bluuebunny/crossref_metadata_2025 huggingface dataset:
Wellsite Diagnosis of Pumping Problems Using Minicomputers
Authors: Gibbs S.G. , Nolen K.B.
Published: December 2007

The truck-mounted computer system described here greatly enhances the efficiency of the sucker rod diagnosis technique. Using an example well, the paper shows how the method and the equipment can be used to increase production and decrease lifting costs. With this system, more definitive production and decrease lifting costs. With this system, more definitive and timely results can be obtained more efficiently, thus lowering the cost of applying the technique.

Introduction

The Sucker Rod Diagnostic Technique was perfected by Shell during the 1960's. Its concept was suggested by the work of British physicians who wanted to analyze human electrocardiograms more accurately and definitively. To do this, they subjected cardiograms to Fourier analysis, hoping to reveal subtle indications of heart disease that might be overlooked if only visual interpretations were made. Similarly the sucker rod method was designed to derive the maximum amount of information from a pumping-well dynamometer card and to make the analysis of the card a science rather than an art. This paper describes a portable computer system for implementing the sucker rod method.

Brief Theoretical Review

The basis for the diagnostic technique is a stress wave propagation problem based on the one-dimensional propagation problem based on the one-dimensional wave equation

(1)

The wave equation models the rod string and permits the use of surface data to deduce down-hole conditions in pumping wells. This is directly analogous to the human cardiogram where easy-to-measure surface data are used to infer conditions within the body. The boundary conditions measured at the surface are time histories of the load and position of the polished rod. These are expressed as truncated polished rod. These are expressed as truncated Fourier series of the following type:

(2)

(3)

Solutions to the wave equation that satisfy the measured boundary conditions give operating conditions in a given well at a particular time in its producing life. The basic diagnostic solutions give producing life. The basic diagnostic solutions give displacement and load at arbitrary depths in the rod string. These are

(4)

and (5)

The procedure for solving and generalizing for the case of tapered strings is detailed in Refs. 1 and 2. By cross-plotting the solution for displacement (Eq. 4) vs load (Eq. 5) at a given depth, a dynamometer card at that depth is obtained, This is equivalent to the card that would be measured with a dynamometer instrument placed at that depth.

JPT

P. 1319
A Hydrothermal Setting Cement for Cementing Ultradeep, Hot Wells
Authors: Maravilla S.
Published: December 2007

Laboratory data show that a unique hydrothermal setting cement can be used as manufactured-without the addition of high-temperature field retarders-to cement oil and gas wells where the bottom-hole static temperature is in the range of 260 deg. to 320 deg. F. If necessary, the retarders and other field additives can be used to extend that range when wells must reach 18,000 to 24,000 ft.

Introduction

In 1969, oil company representatives of API Committee 10 on Standardization of Oil Well Cements expressed concern that difficulties were still being encountered in retarding marketed Class H cements for wells deeper than 14,000 ft.The Committee appointed a task group that not only confirmed the need for a new cement, but adopted, in 1972, a set of tentative specifications based on a specific marketed high-temperature cement. The cement was designated Class J.This paper describes a unique hydrothermal setting cement based on a new concept for oilwell cements, the theory for which is documented in the literature.

Chemical Composition

A natural question that immediately comes to mind is "What is hydrothermal setting cement?" Depending on the starting materials, the product may consist of any mixture of compounds - for example, port-land cement; portland cement and silica flours or silica, lime, and waters that react to form crystalline silicate hydrates under hydrothermal conditions. These reactions take place in the presence of water above 212 deg. F at pressures exceeding atmospheric pressure. pressure. The hydrothermal setting cement composition described here is composed essentially of a binder, quartz sand, and calcium hydroxide. The binder is beta dicalcium silicate (beta- 2CaOSiO.), one of the main mineral constituents of portland cement.Table 1 shows typical chemical analysis, fineness, and specific gravity of hydrothermal setting cement (henceforth referred to as HTS cement) vs Class H plus 60 percent silica flour. plus 60 percent silica flour. It appears from results of chemical analyses shown in Table 1 that the typical HTS cement discussed here is virtually the same as a typical Class H cement to which 60 percent silica flour (SiO.) has been added. However, it must be understood that the HTS cement contains different compounds. Obviously, the thermal history of the hydrothermal cement binder and the fineness of the cement are essential considerations.Data shown in Table 2 clearly show that HTS cement exhibits better thickening time and compressive strength characteristics than unretarded Class H plus 60 percent silica flour. Under ordinary temperatures HTS cement is relatively unreactive. ASTM C109 strength results show that 2-in. mortar cubes cured at 73 deg. - 3deg.F did not set in 9 days. Despite extended curing periods of 28 days and 180 days under comparable conditions, the strength of the specimens developed quite slowly; i.e., 200 psi and 1,000 psi, respectively.

