasing fluid pressure with increasing time. Another aspect of the Group 1 design procedures is that fracture cross-section parallel to its height is elliptical. While this feature of these design methods is more realistic than the Group 2 methods, such a fracture shape cannot be used readily in computing sand transport in the fracture. Instead, the variable fracture width along the height has to be replaced by an average constant width. 

### Group 2 

### Methods-- Introduction The Group 2 Methods, consisting of the works of Kristianovich and Zheltov3, Le Tirant and Dupuy4, Geertsma5, and Daneshy6 use a fracture " width equation similar to the one presented by Kristianovich and Zheltov. In this equation

w = 4(1 -.z) Ape(L) E (a-2)

in which:


### L = fracture length, wellbore to tip
It shows the fracture width to be proportional to its length rather than its height as assumed by Group 1 methods.

Revised 6YH



### HESI303202Since L is a continuously increasing parameter

during the job, fracture width can increase without any need for Ape to increase. Actual computation of Ape based on Group 2 methods shows it to decrease during the early stages of the treatment and then reach a constant value. Since L usually increases at a faster rate than Ape decreases, fracture width consequently increases during the job. Group 2 methods all assume that the fracture width is constant along its height. Such a fracture shape, although admittedly unreasonable, considerably simplifies the problem of computing sand transport in the fracture. As stated earlier, it cannot be positively proved which of the two approaches is superior. While the comparison of the fluid pressure trends with field observations may give an edge to Group 2 methods, it does notprove anything about the fracture geometry. As to the various methods within each group, it can be stated generally that the newer ones are more sophisticated and comprehensive.

Group 1 Methods-- Calculations Perkins and Kern (No Leak-Of0. The design equation derived by Perkins and Kern were the first presented in the literature and the most widely used for a long period of time. The equations presented by Perkins and Kern do not consider the influence of fluid leak-off. They cover both horizontal and vertical fractures, turbulent or laminar flow. For vertical fractures with fluid in laminar flow:



### w(in.) = .38 [ q(bbl/min)  ̄ #(cp)  ̄ L(ft) ]v4

E(psi)

where:
injection rate of the treatment fluid viscosity of the Newtonian fluid Young’s modulus length of fracture


### In this equation all the parameters on the right-hand side are known, except for L. To calculate L use the equality of the injected volume with the fracture volume (no leak-off). This will yield:*

L(fl) = 51.732 x

[ q3(bbvmin)’t4(minutes)" E(psi).]vs

~(cp)" (B-4) in which:

t = treatment time

For vertical fractures in turbulent flow:

w(in.) = 0.6 [ q2(bbl/min). ~  ̄ L(ff) ]1/,

E(psi)  ̄ h(fl) (B-s)

in which:
specific gravity of the fracturing fluid



### and

L(ft) = 1.24 x

[ E(psi)  ̄ h(ft)" q2(bbl/min)  ̄ t4(minutes) (B-6)

The choice between using laminar or turbulent flow equations is based on the value of the Reynolds’ number and is discussed in detail by Perkins and Kern. The equation for fracture width with a non-Newtonian fracturing fluid is more lengthy and can be found in the same reference. 

### Perkins and Kern (With Leak-Off). Equations B-3, 4, 5, and 6 yield fracture widths and lengths for the case of no fluid leak-off. In the presence of leak-off, the computation of the fracture geometry is more complicated but may be carried out by the following trial and error method. First, assume a fracture length and for this length compute fracture width from Equation B-3. Next, for the given length, height, and fluid and formation properties compute the leak-offvolume. (This may be done by several methods, e.g., Carter’s7 equations in appendix of Reference 7 or by Williams’s methods.) Subtracting the leak-off volume from injected volume willyield the fracture volume. From the fracture volume and time, a hypothetical injection rate for fluid forming the fracture volume can be computed. Equation B-4 may then be used to compute a second fracture length. If the two lengths are not equal, it is because the initial value was not a good estimate. Thus, the computations should be repeated with a new assumed length untilthe two values agree. The corresponding length, width, and leak-offvolume will represent the geometrical status of the hydraulic fracture.

