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By J. L. Huitt, B. B. McGlothlin, D. K. Lowe

Published correlations for the principal aspects of hydraulic fracturing were combined into a digital computer program to facilitate the study of interrelated variables. The computer program includes individual relationships for fracture width during pumping, fracture area generated, propping agent embedment, flow capacities of propped fractures and transport of propping agents in horizontal fractures. The effects of more than 20 treatment and formation parameters on the predicted results of hydraulic fracturing treatments were studied. The effects of these parameters were determined for (I) fracture width during injection, (2) fracture width after the overburden comes to rest on the propping agents, assumed not to be crushed, (3) generated and propped fracture area, (4) location and concentration of propping agents in the fracture when injection ceases, (5) flow capacities of the various propped sections of the fracture and (6) expected increase in the well productivity. The effects of propping agent, formation and fracturing fluid parameters on well productivity are discussed. The parameters that were found to have the most pronounced effects on hydraulic fracturing treat~nents are injection rate, treatment volume, fracturing fluid coefficient, size and amount of propping agent, spearhead volume, well drainage radius and formation capacity. INTRODUCTION Many correlations have been published for predicting effects of various parameters that are considered in the design of hydraulic fracturing treatments. The Carter equation' can be used to predict generated fracture radius as a function of fracture width, fracturing fluid leakoff and other parameters. Fracture width can be determined by use of the Perkins and Kern correlation' in which the fracture width is related to the fracture radius, fluid injection rate and certain formation and fracturing fluid parameters. Wahl and Lowe et aL4 have reported methods of predicting the location of propping agents in fractures when pumping ceases. The former study is applicable to the case where the ratio of propping agent diameter to fracture width is less than 0.1. The latter is applicable when this ratio is greater than 0.1. These studies showed that the propping agent placement in horizontal-radial fractures depends principally on how the individual particles are transported in the fracture by the carrying fluid. Particle transport in fractures is determined by local fluid velocity in the fracture, fluid and particle properties, and the size of the particle relative to the fracture width. The distribution of propping agents, effective overburden pressure and formation rock strength control the propped fracture width6 by controlling the extent to which the propping agent particles embed into the fracture faces. From the distribution of propping agents and the propped fracture width, fracture flow capacities can be calculated or the various regions of the fracture. The flow capacities and the radial extent of these regions can be combined with reservoir information to predict the productivity increases for fractured wells. In all these studies, the effects of certain treatment and/ or reservoir parameters on one facet of fracturing can be predicted only if other facets which the parameters affect are fixed. For instance, fracture width and radius are interrelated; that is, to calculate the value of one, the value of the other must be known. Also, some parameters influence more than one aspect of fracturing. For example, prop-pant transport is a function of both fracture width and fluid viscosity. but fracture width is itself a function of fluid viscosity. Since these calculations are complex and the parameters interrelated, it is not possible to write an equation with which the over-all effects of treatment parameters can be solved explicitly. For these reasons, the correlations for determining the effects of the parameters which are most significant in hydraulic fracturing treatments have been incorporated into a digital computer program. COMPUTER PROGRAM The program, which was written for an IBM 7094 computer, can be used to predict results of most of the combinations and values for the treatment parameters that are ordinarily considered for fracturing treatments. A spearhead of fracturing fluid and a propping agent-carrying fluid with different fluid properties can be taken into account. Also, the total volumes and relative amounts of the spearhead and carrying fluids can be varied. Two different propping agents (as used in tail-in operations) and a wide range of formation properties and injection rates are considered. The computer program (Fig. 12) consists of several sets of calculations. First, the final flooded fracture radius and average fracture width at the cessation of pumping are calculated. This is done by simultaneous solution of the Perkins and Kern fracture width equation and the Carter equation for flooded fracture radius (equations used in the computer program appear in the Appendix). The next step is to determine local fluid velocity in the fracture as a function of time and radius. Since it is not possible to write this function in closed form expression, a table of velocity values is generated by the program and stored for subsequent use. The time span from the beginning of

By H. R. Crawford, P. B. Crawford, A. F. Tragesser

A method has been developed to calculate wellbore temperatures during mud circulation and the actual cementing operation to aid in the design of cement slurries. The method agrees within 10F with previously measured values. The calculation technique provides temperatures, as functions of time, at varying depths in both the casing and annulus. The technique also provides this information if a relatively cool cement slurry is pumped into the well immediately following circulation of hot mud. Circulating bottom hole temperatures of brine and a bentonite mud were measured. INTRODUCTION As wells are drilled deeper, greater demands are being made on all phases of the industry, and new technology has been developed to provide satisfactory well completions. However, little or no work has been conducted on accurately determining bottom-hole, static and circulating temperatures.. In designing a cement slurry, such factors as density, fluid loss control, viscosity, deterioration from ternperature, compressive strength and pumping time must be considered. Individual well conditions often make it necessary to include still other factors. Pumping time is a primary consideration and, as wells are drilled deeper, encountering higher bottom-hole temperatures, this property becomes even more important. Cement slurries must be designed with sufficient pumping time to provide safe placement in the well; however, the slurry cannot be overly retarded as this will prevent the development of satisfactory compressive strength. The pumping time of a specific cement is currently obtained by subjecting the cement to simulated conditions of temperature and pressure. A reasonably accurate bottom-hole pressure may be obtained by considering hydrostatic heads of fluids, friction pressure and wellhead pressures. However, accurately determining bottom-hole temperatures is much more difficult. Bottom-hole static temperatures are estimated by considering several sources of information, including logging temperatures, published temperature gradient maps and field experience. This information is usually questionable due to disagreement of data from the various sources. Temperature gradient maps were constructed based on temperatures recorded many years ago while running bottom-hole pressure tests. These thermal gradients then represent an average of well conditions and cannot always apply to a specific well. Also, logging temperatures may be affected by the time since fluid was last circulated, rate of penetration, circulating rate and many other factors. Therefore, even though logging temperatures are available, the question still exists as to the correction factor that should be applied to obtain an accurate static temperature. After obtaining static bottom-hole temperature, it is then necessary to relate this to circulating temperatures actually encountered by the cement slurry. This is accomplished by selecting a test schedule from the API RP-10B corresponding to the estimated well conditions.' The API-recommended practice for testing oilwell cement provides testing schedules for various well depths and conditions. These schedules are intended to simulate down-hole conditions during cementing. They provide a rate at which both temperature and pressure are increased until the estimated circulating conditions are reached. These testing schedules represent circulating temperatures for an average well and, although there is flexibility in choosing the test schedule that most accurately simulates the temperature of an individual well, it still is not possible to consider all the well conditions that will affect the bottom-hole temperature. Many factors affect cement temperatures; for example, the length of time a well has remained static prior to running casing and cementing, the circulation time, the temperature of fluids used in cementing, fluid density and flow properties of fluids. The pumping time for a typical retarded cement could vary from 2 to 4 hours with a 10F change in testing temperature. Variations in pumping time are the most critical in highly retarded cements used in deep, hot wells; yet, predicting bottom-hole circulating temperatures is more difficult in these wells. This work was conducted to develop a means of calculating circulating temperatures as a function of well depth, casing and hole size, pumping rate and time, fluid and reservoir physical properties and thermal status of the well. PREVIOUS WORK In 1941 Farris reported on a study to develop information leading to a more practical laboratory evaluation of oilfield cementing mixtures and performance.' It was then recognized that the pressure factor was being neglected,