JPT

P. 1087
Production of Water-Driven Reservoirs Below Their Bubblepoint
Authors: Dyes A.B.
Published: December 2007

In the operation of a water-driven reservoir, a free gas saturation can be established by maintaining production rates fast enough to cause the reservoir pressure to decline below the bubble point. The benefit of such a procedure on the displacement efficiency of the oil by water is illustrated for two types of sandstone samples from one reservoir. Those rock samples showing the poorest recovery to water drive in the absence of a free gas saturation give the most improvement in the presence of a free gas saturation. Employing one type of reservoir fluid (low shrinkage) the benefit of evolved gas on oil displacement is calculated at several reservoir pressures below the bubble point. This demonstrates the presence of an optimum pressure for water displacement which is several hundred pounds per square inch below the bubble point. Displacement of oil at the optimum pressures results in the removal of 7 to 12 per cent more oil than would be obtained by displacement at the bubble point pressure. In some instances this magnitude of increase may be worthy of consideration in establishing the maximum efficient rate of production from many water-driven fields.

Introduction

For many years the belief that the use of gas could be combined with that of water to result in a better recovery operation than the use of either of these phases alone has been prevalent in the oil industry. This is evidenced by the several field trials which have employed the injection of gas and water in combination. In most cases the small amount of any additional recovery, in combination with the limited knowledge available on the older reservoirs, has left uncertain the influence of gas on recovery in these earlier attempts to combine the use of gas with water.

Research studies in recent years have demonstrated through laboratory floods the magnitude of the benefit of the presence of gas on the displacement of oil from sandstones by water. In addition, studies of the distributions of the phases which are present during the displacement process have developed concepts concerning the mechanism by which this benefit is obtained. It now remains for the engineer to incorporate these findings into the general technology of reservoir operations.
Secondary Recovery Operations in the Tijerina No. 3 Unit Reservoir
Authors: Olansen N.A.
Published: December 2007

Introduction

The purpose of this paper is to present the production history of the Tijerina No. 3 Reservoir from its initial development in April, 1945, through April. 1954, including primary development, unitization, and secondary recovery by high pressure gas injection. Particular attention is given reservoir performance as influenced by the migration of fluids in a continuous but erratic sand of low permeability. It is interesting to note that, from material balance calculations, apparently little or no injected gas goes into solution with the remaining reservoir oil, even though reservoir pressure has been increased an average of 700 psi.

Location and Geology

The Tijerina No. 3 Reservoir is located in the southwest portion of the Tijerina-Canales-Blucher field, approximately 2 miles northeast of the town of Premont. Jim Wells County, Tex. It is the deepest member of a series of lower Oligocene (Frio) Sands productive in the field, lying at an approximate depth of 7,200 ft subsea. Structurally, the reservoir is a permeability trap lying on an erratic monocline, with an average southeast dip of 170 ft per mile. There is no faulting present to break the continuity of the sand. A structure map drawn on the top of the sand is shown in Fig. 1. The productive limits of the reservoir are defined by shale outs and dry tests except in an area to the northwest; where, due to the lack of geological control, the location of the strand line is assumed. The oil column is bounded in this area by a small gas cap, the original gas-oil contact having been established at 7,058 ft subsea by drill stem and production tests run during development. There is no evidence of a water-oil contact in the reservoir. The sand is described as being firm, fine-grained, medium to hard, with scattered shale streaks occurring near the strand line. It possesses a low and erratic permeability as substantiated by PI's which ranged from 0.020 to 0.114 in five wells when measured in April, 1948. A typical electric log is shown in Fig. 2.
Correlation of Steam Stimulation Performance
Authors: Boberg T.C. , West R.C.
Published: December 2007

An approximate correlation has been observed of steam stimulation field results with the product of oil transmissibility and static pressure. This correlation may have application as a rough screening tool for identifying potential candidates for steam stimulation. Theoretical support for this correlation is obtained by observing that the incremental oil-steam ratio (OSR) may be expressed as

........................................(1)

where theta is the time at the end of the injection-soak period, and theta is the time at the end of the production period, and theta is the time at the end of the production phase when the stimulation effect is essentially nil. It phase when the stimulation effect is essentially nil. It constant average values for Jc and Delta p can be assumed,

........................................(2)

Note that for theta greater than, greater than that and J greater than, greater than 1, this simplifies to the approximate equation,

......................(3)

From an earlier paper it follows for the case of steady-state flow that

and

Eq. 3 becomes

The OSR will be a strong function of, where Delta P is the average pressure drawdown over the producing cycle. For pe greater than, greater than pw, producing cycle. For pe greater than, greater than pw, then Delta p can be approximated with pe, and it can be seen that the incremental OSR will be a strong function of the product (koh/mu o) pe. This would suggest a correlation product (koh/mu o) pe. This would suggest a correlation between the incremental OSR and the product of transmissibility and static pressure. The relationship would not be linear, however. As (koh/mu o) pe increases, the prestimulation rate would be expected to increase. prestimulation rate would be expected to increase. For a given treatment size, the stimulated rate would likewise increase, and consequently, the energy withdrawal rate from the formation would increase. Thus, theta p, the stimulation producing time, will be inversely affected by an increased (koh/mu o) pe. The effect will become more pronounced for highly productive wells.

