## SPE 95287

Measurement of Proppant Transport of Frac Fluids Phillip C. Harris, Ronnie G. Morgan, Stanley J. Heath, Halliburton

Copyright 2005, Society of Petroleum Engineers

This paper was prepared for presentation at the 2005 SPE Annual Technical Conference and Exhibition held in Dallas, Texas, U.S.A., 9 - 12 October 2005.
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Abstract The object of hydraulic fracturing is to produce a propped fracture extending from the wellbore. Extensive time and effort are expended in measuring theological properties of crosslinked fluids (without proppant) under simulated downhole temperature and shear-history conditions. Normally, it is assumed that if a fluid meets certain minimum viscosity conditions, it will transport proppant successfully. Measurements of actual proppant transport under dynamic simulated downhole conditions have been attempted and described, but such measurements have been very cumbersome and require significant equipment and expense to execute. Such measurements are well beyond the scope of routine QA/QC analyses. A proppant viscometer recently constructed can measure fracturing fluids containing propping agents across a wide range of concentrations. The device was designed to work as a conventional Farm Model 50-type viscometer. This unique viscometer has been used to measure typical fracturing fluids containing realistic concentrations of proppants, at temperatures and times up to several hours, representative of actual fracturing treatments. The measurements show regions of elastic transport typical of viscoelastic fracturing fluids where proppant is transported efficiently, usually followed by regions of purely viscous transport where proppant slowly settles. The advantage of the new proppant viscometer is that all components of a fracturing fluid, including proppant, can be tested. Shear-history effects of proppants on frac fluids are usually unknown or ignored, but such effects were observed in this work. Breakers were usually added to the fluids, showing reasonable times when the crosslinked fluid no longer transported proppant efficiently and proppant began to settle. This paper shows how different types of fracturing fluids can support proppant based on their chemical type, i.e. metal and borate crosslinked fluids, linear gel fluids, and surfactant gel fluids. Proppant concentrations are also considered. The physical characteristics of the proppant viscometer are also addressed.

Introduction Most hydraulic-fracturing treatments use a gelled fluid to create a subterranean fracture and partially fill the fracture with propping agents. When the fracture closes and the fluid is recovered, a conductive channel into the reservoir remains. Proppant transport is a function of (1) wellbore and fracture geometry; (2) volumetric rate; (3) proppant size, concentration and specific density; and (4) cartier-fluid rheology. Instruments such as Farm Model 50 viscometers are available for measuring viscosity at high temperatures and pressures, but elasticity is much more elusive to measure. Additionally, most viscometers, such as the Model 50, are designed only to handle the "clean fluid systems," e.g. without proppant. By default, we generally assume that higher viscosities will do a better job of transporting proppant, as well as generating the desired fracture geometry. There have been several attempts1-9 to characterize transport properties of fluids using modified bench-scale viscometers or through large slot or pipeline apparatus, but those efforts are very expensive and are not performed using routine quality-assurance measures. Several rheological properties directly impact a frac fluid’s performance: (1) apparent viscosity, (2) yield stress, (3) dynamic viscosity, (4) rheomalaxis (irreversible thixotropy), (5) viscoelasticity (for example G’, G"), and (6) the related issue of turbulent-drag reduction. In laboratory research, sample volume is often very limited, thus necessitating rheological testing and evaluation of small quantities. Also, most bench-top rheometers use batch mode, that is, smallsamples are placed in a testing chamber as opposed to flowthrough testing, as is the case for pipe viscometers. This presents the challenge of simultaneously: 1. Imparting viscometric shear history that simulates the wellbore travel path. 2. Not exceeding the proper mechanical energy input; the bench-top batch process should impart about the same amount of integrated work as the wellbore path. 3. Maintaining satisfactory thermal balance, e.g. beingsure not to create localized "hot spots" in the benchtop process because of its batch mode of operation.

