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By John C. Martin

The discovery of a new gas reservoir demands that the planning of a sottnd well-spacing program be initiated early in the development stage. It is the purpose of this discussion to illustrate by actual field examples the application of basic well-spacing principles, previously developed for oil reservoirs, to the problem of well spacing in natural gas fields. These studies are presented for the field use of geologists and engineers who are concerned with the initial planning of the proper development of the newly discovered gas reservoir. INTRODUCTION The phenomenal growth of a vigorous natural gas industry emphasizes the increasing importance of natural gas as a source of energy, fuel, and raw materials to our nation's economy. Since 1945 marketed production of natural gas for the U. S. has increased 21/2 times to a record high of 10.6 trillion cu ft during 1957. As major participants in the gas industry, we share an added interest to develop and produce our natural gas reserves with constantly improved efficiency. The subject of well spacing is vitally important to the gas industry, for the well itself plays a significant role in the development of the natural gas reservoir and in control of the recovery process. Maximum utilization of wells is an integral part of sound conservation practices. The discovery of a new gas reservoir demands that careful choice of well location and well spacing be made and that the planning of a sound well spacing program be initiated early an the development stage. With the drilling of the first development well, efforts of the geologist and engineer must be directed toward acquisition of adequate technical evidence upon which a firm recommendation for a spacing program may be based. With this technical appraisal as a foundation, operators and state regulatory agencies jointly can go far in providing a framework for sound development of gas fields to achieve a program of conservation that avoids the unnecessary well. WELL-SPACING CONCEPTS Through laboratory and field investigations of the mechanism of the recovery of oil and gas, of fluid behavior, and of effective control of reservoir and well, a crystallization of ideas regarding reservoir behavior has emerged as a well-developed technology. Associated with a better understanding of the fundamental principles underlying reservoir and well behavior has been the growth of concepts concerning the role of wells and their spacing in the development and operation of an oil or gas reservoir. In addition to serving as outlets for the withdrawal of fluids from the reservoir, wells are recognized as having two other important functions: (1) providing access to the reservoir to obtain information concerning the characteristics of the reservoir and its fluids, and (2) serving as a means by which the natural or induced recovery mechanism may be effectively controlled. Beyond a minimum number of wells required to fulfill these two functions, additional wells will not increase recovery. With particular emphasis upon well spacing in oil reservoirs, many studies of the well spacing-recovery relationship have evolved the concept that the ultimate oil recovery is essentially independent of the well spacing.' These fundamental concepts are no different when regarding the role of wells and their spacing in the natural gas reservoir. They are equally applicable to the consideration of well spacing in gas reservoirs. For the gas reservoir, the problem of well spacing then revolves around the question of drainage and the degree or extent to which a well may drain gas from its surrounding reservoir environment. Theoretical and Experimental Work During the past 30 years, theoretical and experimental work carried on to study the physical principles involved in the flow of fluids through porous media has shed light upon the matter of drainage. Fundamental mathematical equations have been derived to describe the mechanism of flow of oil and gas through porous rocks. With the recent advent of high-speed digital computers, attempts have been made with mounting success to develop solutions, employing numerical techniques, to mathematical expressions that describe more rigorously the physical behavior and mechanism involved in the unsteady-state flow of compressible fluids, such as a gas, through porous rock. In 1953, Bruce, Peace-man, Rachford and Ricez published a stable numerical procedure for solving the equation for production of gas at constant rate. The results of these calculations are significant with respect to this matter of drainage, for they indicated (1) that depletion of the gas reservoir resulted in a drop in pressure at the extremity of the