P. 1367
A Graph for Determining Reserves and Spacing
Authors: Sloan R.L.
Published: December 2007

The graph (Fig. 1) accompanying this article presents a quick method to determine reserves under presents a quick method to determine reserves under varying conditions. It can also be used to estimate minimum spacing for an economic recovery.

Example 1 - Recoverable Reserves Reservoir Data Porosity, percent 20 Water saturation (Sw), percent 40 Formation volume factor (FVF) 1.2 Recovery factor, percent 20 Spacing, acres 20 Net pay, ft 50 The solution route is shown on Fig. 1.

Solution Oil originally in place, STB/acre-ft 776 Recovery, STB/acre-ft 155 Recovery, bbl 155,000

Example 2 - Spacing

Assumptions

A recovery of 400,000 bbl is required for an economic return on your investment. Net pay is 100 ft. 3. Recovery is 270 bbl/acre-ft.

Solution

Draw line from 270 BPAF recovery through all spacing curves. Start at 400,000 bbl recovery and go up to the 100-ft net pay line. Go left until you intersect the 270 BPAF recovery line.

This intersection is the spacing required (15 acres). The chart is a simple solution and it will permit on-site analysis. Additional charts can be developed for gas reserve determinations.

P. 1470
Drag Reduction Does Not Always Increase with Increased Flow Velocity
Authors: Sarem A.M.
Published: December 2007

In view of industry's current thinking about drag reduction, an article by Avnapov et al., "The Effect of Adding Polyisobutylene on the Capacity of Pipelines," is of considerable interest. Their Fig. Pipelines," is of considerable interest. Their Fig. 2, when replotted (see Fig. 1) reveals that drag reduction is not a continuously increasing function of the flow velocity as has been postulated by others working in this field. This was revealed by the calculation of drag reduction for 50 ppm polyisobutylene (PIB) in gas condensate based on Curves 1 and 2 of Fig. 2 of the Russian article (see Table 1). These data, plotted in Fig. 1, show that the drag reduction increases as velocity increases up to a "critical" velocity of 9.8 ft/sec. As the velocity is increased beyond 9.8 ft/sec, the drag reduction gradually decreases. To my knowledge, this has not been shown elsewhere, perhaps because no one had tested for drag reduction at perhaps because no one had tested for drag reduction at such high velocities. The Reynolds number for a 0.8-cp, 0.8-gm/cc fluid flowing at 16 ft/sec in a 6-in pipe about 700,000 which is rather high. We have obtained experimental results similar to the above in a drag reduction test in which diesel fuel and gasoline were flowed through a 6-in.-diameter conduit at 8.7 and 11.4 ft/sec, respectively.

TABLE 1 - DATA FROM AVNAPOV ET AL.*

/1 (units unknown) Velocity Drag No PIB 50 ppm PIB Reduction cm/sec ft/sec (Curve 1) (Curve 2) (percent) 200 6.55 3.5 2.5 28.5 250 8.2 6.5 4.0 38.4 300 9.8 11.1 6.0 45.9 400 13.1 19.5 11.0 43.6 500 16.4 28.5 16.5 42.1

P. 673
Sea-Floor Scour Protection for a Semisubmersible Drilling Rig on The Nova Scotian Shelf
Authors: Wilson N.D. , Abel Wesley
Published: December 2007

Suppose you had a modest little upholstery shop in Halifax. How would you feel if someone asked you to slipcover the pontoons of a semisubmersible rig? After 7,500 yards of material, your old Singer would never be the same again.

Introduction

Scour protection is often required to prevent scour from occurring around marine structures. This was the concern when it was proposed to set the semisubmersible drilling rig Sedco H on the sea floor to drill the Mobil-Tetco Thebaud P-84 well in 90 ft of water 6 miles southwest of Sable Island. Fig. 1 shows the location of the well. Normal tidal currents in the area reach a maximum of about 1.5 knots. Scour was expected since it was known that the sea floor was fine sand and that the 80-ft-diameter Sedco H pontoons would cause the current velocities around the pontoons to be accelerated considerably. However, it was impossible from existing information to predict the amount of scour that would occur or the amount of scour protection that would be required. This is mainly protection that would be required. This is mainly because the relationship of current velocity, rate of scour, scour depth, and grain-size distribution is not yet well defined. Also, the geometry, spacing, and size of the Sedco H pontoons are such that correlations from other experimental work could not be made. It was therefore decided to analyze the problem with model tests in a hydraulic tank model basin. Delft Hydraulics Laboratory of The Netherlands, who had previously performed similar scour studies, was selected for the model work. The results from the tests were used to design the scour protection and to plan a successful field installation.