By T. O. Anderson, E. J. Stahl

Tests to increase knowledge concerning the process of hydraulic fracturing have been performed on three wells in the Allegheny field in western New York. The fracture orientation and its physical appearance at the well-bore was determined by impression packers run at appropriate times throughout the program. Fract~tre azi171uth and its dimensions thus determined were compared to the rock properties and treatment conditions. Logs to provide data concerning rock properties and to improve identification of vertical fractures were run before each step of the fracture treatment. Pressure osc~illu~iot~s were studied after each phase of tile treatments surface pressures during treatment. These measurements show that subsurface pressures exhibit many of the same characteristics as surface pressures during treatment of a well; however, transient pressures are dampened and deelayed in time at the bottom of the well when COmpared with surface pressures. Data obtained from this study provides a means to help locale and determine orientation of vertical fractures made in the open wellbore. Although these rests were performed in only one area, much of the information gained may be applied to fracturing programs in orher areas. INTRODUCTION In this study, various tests were made to provide data to better understand formation fracturing in situ. The reservoir studied is the Richburg oil sand which is a part of a series of predominantly grey sandstones and shales with occasional brown sandstone layers, known as the Caneadea unit of the Canadaway group of Upper Devonian age. Average physical characteristics of 12 cored wells in this area are 13-ft thick gross sand formation, 12-ft thick net sand. 1.7 md permeability, 11 percent porosity, 44 percent oil saturation (before secondary recovery) and 16 percent water saturation (before secondary recovery). This particular area of the Allegheny oil field was originally drilled prior to 1890. The first waterflood secondary recovery attempt was made in 1929. The present sustained waterflood development began in 1951 and is being carried out on a 4.5 to 5-acre spacing. Objectives of these tests were to (I) study fracture azimuth and dimension in relation to rock properties and treating conditions, (2) improve fracture identification techniques, (3) compare surface and subsurface pressure during all phases of treatment and (4) compare the periods of the fluid column oscillations occurring after each phase of treatment. Although the areas of investigation listed appear divergent in purpose, the program was designed primarily to increase knowledge of down-hole conditions leading to rock failure and extension of the fracture thus created. TEST PROCEDURES Wells upon which tests were conducted are designated as Wells 1 through 3. Well 2 was located 440 ft north of Well 1, and Well 3 was located approximately 880 ft west of Well 1. Wells 1 and 2 were completed with cable tools, while the producing interval of Well 3 was rotary cored using fresh water as the drilling fluid to obtain oriented cores. Tests were divided into separate phases on each well as the fracturing program progressed and consisted of measurements performed prior to treatment, during and after the formation breakdown operation. during fracture treatment and after treatment. To verify location and azimuth of the fracture created, and to obtain an impression of wellbore irregularities, a packer was used (Fig. 1). This packer was lowered on tubing into the wellbore opposite the interval under study and inflated in stages to allow the impression material to conform to the wall of the wellbore. A magnetic compass was attached to the tool for orientation reference. Impressions made prior to treatment showed no existing fractures in the wells under study. Impressions made after both formation breakdown and treatment pro-

By J. C. Martin

A theoretical analysis of steam stimulation is presented for single sands. The analysis includes the effect of steam production and most of the effects of heat conduction. The results show the effects of a number of important variables on the performance of an idealized well under steam stimulation. Calculated responses are presented which indicate the effects of steam production, amount of steam injected, water production, formation thickness and formation damage. Results indicate that steam production can cause large reductions in the heat contained in the formation. This effect can be eliminated by drawdown control. Water production reduces the amount of oil produced during stimulation. The optimum amount of steam to inject depends on economic factors as well as the well response. In many cases, the increased temperature resulting from stimulation reduces oil viscosity near the well sufficiently to overcome the effects of formation damage even if the damage is not removed during steam injection. Calculated responses for thin sands are more favorable than anticipated. INTRODUCTION Little has been published on the theory of steam stimulation'-' despite the interest it has created and the wide variation in well responses. The results of the present analysis provide an insight into steam stimulation, and the methods employed provide a foundation for future work. Analyses presented in Refs. 1 and 2 are very limited and apply to gravity drainage conditions. Ref. 3 contains an analysis similar to the one presented here. The idealized models used and the assumptions made in Ref. 3 are different from those used in this paper. The analysis assumes that after steam injection has heated a small portion of the volume within the radius of drainage of a single uniform sand, a shut-in soaking period is allowed before returning the well to production. The effects of gravity, capillarity, transient pressure and water-sensitive sands are neglected. The injection and soaking times are assumed short compared to the stimulated production time. The initial temperature is assumed uniform; thus, the results apply primarily to first-cycle stimulation. The effects of gas production other than steam are neglected, and the water-oil ratio during production is assumed constant. Steam stimulation involves the simultaneous variation of the temperature, pressure and saturations. General mathematical equations for these variations are complicated and can be very difficult to solve. Simplified equations based on idealized models are used to reduce the mathematics sufficiently to allow approximate solutions to be obtained. DISCUSSION INJECTION An idealized model for which heat conduction is neglected is used to represent the behavior of a well during steam injection. The mathematics for this model is presented in Appendix A which also contains an approximate solution for the behavior of the no-conduction model. SOAKING During soaking, the well is shut in. Only the temperature, pressure and saturation distributions at the end of soaking are needed in the analysis. During soaking the heat is considered to be conducted in a uniform medium from an initially uniformly-heated circular cylinder confined to the producing interval. At the end of soaking the saturations and pressures are assumed to correspond to the cold zone. Analysis of the heat flow during soaking is included in the next section. The radius of the heated cylinder is calculated from the following heat balance (for constant quality steam injection). At the end of the soaking period it is assumed that little or no free gas is present near the well, and that the soaking period has been sufficiently long that the steam zone has had time to expand and the steam has condensed. The condition where there is no soaking is considered in the next section. PRODUCTION In this section, an approximate method is presented for solving the equations of heat and fluid flow associated with the production of oil and water during steam stimulation. Where initial pressure drawdowns are sufficient to cause steam to flow into the wellbore, steam production is assumed to occur within a short initial adjustment period (Appendix B). The production practices followed soon after the well is returned to production can have a large influence on the amount of oil produced during the stimulation cycle. Under most conditions, there is a period of time in which some or all of the water in the heated zone is converted into steam and produced. This flashing of hot water is caused by the pressure in the heated zone dropping below

By K. E. Brown, J. P. Brill, T. C. Doerr

A wide range of intermittent gas-lift tests way conducted in a 1,500-ft experimental well through 11/4- and 11/2-in, nominal size tubing. The well was equipped with two gas-lift valves, four Maihak electronic pressure transmitters and surface facilities to measure casing and tubing pressures, temperature, liquid production and the rate and volume of gas injected. For each tubing size, tests were conducted varying the slug length, gas volume injected and liquid viscosity and surface tension. From these tests, an empirical "fallback" or liquid loss correlation has been developed. No general fallback correlation could be obtained, and the correlation is presented in the form of one curve for each slug length of a given liquid and lubing size. A conceptual model has been developed which combines the fallback correlation with equarions which govern liquid slug pow. A mathematical simulation of the model in the form of a digital computer program is used to calculate total recovery, gas volume used and clearance time for a given test. Tubing pressures at the gas-lift valve and at the gm-slug interface are calculated as a function of time. Tubing pressures at the surface during slug clearance ore also calculated. The results compare favorably with the test data and verify the conceptual model. The extent to which the model can be used for other tubing sizes, depths, liquids and gas-lift valves can only be determined with additional experimental data. Data are also necessary so that a fallback curve can be constructed for the particular test conditions studied. INTRODUCTION The flow of liquid slugs in vertical conduits has long been an established production method in the petroleum industry. Under the name "intermittent gas lift", many advances have been made in engineering design. However, the unsteady-state nature of liquid slug flow has discouraged attempts to describe the problem analytically. The result has been that intermittent gas lift is dominated by rules-of-thumb engineering practices developed over many years. The advent of slim-hole completions has increased the demand for a more rigorous solution to the intermittent problem. Small-diameter conduits offer more frictional per intermittent cycle. Small-diameter conduits are defined to be 1%-in. nominal size tubing or smaller. When oil is produced from the reservoir in which it is found, and transported to surface tanks by intermittent gas lift, three separate flow stages are encountered: flow of the fluids to the wellbore through a porous medium, vertical flow of a liquid slug from the point of gas injection to the surface, and horizontal flow of the liquid slug through the surface flowlines from the wellhead to the surface tanks. The three stages are depicted schematically in Fig. 1. The present study deals with liquid slug flow in both the vertical and horizontal conduits, ending when the bottom of the liquid slug reaches the surface. Due to the large number of variables involved, the analytical study of intermittent gas lift is extremely complex. The possibility of flow regimes other than slug type, the nature of the force fields acting on the system, the interfacial instabilities involved, the varying operational principles of existing gas-lift valves and the complete unsteady-state nature of the physical phenomena occurring in an intermittent gas-lift cycle relate some of the difficulties encountered.