In the case of most polymer-based fracturing fluids, the capability to transport proppant is directly related to their "rheological equations of state (RES)." Extent of crosslinking, breaking, shear history, and volume-average shear rate are



## HESI3003942 SPE 95287

major factors affecting a fluid’s RgS.10-11As an illustration, Table 1 is a summary showing how fracture height and width affect volume-average shear rates for a Newtonian fluid. Where viscous drag dominates, as in the classical case of a two-winged vertical fracture with parallel-plate geometry, the challenge in proppant transport is to ensure that vertical settling time is much greater than horizontal travel time. Sufficient vertical settling time allows the particle to reach a maximum horizontal distance, thus avoiding a duning effect. Table 2 is a simple illustration of the ratio of horizontal velocity to vertical settling velocity of 20/40 sand being carried by a 500 cp Newtonian fluid. Table 2 illustrates the sensitivity of proppant transport to fracture geometry. The shaded areas were selected as examples in which the horizontal transport time was at least 50 times greater than the vertical settling times. In the case of crosslinked gels, the elastic forces are designed to dominate, preventing any substantial viscous settling during the fracturing and placement of proppant. Morris12 presents the case that a minimum value of G’ (oscillatory elastic modulus) of 10 to 12 Pa’s is sufficient for most 20/40 frac sands. The complex viscoelastic nature of crosslink fracturing fluids presents a dilemma for the fracturing rheologist. Conventional rheometers are designed for measuring viscoelastic properties through well-controlled oscillatory deformations that are small, non-destructive, and within the linear elastic range. However, the actual fracturing process involves large amounts of shear strain of multiple orders of magnitude, well beyond the linear elastic range. As the breaker reaction begins to dominate, the transport mechanism shifts from elastic to viscous, leading to settling caused by the low viscosity of the broken fluid system. The Fann Model 50 viscometer was designed for characterizing fracturing gels under simulated downhole temperature-time conditions. However, the Model 50 and most other bench-top viscometers/rheometers are not adequately equipped to handle proppant-laden fluids. In the case of concentric cylinders, the centrifugal forces tend to stxatify the particles, thus resulting in nonrelevant data. In cone-plate and plate-plate viscometers, the small gaps necessary to provide torque sensitivities result in "particle jamming." Additionally, the large density differences between most proppants and conventional fracturing fluids result in settling during testing, thus producing unreliable results. Many researchers have modeled and/or measured the effects of fluid rheology and particle size, shape, and density on suspension at_tributes in either single-particle systems or at dilute concentrations, in which particle-to-particle interactions are neglected. Others have attempted to include the impact of particle-to-particle collisions.13-15 Morgan et al.16 presented a bench-top device and model for predicting the apparent viscosity of proppant-laden fluids for Newtonian and Power-law fluids with a wide range of particle sizes and concentrations. Their work was based on a viscometer uniquely designed to keep highly concentrateddense particles suspended in fluids while measuring "volumeaveraged shear stresses and shear rates." The work was limited to atmospheric temperature and pressure and did not include crosslinked gels. Table 3 summarizes the experimental limits of the work. The impact of particle concentration followed Huggins theory, that is, that apparent viscosity of the bulk slurry was a function of particle concentration, as shown in Fig. 1. The proppant viscometer described here measures in the highly concentrated range with 7.5 power, according to Fig. 1. We have designed and tested an apparatus capable of routine measurement of gelled fracturing fluids containing wide range of proppant particles under downhole temperatures, ranging from linear to fully crosslinked, to broken gels. By measuring various types of fracturing fluids, it is possible to classify the transport properties of each fluid type. By adding breaker chemicals to fluid, it is possible to determine the length of time a fluid maintains its transport capability, or whether the proppant will settle quickly.