The Scour Process

A sand bed exposed to ocean currents in a sea-floor environment is usually in a condition of equilibrium. In this condition the bottom material is transported but no net deposition or erosion occurs. However, when an object is placed on the sea-bed, current velocities near the object increase and this equilibrium condition is disturbed. Additional turbulence results and there is an increase in the transport capacity of the fluid near the object. The sea bed around the object starts to erode. This erosion is known as scour. The magnitude of scour depends onthe geometry of the object,the characteristics of the seabed material, andhydrodynamic conditions. Current velocity influences both the rate and depth of scour.

The influence of current velocity on the depth of scour around structural piles, bridge piers, and abutments has been studied by Delft Hydraulics Laboratory, among others. The influence of the combination of wave-induced currents and tidal current on scour around structural piles was studied by Abou-Seida and by Delft Hydraulics Laboratory. The above references indicate that scour can be predicted for simple cases such as for a predicted for simple cases such as for a small-diameter isolated circular pile. The Sedco H pontoons, however, are 80-ft in diameter. pontoons, however, are 80-ft in diameter. JPT

P. 381
Canal Field Gas Injection Project
Authors: Pings C.J. , Tempelaar-Lietz W.
Published: December 2007

For the history of the performance of the Canal field gas injection project reference is made to two publications. In the present paper a critical examination has been made of the pressure measurements and of the pressure-volume-temperature data for the reservoir fluid. Material balance calculations were employed to determine the oil in place, the size of the oil reservoir, the size of the aquifer, the amount of water inflow, and the migration of hydrocarbons within the reservoir. The effectiveness of the gas-injection program is discussed.

Introduction

The gas injection project in the Canal field, San Joaquin Valley, Calif., has now a history of 14 years. The performance was discussed in a paper presented by R. P. Mangold before the Pacific Coast District API meeting in Los Angeles, April 11, 1946. This paper was not published, but the pertinent data have been recapitulated by Muskat. In July, 1952, the Bureau of Mines published their Report of Investigations No. 4886 in which an excellent review of the history up to that time is presented, and the reader is referred to that publication. In the present paper a short resume of the history is shown in Figs. 1 through 4. In the last paragraph of the Bureau of Mines' publication reference is made to the gas injection in Well E-11. The additional information on this localized injection now available is presented in the next section. The remainder of the present paper will deal with the technical methods used in a detailed analysis of the various aspects of this project.

A Localized Injection Experiment

Wells A47-14, E-11, and E-14 are located on the southern flank of the field. In the 24 months preceding April, 1948, E-11 flowed 7,541 bbl of oil at an average rate of 12 B/D.
Report of Operations, 1945 Through 1954, Naval Petroleum Reserve No. 1, Elk Hills
Authors: Gooch F.W. , Adams R.H.
Published: December 2007

This paper presents the progress of operations within the Elk Hills field for the period 1945 to 1954. Since World War II and the subsequent shut-in of this field, many projects were initiated to determine the best method of protecting the various reservoirs. All of the Shallow Oil Zone programs were predicated around a reservoir which was in a state of pressure unbalance caused by heavy withdrawals of fluid in relatively short periods of time. The basic studies centered around: the use of gas injection, evaluation of an unrestricted water encroachment and its opposite heavy downdip withdrawals to utilize gravitational drainage, general studies of movement of reservoir fluids, and the protection of surface equipment. These programs have been changed from time to time, depending upon results obtained. Some of the results are unique. Currently the programs involve controlling encroachment through production from invaded areas and remedial measures to stop or minimize the downdip migration of oil. A primary objective of all programs is to maintain the Reserve in a state of readiness whereby it will be able to produce oil in substantial quantities whenever the strategic situation of the United States so requires.

An active drilling program has resulted in further development of the Shallow Oil Zone, the exploration and development of the Stevens Zone, and adding a new and as yet untested pool, the Carneros.

History and Stratigraphy

This paper is intended to supplement an original technical publication titled "Experimental Production Projects and Exploratory Drilling at Elk Hills" by M. C. Eastman and F. L. Ruhlman, which was presented at the Petroleum Branch, AIME, Fall Meeting of 1947. It will report the progress of operations made since January of that year.
An Evaluation of Critical Multiphase Flow Performance Through Wellhead Chokes
Authors: Ashford F.E.
Published: December 2007

_

A multiphase flow equation describing the behavior of orifice flow may be used directly to evaluate well performance as a function of choke size; upstream choke pressure; choke temperature; producing and solution GOR; gas, oil, and water gravities; and a discharge coefficient. The coefficient compensates for nonideal factors excluded in the development of the equation and relates theoretical oil production rates through chokes to field-measured rates.

Discussion

Various developments have been published 1-3 that present theory and correlations for describing simultaneous liquid and gas flow through a restrictive orifice.