By J. B. Cheatham, J. W. McEver

A laboratory investigation of the behavior of casing subjected to salt loading indicates that it is not economically feasible to design casing for the most severe situations of nonuniform loading. When the annulus is completely filled with cement, casing is subjected to a nearly uniform loading approximately equal to the overburden pressure, and, although the modes of failure may be different, the design of casing to withstand uniform salt pressure can be computed on the same basis as the design of casing to withstand fluid pressure. Failure of casing by nonuniform loading in inadequately cemented washed-out salt sections should be considered a cementing problem rather than a casing design problem. INTRODUCTION Casing failures in salt zones have created an interest in understanding the behavior of casing subjected to salt loading. The designer must know the magnitudes and types of loading to be expected from salt flow and he must be able to calculate the reaction of the casing to these loads. In the laboratory study reported in this paper, short-time experimental measurements of the load required to force steel cylinders into rock salt are used as a basis for computing the salt loading on casing. These results must be considered to be qualitative only since rock salt behaves differently under down-hole and atmospheric conditions and also may vary in strength at different locations. The beneficial effects of (1) cement around casing, (2) a liner cemented inside of casing, and (3) fluid pressure inside of casing in resisting casing failure are considered. ROCK SALT BEHAVIOR UNDER STRESS The effects of such factors as overburden loading, internal fluid pressure, and temperature on the flow of salt around cavities have been studied extensively at The U. of Texas. Brown, et al.1 have concluded that an opening in rock salt can reach a stable equilibrium if the formation stress is less than 3,000 psi and the temperature is less than 300°F. At higher temperatures and pressures an opening in salt can close completely. These results indicate that calculations based upon elastic and plastic equilibrium for an open hole in salt should be applied only at depths less than 3,000 ft. In most oil wells the tem- perature will be less than 300F in the salt sections, therefore no appreciable temperature effects are anticipated. Serata and Gloyna2 have reported an investigation of the structural stability of salt. .They assume that the major principal stress is due to the overburden. Other stresses can be superimposed if additional lateral pressures are known to be acting in a particular region. In the present analysis an isotropic state of stress is assumed to exist in the salt before the hole is drilled, since salt regions are generally at rest. This assumption is partially verified from formation breakdown pressure data taken during squeeze-cementing operations in salt. Experimental measurements of the elastic properties of rock salt indicate a value of 150,000 psi for Young's modulus and a value of approximately 0.5 for Poisson's ratio. A value of % for Poison's ratio with finite Young's modulus would indicate that the material was incompressible. Values ranging from 2,300 to 5,000 psi have been reporteda for the unconfined compressive strength of salt. These variations may be due to differences in the properties of the salt from different locations or at least partially to differences in testing techniques. Salt is very ductile, even under relatively low confining pressures. For example, in triaxial tests reported by Handin3 strains in excess of 20 to 30 per cent were obtained without fracture. When casing is cemented in a hole through a salt section, the casing must withstand a load from the formation if plastic flow of the salt is prevented. To determine the forces which salt can impose on casing, circular steel rods were forced into Hockley rocksalt with the longitudinal axis of the rods parallel to the surface of the salt. The force required to embed rods 0.2 to I in. in diameter and 1/2 to 1 in. long to a depth equal to the radius of the rods was found to be F/DL =28,700 psi (± 3,700 psi) , .... (1) where D is the diameter, and L is the length of the rod. CASING STRESSES Since an open borehole through salt at depths greater than 3,000 ft will tend to close, cemented casing which prevents closure of the hole will be subjected to a pressure approximately equal to the horizontal formation stress after a sufficiently long time. As a first approximation the horizontal stress can be assumed to be equal to the overburden pressure. This is in agreement with the suggestion by Texter4 that an adequate cement job can prevent plastic flow of salt and result in a pressure on the casing approximately equal to the overburden pressure. He also advocated drilling with fully saturated salt mud

Jan 1, 1965

By T. C. Boberg, R. B. Lantz

This paper presents a method for calculating the producing rate of a well as a function of time following steam stimulation. The calculations have proved valuable in both selecting wells for stimulation and in determining optimum treatment sizes. The heat transfer model accounts for cooling of the oil sand by both vertical and radial conduction. Heat losses for any number of productive sands separated by unproductive rock are calculated for the injection. shut-in and production phases of the cycle. The oil rate increase caused by viscosity reduction due to heating is calculated by steady-state radial flow equations. The response of successive cycles of steam injection can also be calculated with this method. Excellent agreement is shown between calculated and actual field results. Also included are the results of several reservoir and process variable studies. The method is best suited for wells producing from a multiplicity of thin sands where the bulk of the stimulated production comes from the unheated reservoir. The flow equations used neglect gravity drainage and saturation changes within the heated region. INTRODUCTION This paper presents a calculation method which can be used to predict the field performance of the cyclic steam stimulation process. The calculation method enables the engineer to select reservoirs that have favorable characteristics for steam stimulation and permits him to determine how much steam must be injected to achieve favorable stimulation. While the calculation represents a considerable simplification of physical reality and the results are subject to numerous assumptions which must be made about the reservoir, it has been found that realistic calculations can be made of individual well performance following steam injection. The duration of the stimulation effect will depend primarily on the rate at which the heated oil sand cools which, in turn, is determined by the rate at which energy is removed from the formation with the produced fluids and conducted from the heated oil sand to unproductive rock. A complete mathematical solution to this problem is a formidable task, and finite difference techniques would undoubtedly have to be used. The calculation method pre- sented here utilizes analytic solutions of simple related heat transfer and fluid flow problems. The method is sufficiently simplified that it can be used as a hand calculation, although the calculations are somewhat lengthy and laborious. For that reason, the analysis was programmed for an IBM 7044 digital computer. Well responses observed at the Quiriquire field in eastern Venezuela&apos; have been matched using this program after making suitable approximations for reservoir and wellbore conditions. One of the most valuable uses of this calculation method is to assess the effect of reservoir and proc-cess variables on the stimulation response. This paper contains results of several studies made of key reservoir and process parameters. Among the most important of these is the influence of prior wellbore permeability damage. If a well is severely damaged prior to stimulation, a higher stimulation response will be observed than if it is undamaged. If a portion of this damage is removed, a permanent rate improvement will occur. THEORY I)ES(:KJJ&apos;TION OF CALCULATION METHOD The process of cyclic steam stimulation is essentially one of reducing oil viscosity around the wellbore by heating for a limited distance out into the formation through the injection of steam. Suitable modifications of the calculation technique presented here can be made so that stimulation of wells by hot gas injection or in situ combustion can also be calculated. A schematic drawing of the heat transfer and fluid flow considerations included in the calculation method is shown in Fig. 1. In brief, the calculation assumes that the oil sand is uniformly and radially invaded by injected steam. For wells producing from several sands, each sand is assumed to be invaded to the same distance radially. In calculating the radius heated rn energy losses from the wellbore and conduction to impermeable rock adjacent to the producing sands are taken into account. After steam injection is stopped, heat conduction continues and oil sands with r < ra cool as previously unheated shale and oil sand at r > r, begin to warm. The effect of warming of oil sand out beyond r, has little effect on the oil production rate compared to the effect of cooling of the oil sand nearer the wellbore than ra. Thus, in computing the oil production rate, an idealized step function temperature distribution in the reservoir is assumed where the original temperature exists for r > rn and where an average elevated temperature exists for r < rn. The average temperature in the oil sand for the region r < rn is computed as a function of