*The equations presented here for computing Lare not given i~ the paper butcould be deriv~l from it.



### HESI3032036 hydraulic fracturing



### It should be noted that this method of introducing leak-off in Perkins and Kern equations is not desirable because the width equation and the Ape computation ignore leak-off. Nordgren’s equations are more handy for such computations. As an example of designing fractures by Perkins and Kern method, assume the following conditions (no leak-off):
q = 10 bbl/min E = 6 x 106psi 

### h = 100ft ~x = 100cp

From Equations A-7, A-8 and B-l:

t(minutes) L (~et) w (inches) Ape (psi)
10 295 .179 229 60 1,236 .256 328 100 1,859 .284 363


### The presented values of Ape are the frictional pressure losses due to fluid flow in the fracture. They show Ape increasing with time, as stated earlier. Nordgren. This is an extension of the work of Perkins and Kern and includes the influence of fluid leak-off. To obtain the fracture geometry, Nordgren numerically solves the equations for fracture shape and fluid leak-off. Therefore, in its pure form the use of this design method requires access to a computer. However, Nordgren also presents approximate analytical expressions that can be used readily for hand computations of the fracture geometry. These are as follows:

No leak-off

w(in.) =
[ ~(cp)" qZ(bbl/min) ] !/5 4E(psi)" h(ft) 

### (minutes) (B-7)

L(ft) = 38.5 x
1/5 t4/5 [ E(psi)" q~(bbl/min) ] (minutes) ~(cp)" h4(ft) (B-8)



### Comparison of these equations with those of Perkins and Kern shows that Nordgren’s method yields longer fractures with larger maximum widths at the wellbore. With leak-off

w(in.) = 0.238 x
[ ~(cp)  ̄ q2(bbl/min) E(psi)  ̄ h(ft)  ̄ C_~(ft/minv2) (B-9) 1/4 ] tvs (minutes)

L(ft) = 0.447 x (B-IO)
[ q(bbl/min) ] t~ (minutes) Cw(ft/minV2) ̄ h(ft)



### inwhich:

Cw = Fluid leak-off coefficient 

### Equation B-10 shows that, in the presence of leak-off, fracture length is not a function of fluid viscosity, or the rock properties. This is a tmi.~’que property of this equation and is not found elsewhere. 

### For the example case:

With leak-off
q = 10 bbl/min E = 6 × 106 

### psi h = lOOft V. = 100cp

C~ = .001 ft/min~ 

### FromEquafionsB-7,B-10andBl: t (minutes) L (feet) w(inches) ~p¢(psi) 10 141 0.114 142 60 346 0.143 179 100 446 0.151 189

Without leak.off(assuming Cw = O)

FromEquationsB-7,B-8 andB-l: t(minutes) L (feet) w(inches) ~p¢ (psi)
10 219 0.133 166 60 920 0.190 238 100 1,385 0.211 263

Note: The constant terms in these equations are different than those given by Nordgren because of the units.

Revised 6YH



### HESI303204Group 2 Methods-- Calculations

Kristianovich and Zheltov. All of the Group 2 design procedures are based on the width equation derived by Kristianovich and Zheltov, or variations of it. According to these authors, the maximum width of the fracture at the wellbore is given by



### w = 4(1 -~2) Ape(L)

E (B-11)



### which has the same form as that used in Group 1 procedures except that here the fracture length has replaced fracture height. The basis for the derivation of the fracture width equation is the concept that the fracturing fluid does not wet the entire length of the fracture, i.e., a very small part of the fracture close to its tip is always empty of the treatment fluid. Kristianovich and Zheltov’s method, as well as all the other design methods in Group 2, assume that the fracture width is constant along its height. This assumption, although incorrect in a strict sense, makes the computations of fracture geometry simple enough to be mathematically tractable. Furthermore, this shape fracture also makes the computations of proppant transport in the fracture feasible. The equations derived by Kristianovich and Zheltov can be divided in two parts. Part one consists of the derivation of the width equation which, aside from some typographical errors, are mathematically sound and tractable. In part two, they derive the equation for the computation of Ape. This part of the paper, unfortunately, is not tractable and contains typographical errors. In addition, from the contents of the paper it is not easily possible to follow the authors’ train of throught and replace their equations by any other. The equations presented below are in the form they appear in original paper except for correcting the obvious typographical errors. In order to simplify the writing of the equations, let:
R = pf/ ~y

in which: (B-12)