The correlations of Poettmann and Beck3 were intended to aid in the prediction of gas-liquid flow through chokes. Their development followed the original presentation by Ros1 and was derived for an average orifice discharge coefficient.

Poettmann and Beck considered the polytropic expansion of the gaseous phase of the fluid expanding through the choke. The polytropic expansion theory was used successfully by Ros and is perhaps the most rigorous development in the application of orifice flow theory to oilfield conditions. Basically, the derivation of any orifice relationship is dependent on two main criteria. First, an expression must be written relating the flowing fluid specific volume and velocity to the mass flow rate. Second, an independent equation must be written incorporating the behavior of the gaseous phase of the fluid with pressure. The above stipulations are met by the following relationships.
Vertical Permeability From Limited Entry Flow Tests in Thick Formations
Authors: Raghavan R. , Clark K.K.
Published: December 2007

This paper examines the applicability of the spherical flow equations to a well producing from a limited section of a thick anisotropic formation. Though the method of analysis was suggested by Moran and Finklea several years ago, the applicability of these equations is yet to be demonstrated. Methods of determining the horizontal and vertical permeability of the formation from drawdown and buildup data are described. The effect of producing time on the determination of these parameters is discussed. Time estimates are provided parameters is discussed. Time estimates are provided to obtain the proper straight line.

Introduction

Transient pressure analysis of early time data of limited entry tests precludes the use of conventional semilog techniques. This is principally due to the nonradial flow regime developed in the vicinity of the wellbore at early times Moran and Finklea suggested that early-time pressure behavior from such tests can be adequately described by assuming the limited entry section to be a spherical source rather than a cylindrical source, as in the case of a well completely penetrating the formation of interest. More recently Culham has examined the applicability of the spherical flow equations to well tests wherein the producing interval is a small fraction of the total pay thickness. He developed guidelines for analyzing pay thickness. He developed guidelines for analyzing the pressure buildup data based on the assumption of spherical flow. Culham was principally interested in homogeneous thick formations. The primary objective of this paper, however, is to demonstrate that information may be obtained regarding reservoir heterogeneity specifically permeability anisotropy. This type of information is crucial to predict the performance of zones of interest under a variety of performance of zones of interest under a variety of conditions such as the presence of barriers, and the movement of fluid interfaces.

MATHEMATICAL MODEL

A cross-section of the idealized limited entry model is shown in Fig. 1. The following assumptions are made:The reservoir is horizontal with uniform thickness, h, porosity, phi, and infinite radial extent. It has anisotropic radial and vertical permeabilities, kr and kz, respectively. The well, which may or may not fully penetrate the formation, has an infinitely small radius, rw.A single-phase, slightly compressible liquid flows from the reservoir into the open section at a constant rate, q.The single, horizontal, open section has a radius rw, thickness hf, and is assumed to be located near the center of the producing interval. The midpoint of the open interval is located at a distance zf from the bottom of the pay. Fluid is withdrawn uniformly along the section open to flow.There is no flow across the upper and lower boundaries of the reservoir; and the pressure remains unchanged and equal to the initial pressure as radial distance approaches infinity.

One point regarding the model discussed above requires clarification.

SPEJ

P. 65
Physsicochemical Aspects of Microemulsion Flooding
Authors: Healy Robert N. , Reed Ronald L.
Published: December 2007

Whenever water, an oil, and a surfactant equilibrate at concentrations of surfactant in excess of critical micelle concentrations, one or more microemulsions form.. In view of this, all surfactant flooding processes may involve microemulsions in situ. Ternary diagrams have been constructed for three specific microemulsion systems showing The effects of salinity and cosurfactant on phase behavior, viscosity, resistivity, optical birefringence, and interfacial tension. Using these data, micellar structure maps were prepared for the single-phase region. In this connection, Winsor's concept of intermicellar equilibrium was found consistent with microemulsion systems of interest for tertiary oil recovery. Experimental techniques are described for minimizing the extent of the multiphase region and measuring the low interfacial tensions that obtain there.

Introduction

GENERAL CONSIDERATIONS

It is sometimes difficult to sort out the multiplicity of terminology concerning various kinds of micellar solutions and the structural states in which they exist. For example, Schulman introduced the term "micro emulsion." Winsor objects on the grounds that all emulsions are unstable and a microemulsion must be some kind of an emulsion. Tosch et al. use the phrase "micelle-containing solutions," whereas Shinoda and Kunieda prefer "swollen micellar solution." Nevertheless, the term microemulsion is convenient, is in common use, and it is only necessary to understand precisely what is meant by the term. In this paper a microemulsion is defined to be a stable, translucent micellar-solution of oil, water that may contain electrolytes, and one or more amphiphilic compounds (surfactants, alcohols, etc.). It should be noted that according to this definition a microemulsion is not an emulsion. A microemulsion may have distinct internal and external phases, but in many cases there is no identifiable external phase. phase. Since a microemulsion has at least three components -- oil, water, and surfactant - the compositional state of the system must be specified with at least three numbers. It is therefore convenient and instructive to employ a ternary representation as shown in Fig. 1. The simple situation will involve three pure components, and the multiphase region will be bounded by a continuous binodal curve. Everywhere above the binodal curve a single phase exists that undergoes transitions among various structural states as the compositional point moves about the diagram. These transitions may be gradual, reflecting an equilibrium in which there is significant coexistence of different micellar configurations, as proposed by Winsor. proposed by Winsor. In the multiphase region, the most simple, three-component system involves only two phases throughout; one is oil-external and the other water-external.