Jan 1, 1967

By G. W. Ostroot, S. Shryock

Cementing deep, high-temperature oil wells where static temperatures range from 350 to 400F has become routine in the part decade. In the United States there were 271 wells drilled deeper than 15,000 ft during 1963. Many of these wells had static temperatures higher than 400F. Bottom-hole static temperatures near 700F are now realities in the geother-mal (steam producing) wells of California&apos;s Salton Sea area. The detailed planning initiated prior to drilling the wells is discussed together with the methods, materials and equipment used in solving the cementing problems which are encountered. Data are also presented that lead to development of cementing compositions that provide adequate thickening time, do not retrogress in strength, and maintain low permeability under these extreme temperature conditions. Field data include the cementing programs used on eight relatively trouble-free geothermal steam wells in the Salton Sea area. INTRODUCTION Not too many years ago cementing oil wells with temperatures in the range of 300F caused considerable anxiety. In some areas of the United States it is now fairly common to cement wells having bottom-hole static temperatures in excess of 400F. We are now confronted with the problem of cementing wells with temperatures ranging from 500 to 700F. Temperatures in this order of magnitude are often found in geothermal steam wells. From where does this extreme heat emanate? There are many theories as to the source of this steam flow. The most widely held views are: (1) heat- ing of ground water fairly close to the surface by an intrusive mass of hot rock; (2) steam generation from a reservoir of metamorphic rock, normally found below 25,000 ft and not at the shallower depths of the Salton Sea reservoir; and (3) high-temperature gases (water vapor) escaping and migrating from molten or semi-molten rock (magma) at a considerable depth. Of these. No. 3 seems to be the most generally acceptable explanation. Heat from springs and fumaroles has been used for years as a means of heating and cooking; however, significant progress in harnessing the vast power of underground steam reservoirs has been relatively slow. The first large-scale attempt to use the heat generated by steam from wells was made in Italy around the beginning of the 20th century. In excess of 250,000 kw of electrical power is now being produced from holes around Larde-rello, Italy. Another very active drilling program was initiated in the volcanic area of New Zealand in 1949.&apos; Natural steam for power projects in the United States began in the early 1920&apos;s. An early commercial steam field is located at the Geysers, approximately 75 miles north of San Francisco, an area discovered in 1847 and used for many years as a health resort. Steam originates from 15 wells that have been drilled since 1957. The present output from this project is 25,000 kw. Success of the Geysers operation has been responsible for several companies taking a careful look at the feasibility of producing steam for power generation in the Salton Sea area of Southern California&apos;s Imperial Valley. Geothermal steam activity in this latter area began in 1961 when O&apos;Neill, Ashmun and Hilliard completed Sportsman No. 1, at that time the hottest wellbore in the world.&apos; Since its References given at end of paver. completion seven additional wells have been successfully completed in this area. Many problems encountered in drilling steam wells had to be overcome to make the ventures successful. Formation temperatures encountered in the Salton Sea seemed to be a straight-line function (a gradient of 13F per 100 ft of depth).&apos; This imposed severe conditions on all aspects of drilling and completion. This varied, to some extent, from gradients in the older geothermal areas. Not to be overlooked is the effect of these temperatures on casing creep or elongation by thermal expansion (Table I), because standard API flanged wellhead equipment makes no provision for this kind of performance. Floating equipment was redesigned, and changes in types of downhole equipment were made in an effort to eliminate anticipated problems. In the later completed wells, standard oil-well cementing equipment has been used. During the early development of geothermal steam wells there were some problems resulting from blowouts. However, these were eliminated in the deeper Salton Sea wells and no problems were encountered with the drilling mud. A sodium surfactant mud was used on the Sportsman No. 1 to drill from 2,690 to total depth. Nevertheless, it was necessary that a cooling system be added and the mud cooled before circulating it back into the well. The difficulty in evaluating the size of the steam area and its potential in terms of pounds of steam and years of productivity still has not been resolved. Economic complexities have also entered into the steam play in the Salton Sea. The wells at the Geysers were drilled at a cost of $15,000 to $20,-000, whereas the Salton Sea wells will cost more than $150,000. This cost differential has to some extent been accounted for because of the heavily

Jan 1, 1965

By B. G. Matson, M. A. Whitfield, G. R. Dysart

This paper describes the development of u computer program to calculate changes that occur in the length of tubular goods due to temperature and pressure changes during stimulation operations. Due to the numerous variables involved and the uncertainty of all static and dynamic conditions that could exist, it becomes a staggering task for individuals charged with completions to perform the necessary mathematical calculations. The computer program permits advance calculations for several sets of conditions. INTRODUCTION In the Delaware basin of West Texas alone, 50 wells were contracted or drilled to 15,000 ft or deeper in 1965. Deep well activity is continuing in this and other areas on an expanding scale. Many of these deep wells require extensive stimulation for successful commercial production, and during these operations, pressures and temperatures are encountered that have a pronounced effect on the length of tubular goods. This length change during a large-volume, high-pressure stimulation treatment utilizing fluids considerably cooler than bottom-hole temperature can be of such a magnitude that permanent damage to casing and tubing will result unless mechanical design, pressures and fluid temperatures are evaluated and controlled. These pressure and temperature effects can be calculated. However, the process lends itself well to computer solutions because of the mathematical nature of the problem and the calculating hours involved in arriving at an answer. The engineering-hour demand becomes more severe as tapered strings are involved. On initial treatments on a given well, surface pressure and injection rate conditions are unknown, and offset well conditions have not proven to be a reliable method for making predictions. For these reasons, it has become rather standard procedure for operators to compensate for these uncertainties by placing unnecessary pressure and fluid temperature restrictions on stimulation design. On a number of occasions treating fluids have been preheated to as much as 160F as a means of compensating for thermal contmction resulting from pumping cool fluids. The maintenance of packer seals has been treated by Lubinski, Althouse and Logan&apos;,&apos; and the problem of therma1 effects on pipe has been explored by Ramey." These works were expanded and the results made applicable to everyday oilfield terminology before submitting them to computer programming. The pressure and temperature effects on tubing movement previously mentioned occur simultaneously as fluid moves through the pipe. The pressure changes, for purposes of explanation, are categorized here as to the various effects these pressures have on a tubing string. These divisions are (1) the piston-like results of forces acting on horizontal surfaces exposed to pressure, (2) swelling or ballooning of the tubing along its entire length due to the forces of pressure acting against the tubing walls, (3) the elongation of tubing due to frictional drag and (4) corkscrewing of the pipe due to internal pressure. Thermal changes are also of great importance, as their results may be more significant than any of the pressure effects. Steel is an excellent conductor of heat and the earth is a relatively poor conductor. It has been calculated that pipe temperatures at depths of more than 20,000 ft approach within as little as 25" the temperfature of the surface fluid after pumping for 2 hours, or a drop in temperature in some treatments of more than 220F. The equations presented in this paper were developed for computer programming and simplicity of input information; therefore, numerical constants such as Young&apos;s modulus for steel (28 X 10\ si), the coefficient of thermal expansion of steel (6.9 X 10."IF) and Poisson&apos;s ratio for steel (0.3) are included with unit conversion factors. The moment of inertia of tubing cross-sectional area with respect to its diameter was changed to a constant times (D&apos; — d&apos;) where D is outer diameter and d is inner diameter. Units in the equations are length in feet, diameter in inches, density in pounds per gallon, pressure in psi, rate in barrels per minute and time in hours. PISTON-LIKE REACTIONS A change in tubing internal dimensions and the exposure of other horizontal surfaces to different pressures on the inside and outside of the tubing result in a reaction much like a piston under pressure. Such is the case when the internal diameter changes in a combination string of pipe, when seals of a slick joint assembly are subject to pressure and in the end effects of a tubing string. The change in tubing length due to the piston effects of a slick joint packer is affected by the various diameters involved, the tubing pressure Ap,, the casing pressure ,Ap,, length of pipe L, densities of fluid in the tubing before and during pump-