### pf = fracturing fluid pressure at the wellbore o-y = least in situ principal stress

since pf = cry + Ape, pfis a measure of Ape. The value of R is computed from: R(R- 1)3=84x

2 (1 + ~2)2 .(~). q~ O’y O’y qqt + Pro (B-13)

in which:

Vto = the inidal fracture volume at t = o


### Assumingv = . 15 and Vto = 0 (no fluid in the fracture before fracturing) and substituting engineering units in Equation B-13 we obtain:

R(R- 1)3 = .21243 x 10-6 ×

2 1 [ E(psi) ] )x(cp) (ry(psi) (ry(psi) t(minutes) (B-14)

Use of this equation has shown that the magnitude of Cry does not signiflcandy change the fracture geometry. Thus, assuming a value for cry of, say, 2,000 psi and knowing E, I~, and t, this equation can be solved for R. From R one calculates Ape from:

Ap¢ = (~y(R- 1)


### The fracture length, L, is obtained from:


### L(ft) = .956 x

1/2 

### [ q(bbl/min), t(minutes). E(psi) ]

Ape(psi). h(ft)


### Substituting Ape in the width equation will then yield w.
Le Tirant and Dupuy. These authors consider the influence of fluid leak-offon the equation of Kristianovich and Zheltov. The computations are carried out by a computer. Although the details of the computations are not discussed by the authors, they seem to follow the same logic as presented earlier for introducing leak-offinto the Perkins and Kern equations.
Geertsma and de Klerk. Geertsma and de Klerk introduced fluid leak-offin the design method of Kristianovich and Zheltov. Complicated equations of fluid leak-off and fracture growth were first simplified by assuming simple (but not restrictive) fracture growth behavior and then solved analytically. The resulting equations are too complicated to be solved by hand, but can easily be used by a computer. However, the authors have developed charts that can be utilized for quick hand computations.



### HESI303205These graphical methods (for both horizontal and vertical fractures) require the computations of two non-dimensional terms, after which fracture width and length (or radius) can be estimated through simple computations. The graphical solutions of Geertsma and de Klerk are relatively easy to use requiring only a small hand calculator and the design graphs. The results are generally in good agreement with those of the other Group 2 methods.

For our example problem,



### Without leak-off

q = 100 bbl/min E = 6x 106psi h = lOOft O, = 100 cp
t(minutes) L (feet) w (inches) Ape(psi)
10 227 .189 104 60 751 .343 57 100 1,056 .406 48



### With leak-off
q = 10bbFmin E = 6x 106psi h = 100ff ~ = 100cp Cw = .001fVmin~a
t (minutes) L (feet) w(inches) Ape (psi) 10 166 .155 117 60 456 .257 70 100 607 .296 61
Comparing the first results (no leak-off) with those of Kristianovich and Zheltov shows this method to yield longer but narrower fractures. Comparing the results with leak-offwith those of Nordgren indicate that Geertsma and de Klerk’s method yields narrower and shorter fractures. Daneshy. Daneshy’s method of computing the fracture geometry is the newest of these methods. It is an extension of the other Group 2 methods and includes such features as use of non-Newtonian fluids and static or dynamic fluid leak-offequations. The fracture geometry is obtained on the basis of the least number of assumptions compared to the other methods. The steps followed for the numerical solution are the closest of all methods to the actual physical events occuring during a fracturing
treatment. Daneshy’s numerical solution is obtained through a computer. Thus, the method cannot be used for hand computations.