SPEJ

P. 491
A Material-Balance Technique for Undersaturated, Partially Water-Driven Reservoirs
Authors: Barry Richard A.
Published: December 2007

A modification of the standard material-balance equation for undersaturated reservoirs is presented. The effect of water influx is accounted for by the term, which is the ratio of the aquifer to reservoir pore volumes.For an approximately circular reservoir, values of, may be obtained quite easily by reiteration from the internal-cylinder solution of the diffusivity equation. The technique has been applied to a Colombian field, with acceptable results.

Introduction

Weak water drives that might have a negligible effect below the bubble point may exert a very appreciable influence above the bubble point. Under these conditions, use of the standard material-balance equation (as presented by Hawkins, and by Hobson and Mrosovsky) may lead to considerable error. This paper presents a modification to the standard equation; a field example indicates that the technique yields acceptable results. The method is quite straight-forward, its solution requiring only a desk calculator and a book of six-figure tables.

Derivation of the Modified Equation

Let the reservoir pore volume be Vpo. At any time t, let the effective pore volume of the aquifer that has been influenced by the pressure drop in the reservoir be Vpa.At a pressure drop p, the total pore space will be reduced to . The initial water volume of the reservoir is increased fromto . Hence,=.

Originally,

and

Hence,

Sorting into a more conventional form,

.....(1)

Evaluation of Ritchie and Sakakura have presented a solution to the diffusivity equation for a uniform system of infinite extent, bounded internally by a cylinder of radius rw. It seems likely that the majority of field engineers may be unable to obtain copies of Ref. 3. However, Mortada offers quite a thorough discussion of this solution and its modification for nonuniform aquifers.In oilfield units (and ignoring third- and higher-order terms), the solution reduces to

......................(2)

and

JPT

P. 391^
Solutions to the Diffusion Equation for a Region Bounded By a Circular Discontinuity
Authors: Larkin Bert K.
Published: December 2007

Solutions to the diffusion equation for a line source located anywhere in a region bounded by a circular discontinuity are presented. Such solutions follow automatically from the Green's function presented by Jaeger. Petroleum industry applications of this problem would include transient compressible fluid flow in porous media bounded by a discontinuity. Since several recent papers have treated the subject in less general form, it would appear that many workers in this area of the petroleum industry are not aware of Jaeger's work.

STATEMENT OF THE PROBLEM

In several treatments of the transient flow of compressible fluids in porous media it was convenient to consider a region to be bounded by a circular discontinuity. In such a region (Fig. 1), the properties in Region 1, r less than a, are constant but different from the properties in Region 2, r greater than a. Hurst, using the Laplace transform, obtained solutions for a line source located in the center of such a porous medium. The purpose of this work is to point out that a much earlier paper by Jaeger presents the solution for a line source located anywhere inside the discontinuity. The assumption is made that a line source may be used to approximate a well. In the following material it is convenient to use the terms source and well as being equivalent; however, the reader should remember the distinction in applications.

SOLUTIONS

Jaeger presented the Green's function for a line source, or well, in the composite region shown in Fig. 1. In the most general form, the solution for a system of j wells in Region 1, each producing at a time varying rate, qi(t), is

..................(1)

The Green's function vi corresponds to the solution for an instantaneous line source at position ri, 0i (Fig. 1). Integration in time, previously shown, gives the contribution from a single well, and summing over all j wells in the reservoir gives the total solution. Equations defining v are presented by Jaeger as well as an outline of the method of solution.From Jaeger's work it can be shown that

....(2)

for r less than a, ri less than a

(3)

SPEJ

P. 113^
An Approximate Infinite Conductivity Solution for a Partially Penetrating Line-Source Well
Authors: Gringarten Alain C. , Ramey Henry J.
Published: December 2007

A review of previous studies of transient flow to partially penetrating wells was made. All analytical studies involved the assumption of a constant flux along the open interval. This analytical study is a new solution that closely approximates an infinite-conductivity line source (constant pressure along the producing interval).