By S. G. Gibbs, A. B. Neely

Jan 1, 1967

By H. A. Lesser, H. L. Stone, G. H. Bruce

ESSO PRODUCTION RESEARCH CO., HOUSTON, TEX. A mathematical model that represents the conduction heating of a rock formation of limited permeability is formulated. Heat is introduced by the injection of a hot condensing gas into horizontal fractures through the formation. The fractures are assumed to be equally spaced; the flow of fluid is linear. The model consists of three coupled partial differential equations and two functional relationships. Temperature histories for both fractures and formation are obtained by numerical procedures. Application of the model in predicting in situ heating of oil shale is illustrated with four sample cases. Influences of shale thermal diffusivity, fluid pressure in the fracture and fracture spacing upon heating rate are demonstrated. In all cases considered, several years were required to heat all the formation to 700F with 1,000F steam. Less than 32 per cent of the injected heat was utilized for heating the shale. To facilitate extensive calculations of this type, a set of seven dimension-less quantities are derived. With this dimensionless system, the effect of controllable parameters on economics can be explored. INTRODUCTION Vast deposits of hydrocarbons are contained in oil shale formations in the western United States and in other countries. These hydrocarbons, known as kerogen, are difficult to recover because they are immobile solids and because the rock formations in which they are found have very limited permeability. The kerogen can be converted through pyrolysis to recoverable liquids and gases if the formation temperature is elevated to the range 600 to 800F. To accomplish this heating, the formation might be artificially fractured and a hot fluid injected into the fractures. If the injection and production wells are vertical and the fractures horizontal, interwell communication will be established and the hot fluid will flow from an injection well to a production well. In this process, some of the heat in the fluid will be given up and conducted into the formation. Products of pyrolysis will flow from the heated rock matrix into the fractures and be produced, commingled with the injected fluid. The practicality of such a process is strongly influenced by the rate at which heat can be transferred from the hot fluids to the formation. An analysis of this heat conduction problem is the subject of this paper. Linear flow of a condensing gas through a set of horizontal, equally spaced fractures is considered. Temperature histories for both fractures and formation are obtained from numerical procedures. The analysis also applies to formations containing streaks of natural permeability instead of fractures. Heat flow problems similar to the one treated here have been studied by other workers. Thomas1 has solved a radial problem in which he considers the injection of a noncondensing gas into a single, horizontal fracture and approximates the temperature profile in the fracture by a step function. The solutions to other problems, which are less similar to the present problem than the one treated by Thomas, have been reviewed by Spillette.2 In addition to these mathematical studies, a field test of an in situ shale oil recovery process using hot natural gas as the injected fluid has been reported.3 The first part of this paper is concerned with the mathematical development of the problem. The differential equations, boundary conditions and functional relationships which describe the physical model are formulated and the equations are cast into finite difference form. The method of solution of the difference equations is discussed (Appendix B). The second part of this paper presents results computed for a typical oil shale formation for which steam at 1,000F is the injected fluid. Fracture spacing, horizontal and vertical thermal diffusivities

Jan 1, 1967

By J. A. Knox, R. M. Lasater, J. M. Tinsley

Chemical squeeze treatments have been used to provide temporary relief from certain production problems. The chemical fracture-squeeze technique, combining the effects of a fracturing treatment and a squeeze operation, has been more successful than conventional squeeze operations. Knowledge derived from well stimulation and reservoir engineering research provides a means for predicting the theoretical effective life of such a treatment. Analysis of theoretical equations and concepts developed allows selection of improved treatment techniques based on specific formation conditioins. Theory used in this analysis was developed as an extension of previous electrical model studies made to establish the expected flow and pressure profiles adjacent to a fracture system. The chemical fracture squeeze technique can be utilized in the economic application of corrosion inhibitors, emulsion breakers and paraffin and scale inhibitors. Application of this technique is shown to be effective. The slow return rate of injected chemicals, controlled by the resultant flow profiles and treatment variables, permits extended periods of chemical effectiveness. Results of field treatments are given, showing that the concepts outlined above for chemical fracture-squeeze treatments are valid and that applying this technique can help alleviate many current production problems. INTRODUCTION Much progress has been made in the last 10 to 15 years in developing chemicals for use in stimulating wells, maintaining production and protecting well equipment from damage due to corrosion. Not too many years ago, some wells seemed to dry up or wear out. In many cases the wells were produced as long as possible without any attempt at maintaining productivity. Even with the advent of new and better stimulation techniques, a rapid decline in production was observed. Methods of removing and, in some instances, preventing damage have been developed. Among thosc factors responsible for uneconomical production are scale, paraffin, corrosion, bacteria, water blocks and emulsions. Soluble scale-prevention chemicals have been developed1,2 that can be placed in a formation along with frac- turing sand. As the water produces back across this bed, the solid material dissolves slowly and can provide long-term protection from scale. However, bottom-hole temperature and salinity of produced water vary widely and both these factors influence the rate of solubility. Scale inhibitor composition is also a controlling factor. Some of the solid material may be crushed, increasing the surface area exposed to water and increasing the rate at which it dissolves. Some of the material may never be contacted by water and can be lost. However, this type of treatment has been very successful in many instances and has helped maintain economical production for extended periods of time. Liquid scale inhibitors, which are more widely applicable and more stable, have been developed in recent years; however, because they are liquids, their use has been restricted to treatment down the annulus, using metering pumps to provide proper concentrations in the produced fluid. This has prevented use in wells containing packers, in dually completed wells and in gas-lift and flowing wells. Wells that operate with an open annulus may also experience severe corrosion problems due to introduction of oxygen. Paraffin inhibitors3 have been developed that can be fractured into a well as particulate solids to be slowly dissolved in the produced fluid. These materials are not usually effective in wells with a bottom-hole temperature in excess of 120F since solubility rate may be too fast if that temperature is exceeded or if aromatic content of the oils is unusually high. Corrosion inhibitors have been developed that can be fractured&apos; into a well for long-term feedback, but development of a material with proper solubility or feed rate has been difficult. Corrosion inhibitors are available in many different forms. Liquids have been lubricated down the annulus or sticks or pellets dropped down tubing. Inhibitor squeeze treatments5 devcloped a few years ago led to development of inhibitors with particularly strong film-forming properties.6,7 This technique basically involves displacing a highly concentrated solution of the inhibitor into the formation through the tubing. Kerver and Hanson8 studied the adsorption properties of inhibitors on various types of formations. They showed that, even though the inhibitor was displaced radially into the true permeability, it could be produced back for a long period of time because of slow desorption from the rock. Methods developed for monitoring the return of these inhibitors generally have established 1 to 6 months as the effective limit before retreatment is necessary.9 Inhibitors displaced into the interstices of the formation sometimes cause emulsions that either hamper production or cause treating problems on the surface.