Experimental Base gel fluid was mixed in a blender with polymer, buffers, surfactant, and clay control in tap water. A 500-mL sample of base gel fluid and 725 g of 20/40 mesh proppant (145 g/100 mL) were stirred at moderately high speed with an overhead stirrer. Reactive additives, i.e., crosslinker and breaker, were added while stirring. The slurry was quickly transferred to the cup and placed on the proppant viscometer. The transferring operation required about 1 minute. The cup was rotated at 25 RPM, with an estimated volume-average shear rate of 6 sec-1. Torque was monitored while the sample was heated at 5°F/min. Volume-average viscosity (VAV) and temperature data were plotted vs. time.

Description of Proppant Viscometer The proppant viscometer17 is based on a Fann Model 50-type viscometer with modified bob and cup. The proppant viscometer has an inner sensing surface composed of flags, in place of the concentric cylinder design of the Model 50 viscometer (see Fig. 2). To aid mixing within the cup, protrusions were welded to the inner walls of the cup. Proper clearances were provided between the flags and the wall extensions to help prevent proppant from sticking between the surfaces. As the flags on the moving cup sweep by the static flags on the central sensing shaft, a cyclic torque is measured. The oscillating force contains both viscous and elastic components. The proppant viscometer has complicated geometric surfaces, making calculation of shear rate difficult. However, laboratory personnel approximated volume-average shear rate by studying known fluids. The resistance to movement of a slurry increases as proppant concentration increases. Placement of the mixing and sensing surfaces toward the bottom of the cup allows greater sensitivity to concentrating of proppant as it settles. An increase in torque indicates that proppant is settling.

Theory Viscometry studies by Steffe and Morganis-2° were used todevelop the following equations for estimating volumeaverage shear rates, shear stresses, and viscosities for the device described in Fig. 2.



## vol = kl (RPM) ................................... (1)

HESI300395SPE 95287 3



### fro1 = k2 (Torque) ............................... (2)

where: 7~o1is the volume-average shear rate within the novel

viscometer;’ ~o1is the volume-average shear stress; and ~-~o1 is the volume-average viscosity (VAV) within the modified
Model 50 viscometer. The value of k1 is unique to the geometry of the device and slightly related to the sample volume, while the value of k2 is unique to the torquemeasuring device. Newtonian viscosity standards and Powerlaw fluids were used to quantify the values of kl and k2 for the fracturing fluid/proppant systems used in this study.

Proppant Viscometer Response for Linear Gel Fluids The volume-average viscosity (VAV) is a product of fluid viscosity, particle concentration and cup RPM. When the sandconcentration was held constant at 12 lb/gal and noncrosslinked polymer concentration varied, two separate effects were observed in the curves, as shown in Fig. 3a. The most noticeable effect is that the slope of the curve decreased as polymer concentration increased. Once the elastic transport forces no longer dominate, the particles begin to settle at a rate dependent upon their size, density, concentration, and the viscosity of the fluid medium. The slope of the VAV vs. time curves are defined as rate of viscous settling (RVS) values, which are plotted in Fig. 3b. Proppant settled very rapidly for the 40-1b/Mgal base-gel fluid at 75°F and 6 see-l; whereas settling may not have been complete in the 100-1b/Mgal fluid until about 4 hours. The slope of these lines is useful to describe purely viscous settling behavior in more complex fluid systems, such as those with crosslinker and breakers. The second effect is that higher polymer concentrations have a higher torque at zero time, where all the proppant is evenly distributed throughout the fluid. This zero-time intercept value is a function of base-gel viscosity and particleconcentration. Surfactant gel fluids behaved similarly to noncrosslinked polymer fluids. Micelles and vesicles that comprise surfactant gels are analogous to polymer gels of high molecular weight, whose viscous behavior depends solely on hydrodynamic volume interference and limited entanglement, rather than upon crosslinking.