Introduction

The problem of fluid flow to wells with partial penetration or restricted entry has received much penetration or restricted entry has received much attention in the last 15 years, both in ground-water hydrologyl and in petroleum engineering. A number of steady-state and unsteady-state solutions have appeared in the literature, and methods for analyzing pressure data have been proposed by several authors. pressure data have been proposed by several authors. Some of these methods have been aimed at determining the reservoir vertical permeability. Although many different techniques have been used for solving the partial penetration problem (namely, the point-source solution, Fourier and Laplace transforms, Hankel and Laplace transforms, Green's functions, finite differences, finite elements, an electric analyzer, a thermal model, and a fluid flow model), the analytical expressions and the numerical results obtained for reservoir pressures by the different methods were essentially identical. There were some differences, however, between the values of wellbore pressures computed from numerical models and those obtained from analytical solutions. Analytical solutions were derived by making the assumption of uniform fluid withdrawal along the portion of the wellbore open to flow. With the nomenclature of Fig. 1, this is written as(1)

It appears more realistic to expect the producing pressure to be independent of n Producing pressures pressure to be independent of n Producing pressures would differ only by virtue of the potential head of flowing fluid and friction over the producing interval, assuming the wellbore is open.

SPEJ

P. 140
Field Trial of Caustic Flooding Process
Authors: Graue D.J. , Johnson C.E.
Published: December 2007

A field trial of caustic flooding is reported for a reservoir containing a 20 degrees API oil. Field data showed the process to behave qualitatively as it does in laboratory core floods. Incremental oil over waterflooding for the field trial was estimated at 350,000 STB. The caustic flood resulted in no injection or producing problems. problems. Introduction

In Oct. 1966 an experimental secondary recovery project was begun in a limited portion of the existing project was begun in a limited portion of the existing second and third zones waterflood in the Whittier oil field in Whittier, Calif. The major feature of the oil recovery scheme was a caustic flood conducted in the area shown in Fig. 1 that was in the center of the field. The caustic flooding process was used because laboratory tests had indicated that a considerable increase in oil recovery would result over plain waterflooding in this field. Screening tests on many crude oils for susceptibility to caustic flooding had earlier shown that the Whittier second- and third-zone crude reacted favorably with caustic to give extremely low interfacial tensions. It was believed that these low interfacial tensions, shown in Fig. 2, would result in much improved volumetric sweep efficiencies through a mechanism of in-situ emulsification.

Reservoir Description Formation

A typical well log of the section including the second and third zones is shown in Fig. 3. The top of the second zone occurs at an average subsea depth of 1,500 ft and the top of the third zone is at 2,100 ft. The net oil sand in the two zones averages about 37 and 100 ft, respectively, with porosity of about 30 percent in both zones and arithmetic air permeabilities percent in both zones and arithmetic air permeabilities of 495 and 320 md, respectively. Both zones dip sharply to the south at an angle of 25 degrees to 45 degrees. A fault runs roughly east and west across the middle of the field and forms a natural barrier for the pilot area. pilot area. Reservoir Fluid

The gravity of the oil averaged 20 degrees API and the viscosity at reservoir conditions of 365 psi and 120 degrees F was about 40 cp.

Wells

The well spacing in the 63-acre project area varied between 1 and 2 acres per well. The project began with 45 producers and four injectors in the two zones. Later problems required the conversion of one producer to injection. All of the producers in the project area were completed in both sands except for the three wells noted in Fig. 1. The four initial injectors Wells 48, 75, 157, and 135initially injected controlled amounts into each of the two test zones. The well problems mentioned earlier required shutting off Well 48 injection into the second zone, and injection from Wells 75 and 157 into the third zone. To replace this lost injection, Well 178 was converted to injection in the third zone.

Reservoir Performance During Waterflood

Water injection into the project area began in early 1964.

P. 1353
A Variable-Rate Procedure for Appraising Wellbore Damage in Waterflood Input Wells
Authors: Johnson C.R. , Greenkorn R.A. , Widner G.W.
Published: December 2007

This paper describes a short, simple well-testing procedure evolved from unsteady-state concepts to appraise wellbore damage in water-input wells. Input rates are changed at specific intervals over a 30-minute period and the wellhead pressure recorded at the end of each interval. From these data, the pressure drop due to the "skin" can he computed. This pressure drop in terms of psi/B/D of input rate is referred to as the "skin factor". Two of these variable-rate tests are required to determine change of wellbore damage and to evaluate well-treatment techniques.There are several advantages to the variable-rate procedure. The necessary data can be obtained with wellhead gauges and meters. There is little interference with normal operations. The short testing period eliminates many interpretative difficulties that come from interference from adjacent wells. The shut-in period required for standard tests before the plot of pressure vs log of time attains a straight line is often 12 hours or more. Such a time period is inconvenient, especially when a well must be tested repeatedly to evaluate change in wellbore characteristics.This variable-rate procedure has been successfully applied to water-input wells in three fields. For some of the wells, skin factors were calculated from both the standard and the variable-rate tests. These results show good agreement.