By J. R. Eickmeier

By W. W. Whitaker, C. W. Manry, R. H. McLean

In an eccentric annulus, cement may favor the widest side and bypass slower-moving mud in the narrowest side. Tendency of the cement to bypass mud is a function of the geometry of the annulus, the density and flow properties of the mud and cement and the rate of flow. Bypassing can be prevented if the pressure gradient protluced from circulation of the cement and buoyant forces exceeds the pressure gradient necessary to drive the mud through the narrowest side of the annulus at the same velocity as the cement. In the absence of buoyant forces, one requirement for this balance is maintenance of the yield strength of the cement greater than the yield strength of the mud multiplied by the maximum distance from the casing to the wall of the borehole and divided by the minimum distance. If the yield strength of the cement is below this value, bypassing of mud cannot be prevented unless buoyant forces or motion of the casing significantly aid the displacement. INTRODUCTION Successful primary cementing leaves no continuous channels of mud capable of flow during well treatment and production. Prevention of channels requires care. Tep-litz and Hassebroek provide evidence of channels of mud after primary cementing in the field.&apos; Channeling of cement through mud in laboratory experiments has also been reported.&apos;-&apos; Recommendations for improving the displacement of mud include (1) centralizing the casing in the borehole,&apos;-" 2) attaching centralizers and scratchers to the casing and moving it during displacement,18 "3) thinning the isolating the cement by plugs while it is circulated down the casing,%( (5 establishing turbulence in the cement," and (6) holding the cement slurry at least 2 lb/gal heavier than the mud and circulating the cement slurry at a very low rate of flow.&apos; Although much has been written about the above parameters, the relative importance of each has not been well defined. In this investigation, the mechanics of mud displacement are described through results from analytical models and experiments. The model chosen — a single string of casing eccentric in a round, smooth-walled, impermeable borehole — is analagous to casing centralized in a borehole which is not round and to placing more than one string of casing in a borehole. In each, some paths for flow are more restricted than others. A fluid flowing in the borehole may seek the least restricted, or most open, path. This tendency for uneven flow can lead to channeling of cement through mud unless preventive measures are taken. The analytical models describe channeling and give means of balancing the flow. Experimental data test the analytical models and illustrate effects of motion of the casing, differences in density and mud&apos;s tendency to gel. Results are encouraging. Piston-like displacement of mud by an equal density cement slurry is possible through proper balance of the flow properties of the mud and cement slurries to the eccentricity of the annulus. The more eccentric the annulus, the thicker must be the cement relative to the mud. If proper balance is not achieved. bypassing of mud by cement cannot be prevented without assistance from motion of the casing or buoyant forces. Increasing the rate of flow can help to start all mud flowing but cannot prevent channeling of cement through slower moving mud in an eccentric annulus. Thinning the cement slurry tends to increase channeling although the extent of turbulence in the annulus may be increased. Description of flow in an eccentric annulus begins in the next section. It is assumed that (1) the casing is eccentric and is stationary, (2) the mud and cement slurries have the same density and (3) the gel structure of the mud has been broken and the mud and cement follow the Bingham flow model. Effects related to these restrictions will be discussed. FLOW PATTERNS SlNGLE FLUID IN ANNULUS Flow of a single fluid through an eccentric annulus is illustrated in Fig. 1. Part A shows laminar flow of a Newtonian fluid. This distribution of flow was calculated by Piercy, Hooper and Winney.&apos; In fully developed turbulent flow, the velocity distribution around the annulus is less distorted, but the flow still favors the widest part of the annulus Parts B, C and D of Fig. 1 are a qualitative representation of the flow of a Bingham fluid. The yield strength of the fluid increases the severity of bypassing compared to Newtonian flow. At a very low rate of flow, all flow is confined to that portion of the annulus which has the minimum perimeter-to-area ratio. The fluid shears on the perimeter of that area when the pressure gradient multiplied by the area just exceeds the yield stress of the fluid multiplied by the perimeter. Whether or not the minimum perimeter-to-area region encompasses all of the annulus or only a part (as shown in Part B) depends on the geometry of the annulus. If only a part begins to flow, increasing the rate of flow increases the area flowing until finally there is flow throughout the annulus.

By J. Skrove, C. R. Boardman

In situ permeability of the rock outside the Hardhat chimney was determined by pressurization of long holes with air. Experimental data indicated a remarkable difference between fracture permeability of the rock near the chimney and that at a considerable distance. Although permeable fault zones were known to exist in the granite stock, the measurements of background permeability were quite low, on the order of tenths to several millidarcies. The observed difference is about two or three orders of magnitude above this background in the region 125 to 215 ft radially from the shot point, or 80 to 165 ft radially from the vertical axis of the chimney. The presence of a collapsed drift immediately beyond this region precluded measurements which could have defined the maximum extent of the zone of high permeabilily. INTRODUCTION Previous exploration has revealed that contained nu-clear explosions create cavities which generally collapse, resulting in rubble-filled chimneys and annular fractured zones. These geometries have been shown to result in complex flow regimes which should increase the production rate from hydrocarbon reservoirs.&apos; Empirical scaling equations have been developed for estimatina chimney radii and heights for a variet; of rock media.&apos; The exten; of the annular fractured zone has been documented and associated permeability changes have been observed qualitatively for several explosions. This study was begun to establish the nature and magnitude of the permeability of the latter region. It is anticipated that results will be useful in estimating permeability changes and consequent production stimulation which might ensue from a contained explosion in a hydrocarbon reservoir. The post-shot environment of the Hardhat event (a 5-kt contained nuclear explosion in granitic rock) was c&apos;hosen for the experimental measurements. The Hardhat device was detonated at a depth of 939 ft, and subsequent exploration revealed a chimney of broken rock with a radius of 65 to 70 ft and a height above shot point of 281 ft.&apos; BeFore the explosion, the Hardhat medium was highly jointed and fractured (Fig. I). Jt was expected that differential rock motion along these and other weaknesses induced during cavity growth and collapse would significantly alter the permeability of the rock mass. EXPERIMENTAL METHOD Initially, three 2-in. diameter holes (Nos. 10, 12 and 19) were drilled about 25 ft outward through the walls of the 500-ft level drift (elevation 4,253 ft, Fig. 2). One was drilled near the chimney and two holes, one vertical and the other horizontal, were drilled near the shaft. Order-of-magnitude differences in permeability obtained by pressurization measurements indicated further: investigation was warranted. A series of 3-in. diameter holes was then drilled with water as a coolant into the walls and roof of the drift (Fig. 2). An 11-in. long packer was set from 1 to 8 Et inside each hole and air was injected at measured Row rates. Hole pressures were monitored at the collar. Permeability was low enough in the holes near the access shaft that pressure could be maintained long enough to obtain good pressure decay rates. In the vicinity of the chimney, however, permeability was so high that this was not possible and air was injected under steady-state conditions. About one year later, these same holes were retested to