Proppant Viscometer Response for Crosslinked Gels Crosslinked gels respond very differently from linear-base gels. Their lower RVS slope indicates that even low polymer concentrations of crosslinked fluid may transport better than high polymer concentrations of noncrosslinked fluids. This fact indicates a fundamental difference between the fluids. Noncrosslinked fluids support particles on the basis of viscous forces; whereas crosslinked fluids are tied together in a network structure. The network provides elasticity to the fluid

structure. The initial decline in the proppant viscometer response for crosslinked slurry (lowest curve of Fig. 4) is caused by temperature thinning of the supporting fluid. Once temperature is reached (upper curve), the VAV maintains a stable reading, decreasing only slightly as the breaker works to reduce the polymer network. This stable, low-VAV response is the "elastic transport region," where virtually perfect proppant transport occurs. Eventually, the breaker acts to sever sufficient network connections and allows particles to fall, resulting in the "onset of sand settling." Settling usually begins at a low rate, which may increase as the breaker continues to decrease the degree of networking in the polymer fluid. This response is the "viscous settling region," where settling approximates that of a non-crosslinked polymer solution. The slope in this region may be compared to RVS slopes of Fig. 3 as an indicator of the viscous state of the fluid. Another curve may be superimposed on the VAV curve of Fig. 4. The dashed line (middle curve) represents a typical Fann Model 50 viscometer response of the same sample without sand. This curve shows a decline in viscosity because of the effects of chemically breaking the polymer. By itself, this curve shows no indication of whether the fluid willtransport sand. By coupling the Model 50 curve with the sandtransport curve, it is possible to correlate viscosity with the time the onset of sand settling occurs. Fluids may then be compared to determine the minimum viscosity at which they will give proppant transport. However, both fluids must have similar shear histories during the crosslinking reaction for this procedure to be valid. A clear plastic cup was constructed for the proppant viscometer to allow visualization of proppant settlement to coincide with torque measurements. The clear cup reinforced the VAV measurements to give greater confidence in the technique. Fig. 5 shows a low-temperature, metal-crosslinked fluid with an enzyme breaker. Photographs of the clear cup containing the slurry are superimposed on the plot of VAV at corresponding times. The arrows point to the top of the proppant bed. As the proppant settled from breaker activity over time, the VAV value increased, thus validating similar measurements at higher pressure and temperature in the stainless steel cup. Fig. 6a shows a concentration series of low-polymer metal- crosslinked fluids containing oxidizer breaker at 250°F. The initial low-viscosity region parallel to the time axis is the elastic transport region, where virtually no settling occurs. Proppant is supported by a network structure having crosslink bonds between polymer strands. As the viscometer cup rotates at 25 RPM, the network stretches for about 1A sec and relaxes for 1A sec alternately, producing torque oscillations. For the metal-crosslinked elastic fluid, the oscillations have small amplitude. Breaker actively reduces the network structure within the elastic region until proppant is no longer supported perfectly and the onset of sand settling is reached. Following that point, we encounter viscous settling, where the increasing slope indicates that proppant concentration is increasing at the bottom of the cup. The slopes of the VAV vs. time curves in Fig. 6a were computed and are plotted in Fig. 6b to illustrate the sensitivity of this novel proppant viscometer to characterize both the elastic proppant transport regime and also the rate at which proppant settles during breaking. For the viscous settling region, the amplitude of the torque oscillations is greater and increases as proppant settles out. Oxidizer