### For the example problem of:

No leak-off

q = 10bbFmin E = 6x 106psi h = 100ff ~ = 100cp


### t(minutes) L (feet) w (inches) Ape(psi)
10 188 .230 153 60 640 .408 78 100 890 .483 68

With leak-off

q = lObbl/min E = 6x 106psi h = lOOft p. = lOOcp Cw = .001 ft/minv2



### t(minutes) L (feet) w(inches) Ape(psi)
10 146 .180 154 60 400 .286 89 100 545 .328 75

A comparison of these results with those obtained through Geertsma and de Klerk’s equations shows that for both cases, Daneshy’s method shows a wider but shorter fracture.



### References for Appendix B

1. Perkins, T.K. and Kern, L.R.: "Width of Hydraulic Fractures," J. Pet. Tech. (Sept. 1961) 937-949.



### 2. Nordgren, R.P.: "Propagation of a Vertical Hydraulic Fracture," SPE]. (Aug. 1972) 306-314.

Kristianovich, S.A~ and Zheltov, Yu P.: "Formation of Vertical Fractures by means of a Highly Viscous Liquid," Proc. Fourth World Per. Cong. 2(1955) 579-586.

R©vi~ed 6YH



### HESI303206

## 79

o

°

o

o LeTirant, P. and Dupuy, M.: "Dimensions des Fractures Obtenues Par Fracturations Hydraulic des Couches Petroliferes," Revue de L ’Insfiurur Francais du Petrole(Jan. 1967) Vol XXII, No. 1,44-98.
Geertsma, J. and deKlerk, F.: "A Rapid Method of Predicting Width and Extent of Hydraulically Induced Fractures," ]. Pet. Tech. (Dec. 1969) 1571-1581.
Daneshy, A. A.: "On the Design of Vertical Hydraulic Fractures," f Pet. Tech. (Jan. 1973) 83-98.


### Howard, G.C. and Fast, C.R.: "Optimum Fluid Characteristics for Fracture Extension," Drill an d Prod. Prac., API (1957) 261-270.

Williams, B.B.: "Fluid Loss From Hydraulically Induced Fractures,"f Pet. Tech. (July 1970) 882-888.



### HESI303207

# APPENDIX C

CLAYS

Types of Clays

bon

 ̄ The clays most frequently found in hydrocarproducing formations are: smectite: formerly called montmorillonite, gel or bentonite

 ̄ illite: which can include glauconite and some micas  ̄ mixed-layer: primarily illite-smectite  ̄ kaolinite  ̄ chlorite.Their presence in formation samples and approximate concentrations are usually determinedby X-ray diffraction analysis. However, the position of clays in the rock matrix and their localized concentration in any area are also very important.This is very difficult to resolve by X-ray techniques but can be quickly determined by the use of dyes. Certain dyes1~2 and other chemicals exhibit characteristic colors when they are adsorbed by the different clays. Examination of the treated rock surface with low power magnification can be quite revealing.



### Structure of Clays

Clay minerals consist of two relatively simple building units: the silica tetrahedral sheet, and the alumina or magnesia octahedral sheet (Figs. C. 1 and C.2). The composition of these building units is:  ̄ silica tetrahedral sheet - repeating units ofsilicon atoms that are surrounded by four oxygen atoms to form tetrahedrons  ̄ alumina octahedral sheet - repeating units of aluminum atoms surrounded by six hydroxyl groups to form an octahedron. A three layer, or 2:1, clay would have one alumina octahedral sheet with tetrahedral sheets bonded to it at each side. A crystal of this type isknown as the mineral pyrophyllite. If the octahedral sheet contains all magnesium, the three layer mineral would be talc. O and ~[) = Oxygens