Jan 1, 1967

By J. W. Givens, P. B. Crawford

A potentiometric model study has been made of the effect of vertical fractures existing in the matrix of the reservoir on the flooding or cycling performance. Fractures can have unusual flow characteristics. Fluid entering one side of a fracture can emerge on either the same or opposite side of the fracture, depending on the particular streamline. Fracture orientation has a great influence on the sweep efficiency. However, sustained fluid injection may still permit large areas to be swept. INTRODUCTION One can find considerable information available in the literature on the effect of fractures originating at the wellbore on sweep efficiencies of water-flooding or gas cycling programs.1-5 However, there arc few, if any, quantitative data reported in the literature on the effect of vertical or horizontal fractures existing out in the reservoir matrix on secondary recovery performance. Several papers have been presented on the effect of vertical and horizontal fractures on the productivity or conductivity of waterflood and gas injection patterns, but in all cases the fractures initiated at the well and simulated commercial fractures.6,7 It is believed that natural fractures may exist out in the reservoir matrix and would effect the displacement performance. The purpose of this report was to study the effect of a few isolated vertical fractures existing out in the reservoir matrix on the performance of waterflood or gas injection patterns. DESCRIPTION AND EQUIPMENT Since the potentiometric model was described by Lee8 it has been widely used to study numerous types of fluid displacement problems. The potentio- metric model can be used for fluid displacement studies when the following assumptions are valid: (a) steady-state conditions exist; (b) the mobilicy ratio is one; and (c) the capillary and gravitational effects can be neglected. Five-spot and direct line drive square patterns were studied using a copper strip of the desired length and orientation to simulate a vertical fracture in the reservoir matrix. The 20 x 20-in. model was considered to represent only one element of an infinite array of similar patterns. DISCUSSION AND RESULTS FIVE-SPOT PATTERN — ONE FRACTURE BETWEEN INJECTION AND PRODUCING WELLS Fig. 1 shows a quadrant of a five-spot pattem with the vertical fracture existing out in the matrix along a line connecting the injection and producing wells. Length of the fracture was equal to 35.4 per cent of the distance between injection and producing wells. In this particular pattern it is noted that fluid breaks through from the injection well to the producing well when the dimensionless time is equivalent to 26.9. Dimensionless time is defined as volume of fluid injected divided by the volume of displaceable fluid in the pattem expressed as a per cent. The cross-hatched areas of this

Jan 1, 1967

By H. W. Winkler, Discussion, V. L. Forsyth

The development of a new gar lift valve has removed many of the obstacles limiting over-all gas lift efficiency. The valve is pressure charged in place in a well, and operating pressure can be changed without pulling. Temperature and gas gradient compensation have been eliminated. Intermitting and constant flow installations, using conventional pressure-charged valves, are compared with designs incorporating the new automatic stabilizer controlled valve. Specific well performance data are presented. The means of obtaining and controlling multiple-point injection of gas are explained and contrasted with single point injection. The effect on small diameter strings and multiple string installations is discussed. The effect of flowing temperature gradient on a design using conventional pressure-charged valves, the limitations imposed by such temperature, and the obvious benefits which result from the use of automatic stabilizer controlled valves are shown. Reduction of gas requirements is stated mathematically and demonstrated with specific examples which are identified as to oil company and well. Increased fluid recovery resulting from greater drawdown is illustrated. The economic advantages are mentioned with emphasis on reduction of capital expenditures, as well as reduction in operating expenses. INTRODUCTION Much of the engineering and research work performed with gas lift has been based upon the supposition that under producing conditions gas would be injected at a single point in a well. Many tests were performed in determining the optimum size of the opening through which gas would be passed and the exact placement of the valve equipment. The objectives in a gas lift installation are to unload the well and to efficiently produce the well after it is unloaded. Until recently, the function of upper valves was simply to unload the well. An operating valve located at a proper place in a well served as a single injection point for lifting liquid to the surface. The basic problem in using such equipment is to arrive at operating depth with sufficient operating pressure to efficiently lift the liquid. Few gas lift installations are designed with all required well data available. However, regardless of the quality and availability of data, and regardless of the accuracy of the design, there is the practical problem of preparing and placing gas lift equipment in the well in exact accordance with the plans and intentions of the engineer. In recognition of these and many other problems, attention was directed toward a means of removing the need for temperature and gas gradient compensation, a way to change the gas lift installation to meet the changing requirements of the well itself, and a manner of compensating for changes in oil-water content, fluid volumes, PI, and bottom-hole pressure resulting from flood or repres-suring activity. A device which could actually set and change the operating pressure of gas lift valves in the well would meet most of these needs. There now exists a new gas lift valve which fulfills the original objectives and in so doing actually accomplishes much more. With this device, called an Automatic Stabilizer Controlled valve, there is an exact matching of valve operating pressure and well conditions. Gas is injected at more than one point in the well, thereby making controlled multiple-point injection of gas a reality. Installation calculations are materially simplified and the need for basic temperature and gas gradient data no longer exists. Section I—The Automatic Stabilizer Controlled Valve The operation of the ASC valve is more easily understood by first studying a conventional pressure-charged valve and then inserting the stabilizer element to observe the changes which result. Fig. 1 is a schematic of a conventional precharged pressure-operated valve. The pressure in the dome pd, acts downward, against the area of the bellows A,, to hold the valve closed. The resulting force Bf plus the spring effect of the bellows Sf represents the total force acting to close the valve. Correspondingly, the tubing pressure ptbg works upward against the port area Atbg and the casing pressure pc works upward against a portion of the area of the bellows

Jan 1, 1965

By E. P. Whittemore

Experience with the ASC multipoint gas lift system was obtained in Colonia zone of the West Montalvo field near Oxnard, Calif. The wells in this pool produce from depths varying from 10,500 to 12,000 ft. Oil gravity is generally 14 to 15&apos; API with a few extremes of 12 and 20" API. Some salt water is produced which causes some very viscous emulsions. Viscosities at 150F (which is the approximate wellhead temperature) vary from 5,000 to 100,000 SSU. Most of the production is by gas lift, although a few wells are produced by rod and hydraulic pump. About half of the gas-lift wells are on continuous flow and the remainder are on intermittent lift using large, ported, pilot-operated valves for single-point transfer of gas from casing to tubing. Gas-liquid ratios vary from about 6 to 10 Mcf/bbl of gross fluid lifted. Wells are produced to a 450-psi trap system. The following remarks will be confined to intermittent lift only, since this is the type of lift which has been achieved with the ASC valve system. The maximum gross fluid which has been produced by single-point intermittent lift is about 350 B/D in 3-in. tubing and 200 B/D in 21/2-in. tubing with gas-liquid ratios of approximately 7 to 9 Mcf/bbl. Some design changes could reduce this ratio. The ASC multipoint system has provided production as high as 480 BOPD in 21/2-in. tubing with gas-liquid ratios just under 4 Mcf/bbl. To be able to apply the multipoint system, it is recommended that a detailed explanation be obtained concerning transition-point pressure and stabilizer setting—what its significance is to the string design, how it may work for or against the operation of the well, how it is related to tubing sensitivity and how it affects the unloading operation. The unloading operation may only be of academic interest in a technical paper, but to the production foreman, unloading and setting the valves in operation is a very real problem and should be understood in detail. One item touched lightly in the paper was the unloading valve. This valve controls the maximum pressure at which the well can be operated. When lifting heavy viscous fluids, it is most important to set this valve for the maximum possible realistic operating pressure at the surface. If the well lifts easily, it is simple to set the ASC valves at a lower operating pressure and the unloading valve will remain closed; but if the well happens to be heavier to lift than anticipated, it may be desirable to operate on the unloading valve itself and use all the energy obtainable at the bottom of the hole. In the Colonia pool very heavy wet-gas gradients are experienced due to the viscosity of the liquid and the dense mist which is left behind a slug of fluid. There are many combination strings of 3- and 21/2-in. tubing. This aggravates the wet-gas gradient problem and provides wet-gas gradients of about 50 to 70 psi/1,000. An advantage which multipoint lift has provided is increased slug efficiency through better maintenance of pressure under the slug and decreased fall back as the slug passes up the tubing. By using multipoint injection, wet-gas gradients have been reduced to about 30 psi/1,000. This has reduced bottom-hole operating pressure and given a production increase. The ASC valve is not a simple device. It&apos;s operation is difficult to understand, and it must be understood to be used efficiently in gas-lift design. Operating problems are difficult to diagnose—whether they be caused by the fluid lifted, valve malfunction, lift gas rate, or operating pressure. Calculations and reasoning are required to find out what is causing the problem. Inherent in the ASC valve is the inability to create large pressure differentials across a slug. Large differentials may be required to overcome the inertia of very viscous fluid as it is being accelerated in the bottom of the hole. This is tied back to the design of the unloading valve and is one reason for the importance of setting the unloading valve for the highest possible operating pressure. ~u; to the narrow spread the ASC valves provide, it is impossible to cycle slower than about 24 cycles/day on choke control. If small production of 150 BOPD and less is expected, a surface time-cycle controller will be required if the most economical operation is to be achieved. To achieve a satisfactory operation, the operator must keep a record of any changes made in the operating pressure of the ASC valves. Anything which may cause changes in casing pressure in excess of the stabilizer setting will change the valve operating pressure, and if this is not noted from daily inspection of the well casing-tubing pressure recorder charts, the operator will lose control of the well. Significant results can be achieved using ASC valves; however, considerable knowledge is required to design with them, and attention to detail is required for satisfactory field operation.