## HESI3003964 SPE 95287

breaker was a practical addition to these tests, because without breaker, the onset of sand settling would be much longer. The capability of the metal-crosslinked fluid to transport proppant elastically (judged by constant VAV value) was not improved by higher polymer concentration up to the onset of sand settling. The higher polymer concentration did increase the time to arrive at the onset of sand settling. Undoubtedly the fluids with higher polymer concentration had more molecular interaction or entanglement, and longer time was required for the breaker to reduce those network interactions to the point of releasing sand for settlement. Fig. 7a shows the effect of breaker concentration on a metal-crosslinked fluid at 250°F. With no oxidizing breaker present, the fluid continues to support proppant elastically for an extended period. When breaker is added, transport capability is relatively sensitive to breaker concentration, indicating that accuracy of metering the breaker is important to good proppant placement. Once again, the RVS were computed and are shown in Fig. 7b. Note the sensitivity of the proppant viscometer to detect changes in dynamic settling of the proppant. Another breaking mechanism for metal-crosslinked fluids is acid hydrolysis. Fig. 8 shows a fluid that can be crosslinked from pH 5 to 10. The fluid can be readily stabilized at neutral and alkaline pH values, but acid hydrolysis will eventually break down the polymer network. The fluid character changes from elastic to viscous transport, allowing proppant to settle.The appearance of proppant transport plots for boratecrosslinked fluids differed significantly from plots for metalcrosslinked fluids (Fig. 9). Short-term oscillations for these fluids at 100°F were more intense than for metal-crosslinked fluids, indicating greater elasticity. The intensity of the oscillations makes the curves more difficult to interpret. Approximate VAV values for proppant transport (22,500 cP) and proppant settling (37,500 cP) are indicated by dashed lines. Below the lower line, proppant is transported elastically. Above the upper line, proppant is being deposited. Between the two lines, proppant settles in a viscous mode. Very low polymer concentrations, i.e. 15 lb/Mgal, showed elastic transport for a very short period of time, then the proppant settled very quickly. At 20 lb/Mgal, the fluid maintained elastic transport for about 2 hours before rapid settling occurred. The 25-1b/Mgal fluid without breaker transported proppant for almost 3 hours before a rapid increase could be detected; the transition from elastic to viscous transport is not very obvious.

Discussion Data for fracturing fluids in the proppant viscometer illustrate three major fluid classes having differences in capability to transport proppant. The first class of fluids does not have a network structure and does not transport proppant perfectly. These fluids include Newtonian fluids (oil and water), and non-Newtonian, non-crosslinked polymer fluids, oil gels, and surfactant gels. This first class transports by viscosity alone and settling occurs during transport, depending upon flow rate and viscosity. It may be possible to transport proppant efficiently with combined rate and viscosity if the settling time is not too long, but such a combination would likely result in very high pumping pressures. A second class of fluids is the metal-crosslinked group. These fluids exhibit viscoelasticity. When polymer concentration and crosslink density are high enough, proppant is transported perfectly, without settling, usually at a low pumping pressure. Once the perfect transport threshold is achieved, adding more polymer or crosslinker to increase viscosity does not improve transport, but may increase pumping pressure. Some breaker mechanism is required to initiate disruption of the network structure and allow settling to begin. A third class of fluids is the borate-crosslinked group. Borate fluids have a transient network structure. The state of the crosslink network is dependent upon shear rate as well as fluid composition. When borate fluids are static long enough to become relaxed, settling of proppant may occur in the viscous settling mode. However, when some small shear rate is imposed on the fluid, elasticity increases and the fluid acts to transport perfectly. Some minimum degree of shear must be maintained on borate fluids to maintain the elastic network condition. Foamed fluids were also measured on the proppant viscometer. Foams made with noncrosslinked polymers exhibited viscous settling, but at a slower rate than the neat liquid phase alone. The retarded settling of 70% quality foams indicates the presence of some fluid structure, although not necessarily the same as a crosslinked polymer network. It may be that the retardation is an indication of a yield point in the foam. One would expect that crosslinked foams would transport at least as well as the external liquid-phase gel. The proppant viscometer shows that borate-crosslinked and metal-crosslinked fluids are very different in structure and in capability to transport proppant. It also indicates that measurements of viscosity, such as in a couette viscometer, do not forecast the capability of a fluid to transport proppant. We found that low-polymer metal crosslinked fluids can transport proppant perfectly for long periods of time, even though their couette viscosity readings are not very high. On the other hand, low-polymer borate fluids produce very impressivecouette viscosity values, often 10 times as high as the metalcrosslinked fluids, but their proppant transport may not be as good.