O and O = Silicons
F]g. C.1 - Tetrahedral Sheet

O and (]’ = Hydroxyls (OH) OAluminums, magnesiums, iron

Fig. C.2 - Octahedral Sheet



### Smectite. Where some of the aluminum inthe octahedral sheet is substituted with magnesium, and a small amount of silicon in the tetrahedral sheet is substituted with aluminum, the clay mineral smectite is formed. These substitutions develop a charge deficiency in the crystal lattice which is represented by a net negative charge shown at the faces of the clay crystal. This clay has been known by several different names; however, the name "smectite" is preferred now.
Illite. This is similar to smectite in structure,but has a greater degree of substitution, particularly in the silica tetrahedral layer. This develops more negative charges in the illite crystal than in smectite. Where an excess of potassium was present during clay development, the potassium was attracted to the clay at the cation exchange sites. With the help of pressure, all water wassqueezed from the stacks of crystals and the potassium became "fLxed" between the illite platelets. It is very difficult for water to separate illite crystalstacks. With most of the potassium ions being obscured in the stacks, illite exhibits a lower cation exchange capacity than smectite although itscharge density is greater. Its main cause of permeability damage is due to clumps of clay breaking

Revised 6YH



### HES1303208

### loose, migrating, and then bridging at flow restrictions in the rock matrix. Kaolinite. This is a two-layer clay consistingof one silica tetrahedral sheet and one alumina octahedral sheet. There is essentially no substitution in the crystal lattice. Kaolinite’s cation exchange capacity comes from broken bonds on the edge of the crystals. Chlorite. This is a family of clay minerals which consist of stacked mica-like (similar to illite) and brucite Mg3(OH)~ layers. Two layers of each type form a unit cell. Chlorites are not found in hydrocarbon formations as often as the other clays, and usually exhibit no swelling properties in water.However, they have been known to cause permeability damage by migrating and bridging at flowrestrictions, or by creating fluid retention problems in the pore spaces. 

### Mixed-layer clay. Any combination of clays where the individual clay crystals are stacked on each other to form an irregular arrangement may make up mixed-layer clays. A stacking where twoclays are regularly alternated is seldom encountered. The most frequent mixed-layer clay foundin hydrocarbon producing formations is the illitesmectite combination. Less frequently detected is the chlorite-smectite stack. Thus, the degree ofswelling primarily depends on the amount of smectire that is present in the mixed-layer stacks. These days can cause considerable permeability damage through migration and bridging actions in addition to possible swelling.



### Clay Distribution
Examples of these clay types are shown in Figure C.3. Some correlation has been developedas to the type of clay that may be present at various depths along the Gulf Coast. Weaver3 reported smectite predominated to 7,000 feet with some mixed-Layer day and discrete smectite was detected in the 7,000 to 12,000 feet depth range. With deeper burial (to 17,000 feet), discrete smectite decreased to essentially zero while the mixed-Layer clay concentration increased. Perry and Hower*extensively studied the composition of shales obtained from wells drilled in the Galveston area of Texas and offshore Louisiana. Shale samples were investigated from 3,364 to 17,000 feet in the Galveston area. Generally, the predominant clay found was smectite-illite mixed-layer with thesmectite component being the predominant fraction (up to 85%) at the shallower depths. The percentage of the smecfite component decreased regularly in the mixed-layer clay with depth until only 20% smectite was present in the 10,300 to 17,000 feet shales. Small amounts of kaolinite andchlorite were usually present at all depths. However, content of both of these clays and discrete illite increased at depths below 9,200 feet. The clay content of the offshore Louisiana shales (410 to 18,400 feet) was very similar to the above except that smectite content of the mixed. layer clay was greater at equivalent sub-sea depths. For example, mixed-layer clay contained 35% smectite at 15,500 feet and did not reach the 20%level until 18,000 feet. This difference can be explained by a greater temperature gradient for the Texas wells since higher temperatures favors the development of illite. If the clay content in sand bodies is similar to the adjacent shales, predictions regarding the clays to expect at various depths in the sands can be made. Formation samples from other areas of the United States (east of the Rocky Mountains) havealso been examined and the same general clay distribution found as described above. However, concentrations of discrete i11ite and smectite weregenerally lower than in the Gulf Coast area. Kaolinite was almost always the predominant clay detected, regardless of the depth of burial.The relatively small number of carbonate sampies evaluated in the Gulf Coast studies showed zero to moderate amounts of these chys to be present. Kaolinite, illite, and mixed-layer clay were the predominant days found.West of the Rocky Mountains, most productive sandstone formations are much younger in geologic age. A higher percentage of both feldspar and day minerals is common.