By John P. Dolan, Charles A. Einarsen, GiIman A. Hill

his paper discusses how the following formation characteristics can be determined mathematically from drill-stem test pressure charts: true formation pressures, effective permeability of the entire section tested, well productivities, wellbore damage, and possible detection of barriers (faults, pinchouts, etc.). This paper also presents a practical method for im-mediate determination of eflective permeability and well-bore damage from successful double shut-in pressure tests. A list of recommendations for improving the reliability of drill-stem rest pressures is also presented. INTRODUCTION A drill-stem test is a temporary completion designed to sample the formation fluid and to establish the possibility of commercial production. Early pressure recording devices were used merely to verify proper operation of the testing tool. Until recently the accuracy of the pressure gauges has been insufficient for any reliable quantitative use of the recorded pressures. In view of the need for more reliable formation evaluation and as a result of the recent interest in exploration work employing the concept of hydrodynamic en-trapment,1,2,3,4 better pressure recording gauges are now in use. These devices can record pressure within 1 per cent above 1,000 psig and can detect differential pressures as low as 1/2 psig. In addition to formation pressure, several other reservoir characteristics can be determined from DST charts; namely, well productivity, formation permeability, wellbore damage, and the possible existence of bar- riers (faults, pinchouts, changes in permeability, etc.). This paper presents a practical method to interpret DST pressure charts for formation pressures and many other reservoir properties, a method that has been developed in analyzing approximately 4,000 DST charts during the last five years. The techniques used are a composite of published articles on drill-stem testing5,6, together with well-known pressure build-up analysis methods. THEORY It has been shown7,8 that the following equation may be used for analysis of pressure build-up curves: Po - Pw = 162.6 qu/kh log ( to + ?/?) .....(1) When this equation is applied to the curves obtained in drill-stem testing, the assumptions and boundary con-ditions are more nearly realized than in conventional flow and build-up tests on producing wells. Zak and Griffen9 have recently discussed in detail the use of this equation in analyzing DST charts. One of the problems with DST curves is the lack of reservoir data for precise analysis. Therefore, it is necessary to develop empirical rules and field methods for analyzing DST charts in quantity. For this reason, the empirical methods presented in this paper have been developed, and their derivation is found in Appendices A and B. METHOD USED FOR ACCURATE READING OF DRILL-STEM TEST CHARTS In order to apply the pressure build-up theory to DST charts, it is necessary to obtain a digitized expression for the pressure and time data recorded by the pressure gauge. These data may be either provided by the service company or interpolated by projecting a

Jan 1, 1958

By J. R. Jargon, H. K. van Poollen

Non-Newtonian fluids may be injected into a reservoir during secondary recovery operations. The non-Newtonian fluid used in this work is a power-law type of fluid that is, the viscosity of the fluid decreases as the flow rate or rate of shear increases. This paper presents equations for steady-state linear and radial flow of such fluids, transient behavior results from a finite difference model of a radial system, and transient behavior results from a field test. The equations that describe the flow of a non-Newtonian fluid are non-linear and are solved numerically. Finite difference solutions are presented as curves of dimensionless pressure drop at the wellbore us dimensionless time for a constant injection rate. Solutions were obtained for 5-percent, 10-percent and 100-percent PV of a non-Newtonian fluid for injection rates of 1, 10, 100 and 1000 cc/sec and for a 5 percent PV of non-Newtonian fluid located at T = Tw' 3, 10, 20, 50 and 100 ft for a flow rate of 1 cc/sec. The buildup curves do not exhibit a stmight-line portion as is the case for Newtonian flow through porous media. Correlations also are shown for the productivity index vs rate for the computer model study and the field tests. INTRODUCTION During various secondary recovery operations non-Newtonian fluids are injected. Such fluids, in general, include thickened water and gelled fluids. The term "non-Newtonian" implies that the viscosity is not only dependent upon temperature and pressure, but also on the rate of shear that is applied to the fluid. For example, water, which is a Newtonian fluid, will have essentially the same viscosity no matter what rate of shear is applied. A pseudo-plastic fluid exhibits a decreasing viscosity when higher rates of shear are applied; a dilated fluid has an increasing viscosity with increasing rates of shear. The objective of studies performed and described in this report is to obtain relationships and mathematical and empirical descriptions of the flow of non-Newtonian fluids through porous media. Simple mathematical relationships, computer studies that include the unsteady-state behavior of such fluids, and field tests are used. PREVIOUS LABORATORY STUDIES Laboratory studies have been performed by several investigators. The fluids used in one investigationl were surfactant-stabilized dispersions of water in hydrocarbons. Its Fig. 6 is reproduced as our Fig. 1. This effective-viscosity vs frontal-velocity diagram shows that this fluid is of the power-law type over a fairly large range of frontal velocities. Gogartyl developed an equation for the effective viscosity as a function of shear rate that reduces to Eq. 2 for frontal velocities greater than about 2 ft/D. The fluid characteristics used in the present study are similar to those reported by Gogarty. Christopher and Middleman2 performed experiments with power-law fluids flowing through pipes packed with glass beads. They used a modified Blake-Koteny