Conclusions A modified Farm Model 50-type viscometer has produced measurements indicating the capability of a fracturing fluid to transport proppants. The proppant viscometer can further distinguish between fluid types having either viscous or elastic components. Proppant is included as a component of the fluid, so chemical effects from the presence of proppant material can be observed. Three main classes of fracturing fluids were described according to transport capability:

 ̄ Purely viscous fluids. These fluids include Newtonian fluids (oil and water), non-Newtonian non-crosslinked polymer fluids, oil gels, and surfactant gels. This class transports by viscosity alone and settling occurs during transport according to flow rate and viscosity. In these cases, it isimportant to ensure that the ratio of the fracture

## HESI300397SPE 95287 5

transport velocity is much greater than the verticalsettling velocity.Metal-crosslinked viscoelastic fluids. Metalcrosslinked fluids have a permanent network structure. When polymer concentration and crosslink density are high enough, proppant is transported efficiently, without settling,Borate-crosslinked viscoelastic fluids. Boratecrosslinked fluids have a transient network structure. The state of the crosslink network is dependent upon shear rate as well as fluid composition. Some minimum degree of shear must be maintained on borate fluids to maintain the elastic network condition.

Acknowledgements The authors would like to acknowledge the support of management of Halliburton for the opportunity to present this work. Special thanks are also due to Harold Walters, Billy Slabaugh, Johnny JohnsolL and David Bamck for their contributions to constructing the apparatus and implementing the experimental work.