Description of Clays

All of the clays noted here are flat crystals. They exist as thin platelets that are normally stacked like a deck of cards to form packets. Stacking is not necessarily even, since platelets can overlap in the packets.



### HESI303209Miocene Formation, South Louisiana showing

smectite and mixed layer clay in pore. Mag.- 10,500X. Douglas Formation showing illite and kaolinite around pore. Mag.-2,000X.

Norphlet 7ormation, Mississippi showing fibrous illite in pore. Mag.-1,000X. Tuscaloosa Formation showing iron rich chlorite coating sand grains. Mag.-1,00OX.

Fig. C.3 - Scanning Electron Microscope Photographs

Through the use of the dye staining procedure mentioned previously, it has been found that these packets are distributed throughout a sand in many ways. Quite frequently they are concentrated at iuncfions of sand grains and are more concentrated in the sand near shale lenses. Although variations will occur depending on the concentration of clay in the sand, generally the extensive studies of the Gulf Coast sands indicated:

 ̄ kaolinite is concentrated in isolated spots

 ̄ smectite is smeared throughout the area

 ̄ illite appears in streaks close to shale lenses  ̄ mixed-layer clay is present in irregular streaks throughout the sand. 

### Cation Exchange

All Clays are negatively charged. With smecrite, these charges are predominant on the faces of the clay crystal while the edges of the crystal are positively charged. The density of the negativecharges can be measured by determining the number of positive charges required to neutralize thecrystal. This is known as the cation exchange capacity (CEC) of the clay and is expressed in milliequivalents (ME) for 100 grams of clay. Figure C.4 lists the CEC of several clays.

Reviled 6YH



### HESI303210Clay Range of Cation Exchange Capacity

Smectite

Illite

Kaolinite
Chlorite Sand (2 to 62 microns) 80 to 150

10 to 40

3to 15

10 to 40

0.6

Rg. C.4 - Cation Exchange Capacity of Selected Clays and Sand

The replacement of one cation by another on any clay is governed mainly by the law of mass action and the valence of the cation. Generally, where mono- and divalent cations are present in the same concentration, the divalent cation will bepreferentially attracted to the clay. If a water solution containing only one cation is brought in contact with a clay, it will tend to replace anothercation, regardless of its valence. Among monovalent cations, potassium and ammonium are more effective than sodium in replacing divalent calcium on smectite.



### Water Adsorption by Clays

Clays may be loosely classified as swelling and non-swelling. Smectite is the only clay that swells by adsorbing ordered water layers between clay crystals. Mixed-layer clay, which contains smectite, will also swell with water but the illite portion ofthis clay is relatively nonwater swelling. In addition to illite, kaolinite and chlorite may be classedas nonwater swelling clays. They do not build viscosity in water as effectively as smectite since their crystals tend to remain as packets instead of being dispersed as do the smectite crystals. However, these so-called nonwater swelling clays do adsorb some water. Routson~, et. al., reported that some water is adsorbed in illite crystal packets.Aylmore’, et. al., examined kaolinite under a variety of conditions and found that water is associated with this clay and that the cation attracted to the clay and its concentration have little effect on the water content. Thus, all clays do adsorb water with smectite adsorbing the most. Water adsorption or layering between smectite crystals is due to hydration of the cation attracted to the clay and hydrogen bonding. Degree of swelling depends on the cation associated with the clay and the amount of dissolved salts in the water in contact with the clay. Hydration numbers indicate the number of water molecules that may be carriedto the clay surface by the cation. These water molecules act as a nucleus for the development of water layers on the clay surface. Figure C.5 lists the ionic diameters and range of hydration numbers for several cations. X-ray diffraction can be used to determine thenumber of layers of water between smectite crystals. The thickness of an absolutely dry smectite crystal is generally accepted to be 9.5 A and a layerof water is approkimately 3 A thick. (J~ is the abbreviation for Angstrom units. One Angstrom equals 10.7 millimeters or 4 x 10" in.). Thus, if xray indicates the clay-water system is 15.5 A thick, then two layers of water are present. The fhst three to four layers of adsorbed water are very ordered and have an average density of 1.2. Some authors have called this crystalline water since its general configuration is different from bulk water. Where only one layer of water exists between smectite crystals, its density is close to 1.4 and it isvery difficult to remove. As a result, the dry bentonite normally used for drilling mud has one layerof water between the clay crystals which is equivalent to about 9% of the total weight of the clay. The surface of the smectite crystal is a series of oxygen atoms formed in repeating hexagonal rings. There is a cavity inside each ring that is approximately 2.8 A in diameter and 2.4/~, deep. When the cation attracted to the clay has a small hydration number and ionic diameter, it is entirely possible for the cation to fit into the cavity and be relatively difficult to remove.