Jan 1, 1970

By William Hurst

Muskat's depletion performance equation is here derived considering the expansion behavior of the reservoir hydrocarbon system and a simple fractional-flow equation. This nietkod of derivation leads logically to the two extensions that follow. The first of these is concerned with gravity segregation in a depletion-drive reservoir. The second is concerned with including an empirically determined tern? for water influx in the performance equation. The more general equation for gravity segregation when there is a primary gas cap and empirically-determined water influx is stated for completeness. These equations have been found useful in reservoir performance calculations in Eastern Venezuela. A discussion on the methods of solving these equations follows, and considers firstly the effect of taking finite intervals in the numerical integration, and sec-ondly, methods of incorporating the time functions involved in segregation in with the expansion behavior. The paper concludes with a brief general discussion on further extensions to the depletion performance equation. INTRODUCTION The two fundamental sources of energy by which oil is produced from a reservoir result from pressure depletion inside the boundaries of the reservoir and fluid encroachment across the boundaries of the reservoir. The wells in either case form low pressure outlets through which oil and gas may be produced by the expansive force of the reservoir fluids and associated encroaching fluids. When the reservoir pressure is higher than the bubble-point pressure of the oil, so that there is no free gas in the reservoir, these expansive forces are the only ones available for the production of oil. However, when the reservoir pressure is less than the bubble-point pressure of the oil, free gas is vaporized as the pressure falls. With both oil and free-gas phases present, the additional forces of gravity and capillarity may operate on the gas-oil system, as they have previously operated on the oil-interstitial water system. Gravity tends to segregate the free gas from the oil due to their density difference. Capillarity opposes and eventually balances gravity as the more extreme free gas and oil saturations are reached, preventing the independent move- ment of free gas until it is above a certain saturation, and the independent movement of oil when it is below a certain saturation. The type of depletion performance equation chosen for predicting the future performance of a reservoir depends on the amount of past history available. When the reservoir is somewhere past the halfway mark in depletion, some form of decline curve is often used. With less past history, material balance equations which incorporate empirical factors based on the past performance are often used. When, however, the amount of past history is small, the Muskat depletion performance equation will usually be used. The distinguishing feature of this type of equation is that empirical factors based on the over-all or macroscopic reservoir behavior are almost or entirely absent. Each parameter affecting the reservoir performance is ascribed an independent set of values based on measurements made on laboratory samples; that is, incorporating microscopic empirical factors. In establishing Muskat-type depletion performance equations, it is necessary to consider the reservoir as consisting of a number of associated blocks, in each of which the saturations and pressures may be considered uniform, and in each of which all substances have uniform pressure-volume characteristics. Thus, a primary gas cap can usually be considered as one block and an aquifer as another. Gravity segregation may be negligible for practical purposes when the rock and oil properties are adverse and/or the dip or thickness of the reservoir is too small. In this case the whole oil leg may be considered as one block, except in very large reservoirs. In very large reservoirs the fluid and rock properties may vary enough, particularly in the dip direction, for it to be necessary to divide the oil leg into a number of blocks, in each of which the relevant quantities may be considered uniform. When gravity segregation of the oil and free gas is not negligible, it is necessary to consider the space occupied by the initial oil leg as divided into two blocks, a secondary gas cap and an effective oil leg, in each of which saturations may be considered to be uniform. The total volume of these two blocks is thus constant, but the secondary gas cap grows continuously at the expense of the oil leg. Muskat1 derived depletion performance equations for the basic case of an oil reservoir with closed boundaries and without segregation, and for the case of an oil