Jan 1, 1965

By G. W. White

Over the past several years, the steady progress of gas lift from a mysterious art into a developing science has been traceable through the many fine papers that have appeared in Journal of Petroleum Technology. Consequently, this magazine has rightly become a standard for the serious students of gas lift all over the world. The following discussion is offered in a sincere attempt to accurately present certain topics covered in the subject paper in the light of acknowledged state of the art procedures. INSTALLATION DESIGN The first point to be questioned is the author&apos;s installation design, beginning with Eq. 6. The use of 1,200 psi in the spacing equation instead of the 1,275 psi noted as available seems, at first glance, to be a simple arithmetic error. Upon further examination, it appears evident that both this 75 psi plus the 100-psi safety factor must be subtracted from available kickoff pressure because of conditions imposed by the characteristics of the ASC valve (see Fig. B-1). Pressure-charged valve design is incorrectly penalized by spacing the first valve using only 1,100 psi. The use of such a high back-pressure makes it appear that a typical ASC installation would require no more valves than a comparable conventional valve installation. Using a value of 100-psi tree pressure, the well could be valved to 11,000 ft very conservatively with seven pressure-operated valves, but would still require 11 ASC valves. The use of 400-B/D spacing gradient for a 140-B/D rate is not an accepted practice using precharged valves. The author would have done well to note the advantages to be gained by reducing the 500-psi tree pressure, which is clearly explained by Beadle, Harlan and Brown.&apos; In Step 1 of Part III of the continuous flow discussion, the author incorrectly applies the Poettmann and Carpenter curves.2 Item 2 is an incorrect statement. An excellent reference on this point is the paper by Baxen-dell and Thomas.&apos; VALVE MECHANICS The next topic relates to the mechanics of precharged valves. Eq. 2 for the ASC valve can be used to describe the condition of equilibrium, wherein the valve is closed with opening pending. When this equation is used to determine relative values of casing, dome and tubing pressure with conditions approaching the transition value, some strange results are obtained. The following uses the author&apos;s symbols and values given on page 689. Fig. B-1 shows the condition that exists at the moment an ASC valve has been uncovered during the unloading process (Condition I). The obvious result is a locked condition. The basis for the curve is shown on the figure which includes 1,000 psig casing pressure to uncover the valve. If injection gas is not bled off the casing until the pressure is decreased by an amount exceeding the stabilizer discharging valve pressure, upward adjustment of the casing pressure is mandatory for the valve to open and unloading operations to continue. In Condition I the dome pressure exceeds the casing pressure by 20 psi, and the tubing pressure required to open the valve is 1,212 psig. This tubing pressure would not exist under the assumed conditions. In Condition I1 the casing pressure is increased to the dome pressure, and the tubing pressure required to open the valve is 1,102 psig. It is apparent that the casing pressure must be increased to a value exceeding the dome pressure before unloading operations could continue. In Condition I11 a maximum casing pressure of 100 psi (stabilizer charging valve set pressure) above the dome pressure is reached, and the tubing pressure required to open the valve is 549 psig. The author&apos;s statement after Eq. 5 that "the minimum tubing pressure required to open an ASC valve is equal to the casing pressure at depth less the transition pressure of the valve" is incorrect except for Condition I11 only. Otherwise, the equation is invalid.

Jan 1, 1965

By B. Haimson, C. Fairhurst

A criterion is Proposed for the initiation of vertical hydraulic fracturing taking into consideration the three stress fields around the wellbore. These fields arise from (1) nonhydrostatic regional stresses in earth, (2) the difference between the fluid pressure in the wellbore and the formation fluid pressure and (3) the radial fluid flow through porous rock from the wellbore into the formation due to this pressure difference. The wellbore fluid pressure required to initiate a fracture (assuming elastic rock and a smooth wellbore wall) is a function of the porous elastic constants of the rock, the two unequal horizontal principal regional stresses, the tensile strength of the rock and the formation fluid pressure. A constant injection rate will extend the fracture to a point where equilibrium is reached and then, to keep the fracture open, the pressure required is a function of the porous elastic constants of the rock, the component of the regional stress normal to the plane of the fracture, the formation fluid pressure and the dimensions of the crack. The same expression may also be used to estimate the vertical fracture width, provided all other variables are known. The derived equations for the initiation and extension pressures in vertical fracturing may be employed to solve for the two horizontal, regional, principal stresses in the rock. INTRODUCTION Well stimulation by hydraulic fracturing is a common practice today in the petroleum industry. However, this stimulation process is not a guaranteed success; hence, the deep interest shown by the petroleum companies in better understanding the mechanism that brings about rock fracturing, fracture extension and productivity increase. Geologists and mining people became interested in hydraulic fracturing from a different point of view: the method may possibly be employed to determine the magnitude and direction of the principal stresses of great depth. Numerous articles in past years have dealt with the theory of hydraulic fracturing, but they all seem to underestimate the effect of stresses around the wellbore due to penetration of some of the injected fluid into the porous formation.1-4 Excellent papers on stresses in porous materials due to fluid flow have been published5,6 but no real attempt has been made to show the effect of these stresses in the form of a more complete criterion for vertical hydraulic fracturing initiation and extension. This paper is such an attempt. ASSUMPTIONS It is assumed that rock in the oil-bearing formation is elastic, porous, isotropic and homogeneous. The formation is under a nonhydrostatic state of regional stress with one of the principal regional stresses acting parallel to the vertical axis of the wellbore. This assumption is justified in areas where rock formations do not dip at steep angles and where the surface of the earth is relatively flat. This vertical principal regional stress equals the pressure of the overlying rock, i.e., S33 = —pD, where S33 is the total vertical principal stress (positive for tension), p is average density of the overlying material and D is the depth of the point where S33 is calculated. The wellbore wall in the formation is considered to be smooth and circular in cross-section. The fluid flow through the porous elastic rock obeys Darcy&apos;s law. The whole medium is looked upon as an infinitely long cylinder with its axis along the axis of the wellbore. The radius of the cylinder is also very large. Over the range of depth at which the oil-bearing formation occurs, it will be assumed that any horizontal cross-section of the cylinder is subjected to the same stress distribution, and likewise that it will deform in the same manner. STATE OF STRESS PRIOR TO DRILLING OF WELLBORE At a depth D from the earth surface within the oil-bearing strata, it is assumed that the following are 1References given at end of paper.