### HESI3032114 hvdrtul:¢ trteturm[

Potassium has an ionic diameter of 2.66 A anda small hydration number which fits these requirements quite well. However, a cation that has a large hydration number would not be able to fit into the cavity even if it had a relatively small ionic diameter. Figure C.6 lists the effects of different salts on the amount of water held between smectite crystals under atmospheric pressure conditions.

I 

### Permeability Damage by Clays

As stated previously, the major permeability damage that can occur in a clay-containing rock is due to the migration of the clays and subsequent 

### bridging of these particles in pore channel restrictions. With smectite, the adsorption of additional water between crystals forces them farther apart and enhances their possibility of breaking loose and migrating. This clay can migrate as single crystals or small packets. Smectite can then beseen as the weak points in mixed-layer clay structures. Here, packets of iRite can break loose and migrate and these larger particles, combined with the individual smectite crystals, cottld be more damaging than smectite by itself. KaoLinite, illite, and chlorite will also migrate as packets when their natural equilibrium is disturbed by a foreign water invading their environment.

Cation Ionic Diameter Hydration Number

Sodium 1.90A 5 to 11

Potassium 2,66A 1 to 4

Ammonium 2.86A 2 to 4

Calcium 1.98A 10 to 22
Magnesium 1.30A 12 to 33 A range in hydration numbers is given which represents data from several sources. The variation in values is due to the method of obtaining the data and the concentration of the various salts in solution.
Fig. C.5 - Ionic Diameter and Hydration Numbers of Several Cations

Salt Sodium Potassium Calcium
Concentration* Clay Clay Clay

Distilled Water 32 27 4

0.4 percent 14 2 4

2 percent 3 2 4

8,5 percent 2 2 3 to 4

10 percent 2 1 to 2 3

13 percent N.D. 1 3

16 percent N,D. 1 2

N.D.- Not Determined *The salt concentration shown is used to express the percentage of sodium chloride with sodium smectite, potassium chloride with potassium smectite and calcium chloride with calcium .smectite.

Fig. C.6 - Effect of Salt Concentration on the Number of Water Layers (Swelling) Between Smectite Crystals

Rcvi~¢d 6YH



### HESI303212

### Pressure and Salt Effects

Conf’ming pressure has an effect on the amount of water that will be held between smectite crystals. Handy9, et. al., have used a consolidometer and x-ray to determine the degree of water expulsion from between smectite crystals at pressures to 44,500 psi. No salts were present in the water for this study. Their results are summarized in Figure C.7. It may be seen that sodium smectite retains more water than calcium smectite under similar pressures.

SODIUM SMECTITE

Pressure, X-Ray PSI Spacing Approximate Numbers Of Water Layers

392 20.6A 1,020 20.1]k 2,825 18.7A 9,020 17.0]~ 17,980 15.9A 44,500 13.6A 1,365 17.8A 2,730 16.5A ~9,110 ’ 