References 1. Biot, M.A. and Medlin, W.L.: "Theory of Sand Transport in Thin Fluids," paper SPE 14468 presented at the 1985 SPE Annual Technical Conference and Exhibition, Las Vegas, NV, 22-26 September. 2. Prud’homme, R.K.: "Rheology of Fracturing Fluid Slurries: Topical Report," Report No. NTIS PB94- 159183, January 1992, Gas Research Institute. 3. Fan, Y. and Holditch, S.A.: "Testing Crosslinked Fluids on the Farm 50 Viscometer Using The Volumetric Average Shear Rate," paper SPE 26895 presented at the 1993 SPE Eastern Regional Meeting, Pittsburgh, PA, 2-4 November. 4. Penny, G.S., Conway, M.W., and Schraufnagel, R.A.: "The Evaluation of Proppant Transport and Cleanup of Foamed Fluids Used in Hydraulic Fracturing of Shallow, Water-Sensitive Reservoirs," paper SPE 26923 presented at the 1993 SPE Eastern Regional Meeting, Pittsburgh, PA, 2-4 November. 5. De Kruij£ A., Davies, D.R., and Fokker, P.A.: "Novel Rheological Equipment for the Characterization of Hydraulic Fracturing Fluids," paper SPE 27398 presented at the 1994 SPE Formation Damage Control International Symposium, Lafayette, LA, 9-10 February. 6. God, N., Willingham, J.D., Shah, S.N., and Lord, D.L.: "A Comparative Study of Borate-Crosslinked Gel Rheology Using Laboratory and Field Scale Fracturing Simulations," paper SPE 38618 presented at the 1997 SPE Annual Technical Conference and Exhibition, San Antonio, TX, 5-8 October. 7. Thesing, A.: "New Device for Rheology Measurements of Proppant-Laden Fluids with the Farm 50 Viscometer," paper SPE 58759 presented at the 2000 SPE International Symposium on Formation Damage Control, Lafayette, LA, 23-24 February. 8. Tremblay, B., De Rocco, M., Ridley, R.K., Scott, K., Singh, S., Browne, D., Lukos, B., and O’Neil, B.: "A Device and Method of Determining the Rheological Quality of Gelled Fracturing Fluids," paper CIM 2000-58 presented at the 2000 Annual CIM Petroleum Society Technical Meeting, Calgary, Canada, 4-8 June. 9. Asadi, M., Conway, M.W., and Barree, R.D.: "Zero Shear Viscosity Determination of Fracturing Fluids: An Essential Parameter In Proppant Transport Characterizations," paper SPE 73755 presented at the 2002 International Symposium and Exhibition on Formation Damage Control, Lafayette, LA, 20-21 February. 10. Harris, P.C. and Walters, H.G.: "Real-Time Control of Low-Polymer Fracturing Fluids," paper SPE 63238 presented at the 2000 SPE Annual Technical Conference and Exhibition, Dallas, TX, 1-4 October. 11. Walters, H.G., Morgan, R.G., and Harris, P.C.: "Kinetic Rheology of Hydraulic Fracturing Fluids," paper SPE 71660 presented at the 2001 SPE Annual Technical Conference and Exhibition, New Orleans, LA, 30 September-3 October. 12. Morris, J.F.: Personal communication, City College of New York (2004). 13. Morris, J.F. and Brady, J.F.: "Pressure-driven Flow of a Suspension: Buoyancy Effects," Int. J. Multiphase Flow, Vol 24: 105-130, 1998. 14. Asmolov, E.S.: "The Inertial Life on a Spherical Particle in a Plane Poiseuille Flow at Large Channel Reynolds Number,"J. Fluid Mechanics, Vol 381: 63- 87, 1999. 15. Cherukat, P. McLaughlin, J.B. and Dandy, D.S.: "A Computational Study of the Inertial Lift On a Sphere in a Linear Shear Flow Field," Int. J. Mulltiphase Flow,Vol. 25: 15-33, 1999. 16. Morgan, R.G., Lord, D., Kannan, R. and Srinivasa,A.R.: "Rheology of Highly Concentrated ParticleLiquid Systems," presented at the 74th Annual Meeting-Society of Rheology, Minneapolis, MN 13- 17 October, 2002. 17. Walters, et.al.: "Testing Device and Method for Viscosified Fluid Containing Particulate Material," U.S. Patent 6,782,735, Aug 31, 2004. 18. Steffe, J.F. and Ford, E.W.: "Rheological Techniques to Evaluate the Shelf-Stability of Starch-Thickened, Strained Apricots," J. Texture Studies. 16:179-192. (1985). 19. Steffe, J.F., Castell-Perez, E.M. and Zabik, M.E.: "Rapid Testing Method for Characterizing the Rheological Behavior of Gelatinizing Corn Starch Slurries," Cereal Chemistry 66:65-68. (1989). 20. Stef£ J.F.: Rheological Methods’ in Food Process Engineering, Freeman Press, 2807 Still Valley Dr., East Lansing, MI. ISBN 0-9632036-0-6, (1992).



## HESI3003986 SPE 95287

Table lmExample Effects of Fracture Geometry on Vol.-Avg. Shear Rate Wf, in. hf=10 20ft 30ft 40ft 50ft 60ft

ft 0.1 4,436 0.2 1,109 0.3 493 0.4 277 0.5 177 0.6 123 0.8 69 1.0 44 Assumptions: 2,218 1,479 1,109 887 444

555 370 277 222 111 246 164 123 99 49 139 92 69 55 28 89 59 44 35 18 62 41 31 25 12 35 23 17 14 7 22 15 11 9 4

Wellbore flow rate = 35 bbl/min Average leakoff rate = 50% hf = average vertical height of fracture, wf = average width of fracture, in.