THEORY OF THE VARIABLE-RATE PROCEDURE

In many waterflood input wells, the pressure in the wellbore differs from the pressure in the reservoir immediately adjacent to the well because of the restriction of flow through the skin of the well. If the true pressure of the reservoir at the well, pt, is that pressure which would exist in the well if no skin were present, and pt' is the actual pressure as measured in the well, this difference, pt'-pt, is the skin effect.Fig. 1 shows the change in skin effect with change in flow rate. As the flow is reduced, the skin effect pt'-pt is reduced by an amount equal to the change in wellbore pressure minus the change in reservoir pressure.The equation of pressure change without skin using the point-source solution of the diffusivity equation is (after van Everdingen)

........................................(1)

where q = flow rate, B/D, k = permeability, md, h = thickness, ft, = porosity, psi,= viscosity, cp, c = compressibility, vol/vol/psi, rw = well radius, ft, and t = time, minutes.

With skin factor S, it may be written

..............(2)

JPT

P. 85^
Log Interpretation Problem in Low Resistivity Sands
Authors: Blum Harold A. , Martin John L.
Published: December 2007

All recent investigations have attributed low electric log resistivities in producing formations to a conductive ion layer associated with clay material present in the sands. In this study another mechanism is proposed. It is believed that connate water saturation variations (which may or may not be associated with shale contact) also contribute to low resistivities. In addition to the mechanistic studies, evaluation of various recently proposed interpretation methods have been made. Of these, the Poupon, Loy, and Tixier and de Witte methods seem best.

Statement of Problem

Low resistivity sands are often encountered which turn out to be commercial hydrocarbon zones but appear from electric log data to be water bearing. Adequate methods of recognizing these cases are needed. Industry-wide interest in this problem is evidenced by the number of papers published in recent years. It seemed that several zones in the Mustang Island field (Nueces County, Tex.) were affected by the shaly sand problem. This was evidenced by:low hydrocarbon saturation calculations from logs and measured formation factor data in producing zones,changes in apparent measured formation factors with changes in water resistivity, andcore descriptions which indicated the presence of shaly "streaks" or "spots."

A section of a typical log is shown in Fig. 1. All sands on this log are hydrocarbon zones.

Scope of Investigation

The Mustang Island field, Nueces County, Tex., has been chosen for the study of the shaly sand problem because the oil-water contacts are well established for most of the sands and some core data were available for study. This problem has been approached by both empirical and experimental methods. The empirical portion of this study is a comparison of calculated hydrocarbon saturations from logs by various methods with expected or known production (oil, gas, or water).
Effects of Compressibility and Solution Gas on The Gas Drive Mechanism for Linear and Radial Systems
Authors: Carlson F.M. , Land C.S.
Published: December 2007

A numerical model was constructed to investigate the effects of compressibility, and solution on the immiscible gas drive mechanism. Based on the results of this model, these effects can be predicted using a modification of the Buckley-Leverett and Kern solutions.

Introduction

A theory describing linear displacement of one fluid by another in porous media was developed in 1941 by Buckley and Leverett. The validity of two of the simplifying assumptions made in their development would seem to depend on the type of fluid used as the displacing phase. The first assumption is that the density of each phase remains constant throughout the reservoir. This supposition is realistic when the oil is displaced by water owing to the relative incompressibility of the two phases. However, when the oil is displaced by gas, this assumption becomes somewhat incredible owing to the fact that the gas is extremely compressible. The other assumption, peculiar only to the displacement of oil by gas, is the constancy of the solution gas during the period of injection. This conjecture would seem unreasonable, inasmuch as when gas is injected at a pressure greater than the saturation pressure of the oil, an pressure greater than the saturation pressure of the oil, an increase in the amount of solution gas per volume of oil undoubtedly occurs.

Recognizing these limitations of the Buckley-Leverett theory, Kern presented a modification that takes into account a change in solution gas when gas is injected into an undersaturated reservoir. In this derivation, gas is assumed to be compressed to the volume it would occupy at the injection pressure, and it is postulated that gas remains in this compressed state until breakthrough of the gas. The saturation pressure of the oil is considered to change from the initial bubble-point pressure to a new value equivalent to the injection pressure. Pirson offered a graphical technique for solving Kern's equations. Using this method, saturation at the front and average saturation behind the front can be found in a manner similar to that proposed by Welge.

Consequently, the object of this study is to demonstrate with the aid of a numerical model the effect of compressibility and changing fluid properties on the gas displacement mechanism. Complete details of this study can be found elsewhere. A digital computer is used to solve the finite-difference representations of the partial differential equations of motion for the simultaneous flow of oil and gas through porous media. Results from the solutions of Buckley-Leverett, Kern, and the numerical model are contrasted. Suggestions are made as to the reasons for the differences in the three solutions. A variation to the Kern solution for both linear and radial systems is presented for estimating recoveries at breakthrough when injection, production, and initial bubble-point pressures are known.

JPT

P. 1079