### 15.5A 27,50O 14.0A 

### 27,500 14.0A 4 4 3 2to3 2 1 to2 3 2to3 2 2 1 to2

CALCIUM SMECTITE

Approximate Pressure, X-Ray Numbers PSI Spacing of Water Layers

1,365 17.8A 3 2,730 16.5,~ 2 to 9,110 15.5A 2 18,220 14.7~, 2 27,500 14.0A 1 to

Fig. C.7 - Effect of Pressure on Water Retention on Two Types of

Srnectite 

### Unfortunately, there is no published data on the effect of both pressure and salt concentration on the amount of water that is retained between smectite crystals. However, a study of Figure C.7 indicates that, for most well conditions, two layers of water will be retained between smectite crystals 

### under naturally occurring conditions. Tlfis conclusion is based on the normal salts and their concentration found in most brines combined with theeffect of overburden pressure. Therefore, to minimize the possibility of clay crystals or packets of crystals breaking loose and migrating, any water that may penetrate a clay containing rock should contain a chemical that will not alter the naturalwater retention of the clay. This can be accomplished with the potassium cation. The use of potassium chloride in water forfracturing procedures constituted the first successful application of this chemical.’° Potassium chloride also has been used in drilling fluids to stabilize water sensitive shales."12 In addition, potassiumchloride is being used in cement slurries to minimize damage that could be caused by the high pH cement filtrate. The ammonium ion has also shown a greatdeal of promise for this use. Its use in the oil industry has been limited since salts of this ion are more expensive than potassium salts. Ammonium chloride has been used successfully in a few areas in conjunction with hydrofluoric acid treatments and water base fracturing fluids. Potassium and ammonium cations are used to maintain the "status quo" of clays to minimizepermeability reduction due to clay migration during a particular phase in the life of a well. They arevery effective for this use but are not recommended for conditions where a relatively dilute brine will be flowing continuously through the sand or where severe water conning develops.



## References for Appendix C

1. Dodd, C.G.: "Dye Adsorption as a Method of Identifying Clays; Clays and Clay Technology, Bull. 169, Division of Mines, California (1955) 105-111. 

### Mielenz, R.C. and. King, M.E.: "Identification of Clay Minerals by Staining Tests," Am. Soc. for Testing Matedals Prec. (1951) Vol 51, 1213-1233.

3. Weaver, C.E.: "The Clay Petrology of Sediments," Clays and Clay Minerals (1957), Vol. 6, 154-187.



### HESI3032134. Perry, E. and Hower, John: "Burial Diagenesis

in Gulf Coast Sediments; Clays and Clay Minerals (1970)Vol 18, 165-177. 5. Routson, R.C.; Kittrick, J.A.; and Hope,E.H.: "Interlayer Hydration and the Broadening of the 10A X-ray Peak in Illite;’ Soil Science (1972)Vol 113, No. 3, 167-174.

6. Aylmore, L.A.G. and Quirk, J.E: "Adsorption of Water and Electrolyte Solutions by Kaolin Clay Systems;’ Soil Science (1966), Vol 102, No. 5,339-345.

7. Hewett, C.H.: "Analytical Technique for Recognizing Water-Sensitive Reservoir Rocks," J. Pet. Tech. (Aug. 1963), 813-818.
8. Thomas, R.D. and Ward, D.C.: "Effect of Overburden Pressure and Water Saturation on Gas Permeability of Tight Sandstone Cores," ]. Pet. Tech. (Feb. 1972), 120-124. 9. Handy, R.L.; Demirel, T.; Ruenkrairergsa, T.; and Olson, T.: "Adsorption Energies and Swelling Pressures of Montmorillonite," ERI Project 987-S (1973), Engineering Research Institute, Iowa State University, Ames, Iowa.

10. Black, H.N. and Hower, W.E: "AdvantageousUse of Potassium Chloride Water for Fracturing Water Sensitive Formations;’ API 851-39- F, presented at Wichita, Kansas, April 3, 1965.11. O’Brien, D.E. and Chencrvert, M.E.: "Stabilizing Sensitive Shales with Inhibited, Potassium-Based Drilling Fluids;’ J. Pet. Tech. (Sept. 1973) 1089-1100.

12. Scheuerman, R.E: "Drilling Process Using aShale Protecting Polymer Drilling Fluid System;’ U.S.E 3,738,437.

ReUsed 6YH



### HESI303214