0.1 230 0.2 115 0.3 77 0.4 58 0.5 46 Assumptions: Table 2mRatio of Horizontal to Ve~ical Velocity in Fracture Wf, in. hf=10 20 ~ 30 ~ 50 ~

115 77 46 58 38 23 38 26 15 29 19 12 23 15 9

Wellbore flow rate = 35 bbl/min Average leakoff rate = 50% Particle size, microns = 500 (20/40 sand) Newtonian viscosity, cP = 500

Table 3~Range of Conditions for Computing Viscosity of Fracturing SlurriesTM Particle size 250 to 1,020 microns Particle density 1.13 to 3.6 gm/cc Sphericity 0.7 to 0.95 Power-law consistency 950 to 17,000 mPacoefficients secn Shear thinning index 0.2 to 1.0 Volume fractions of particles 0.0 to 0.55



## HESI300399SPE 95287 7

1.00E+06

1,00E+05

1.00E+04

1.00E+03

1.00E÷02

1.00E+01

1.00E+00
0.01 Dilute Range

Single Particle VAV = f(C~) Random Bump,ins and Colliding - VAV = f(C~)

: :

Constant siidin~touching /crowding VAV : f(C’ ~) ;

; :

: ; ;
:
:

0.1 

### Particle Concentration, v/v

Fig. 1--Effect of particle concentration on fluid viscosity.

Fig. 2--Diagram of proppant viscometer.17



## HESI3004008 SPE 95287

40,000

o 0 O~ 30,000

20,000

10,000 40 lb/Mgal 1 O0 Ib/Mgal

0



### Time, min

Fig. 3a--Proppant settling in noncrosslinked base-gel fluids.

6,000

5,000

4,000

3,000

2,000



### 1,ooo

20 40 60 80 100 

### Polymer Concentration, Ib/Mgal

Fig. 3b--Rate of viscous settling slopes computed from Fig. 3a. 120



## HESI300401SPE 95287 9

50,000

40,000

30,000



# ~ " 20,000

10,000

o 0:00 Temperature

Model 50 Viscous ’~ ~Viscosity ~effling Region

400 cP Ref Viscosity ~-" ~-~ ~ ~ ___

Elastic Sand Transport X~.~ of Sand Settling Sand Transport

1:00 2:00 3:00 4::00 Test time, hr

Fig. 4--Response of a viscoelastic crosslinked slurry with breaker. 250

30,000

20,000

35

Fig. 5--Transport visualization with metal crosslink fluid with enzyme breaker.



## HESI30040210 SPE 95287

40,000 300

30,000

20,000

10,000 Temperature

25 Ib/Mgal 30 Ib/Mgal

Viscous Settling

of Sand Settling

50 100 150 200



### Time, min

Fig. 6a--Effect of polymer concentration in metal-crosslinked fluid. 250

20O

5O

0 25o

800

~ 600

~ 500

~ 400

oO 300

1oo



### Polymer Concentration of Metal Crosslink Fluid, Ib/Mgal

Fig. 6b--Rate of viscous settling as affected by gel loading.



## HESI300403SPE 95287 11

50,000, 300

40,000,

30,000.

20,000.

10,000. 5gaVMgal

Breaker Temperature



# .... ......

o o 

## o 1~o Time, min

Fig. 7a--Effect of breaker concentration on metal-crosslinked fluid. 250

200

150

10o

5o

15,000

5,000 :::::::::::::::::::::::::::::

:::::::::::::::::::::::::::::

:::::::::::::::::::::::::::::

0 1 2 3 4 5



### Breaker Concentration, Cb (gal/Mgal)

Fig. 7b--Rate of viscous settling as affected by breaker content.



## HESI30040412 SPE 95287

50,000 3O0

40,000



### ~ 3o,ooo

>~," 20,000

10,000

pH 7

0



## ~o ~o ~o ~o ~.~o 3oo

Time, min

Fig. 8--Effect of acid hydrolysis on crosslinked polymer. 250



### 200 ou-

 ̄ ~5o ~ 

## 8. E

100

5O

60,000

50,000

40,000

30,000

20,000

10,000 25 Ib/Mgal

..... p.r£ppa£t .... Deposited

Proppant Transported

Time, min 3OO

Fig. 9--Transport with borate crossliked fluids at 100°F.



## HESI300405