By J. C. Melrose

The contact angle is one of the boundary conditions for the differential equation specilying the configuration of fluid-fluid interfaces. Hence, applying knowledge concerning the wettability of a solid surface to problems of fluid distribution in porous solids, it is important to consider the complexity of the geometrical shapes of the individual, interconnected pores. As an approach to this problem, the ideal soil model introduced by soil physicists is discussed in detail. This model predicts that the pore structure of typical porous solids will lead to hysteresis effects in capillary pressure, even if a zero value of the contact angle is maintained. The model is generalized to situations in which the contact angle takes on values between zero and 40 degrees. For the imbibition branch of the capillary- pressure function, the model predicts a considerable departme ftom the usually assumed cos 0 relationship. In fact, according to the model, it is possible that a displaced wetting phase will not be able to reimbibe, even when the contact angle does not exhibit hysteresis. INTRODUCTION The subject of capillarity in porous media has long been of interest in many branches of engineering and applied science. The earlier investigators were those concerned with the physics of soils. 1-5 More recently, petroleum engineers and others dealing with the problems of petroleum production from reservoir rock have given much attention to the subject.6-10 Also, important additions to the literature of capillarity have been contributed from the field of chemical engineering.11-12 These attest to the wide range of industrial applications in which capillary phenomena play a role. The present paper is concerned with the role which wettability plays in capillary action in porous media. As is well known, capillary-rise (or capillary pressure) phenomena have frequently been interpreted with the aid of a model employing the concept of a cylindrical capillary tube. This approach has enjoyed a certain degree of success in correlating experimental results.13 The generalization of this model, however, to situations which involve varying wettability, has not been established and, in fact, is likely to be unsuccessful. In this paper another approach to this problem will be discussed. A considerable literature relating to this approach exists in the field of soil science, where it is referred to as the ideal soil model. Certain features of this model have also been discussed by Purcel114 in relation to variable wettability. The application of this model, however, to studying the role of wettability in capillary phenomena has not previously been attempted in detail. In the present paper, additional features of the model are introduced. These features are critical in determining the quantitative behavior of the model. GENERAL FEATURES OF CAPILLARY HYDROSTATICS BASIC PRINCIPLES When the interstices of a typical porous solid are occupied by two or more immiscible fluid phases, the fluids are microscopically commingled. Hence, fluid-fluid interfaces are found within a certain fraction of the pore openings. The fundamental equation of capillarity specifies the configuration of these fluid-fluid interfaces. This is known as the Laplace equation, when derived from mechanics, and as the Gibbs-Kelvin equation when derived thermodynamically.15 Given two fluid phases, a and ß, in hydrostatic equilibrium, the Laplace equation states that the respective fluid pressures in regions close to the interface are related by Here oaß is the surface or interfacial tension and rl and r2 are the principal radii of curvature of the surface or interface. The pressure difference, Pa-Pß, is the capillary pressure, PC. As Buff15 has shown, Eq. 1 states the condition for hydrostatic equilibrium within the two-phase confluent region, which is referred to as the interface. It thus can

Jan 1, 1966

By T. G. Richardson, F. M. Perkins

In the recent paper of Richardson and Perkins entitled "A Laboratory Investigation of the Effect of Rate on Recovery of Oil by Water Flooding,"' the authors found very little appzrent effect on oil recovery of having free gas saturation present prior to water flooding in unconsolidated sands. We agree that the effect in this particular system was small but do not feel that the data presented should be regarded as disproving work of others which has shown an appreciable effect. The authors do not make such a claim, but neither do they advance an explanation of the difference. In our experience the following factors must be carefully considered when studying the relation between residual oil saturation after water flooding and initial free gas saturation: (1) the magnitude of the inherent residual oil saturation, i.e., the residual oil saturation with no free gas; (2) the increase in oil-water viscosity ratio with pressure lowering if the gas saturation is obtained by solution gas drive; and (3) the oil shrinkage which occurs with pressure lowering and gas evolution. The system studied by Richardson and Perkins gave residual oil saturations as low as 20 per cent without free gas present, and one should perhaps not expect much further lowering. As an illustration of the magnitude of the effect when the residual oil saturation is inherently higher we submit the accompanying figure. These data were obtained on an unconsolidated sand under elevated pressure in a system similar to the one described by Richardson and Perkins. Gas saturation was established by gas drive before water flooding. The viscosity ratio was 600:1 under the conditions of the displacement. Here the gas was extremely effective in reducing residual oil saturation. This fact was also indicated by Kyte, et al.2 Their plots of residual oil saturation vs initial gas saturation show trends of greater free gas effect with higher oil viscosities. The pressure-dependent effects were not discussed by Richardson and Perkins. They should be separated from the free gas effect if the objective of the study is a correlation of residual oil saturation vs initial free gas saturation. The increase in oil viscosity when gas is released from solution tends to increase residual oil saturation. This effect is rather small in the viscosity range of kerosene. A Buckley-Leverett calculation, assuming an increase in viscosity ratio from 1.2 to 1.8, indicates an increase in residual oil saturation of about 1 per cent of pore volume. Thus, one would expect this system, if operated at constant viscosity ratio, to show a slightly greater free gas effect. As Dyes- as shown, oil shrinkage can offset the beneficial effect of free gas on waterflood oil recovery, if the gas saturation is established by depletion. Since

Jan 1, 1958

By Charles R. Stewart, William W. Owens

Reservoir performance predictions based on laboratory core test data assume that fluid flow is laminar for the laboratory test. A study has been made to determine the validity of this assumption for laboratory tests on various types of porosity found in producing limestone formation. Data are presented which show that turbulence and slippage can occur during laboratory tests on hetero-geneous-type porosity limestones, thus causing serious errors in measured single-phase permeabilities and two-phase relative permeability characteristics. In single-phase flow tests it is possible to eliminate turbulence and correct for slippage or to eliminate both factors by controlling test conditions. It is not always possible to control test conditions and thereby eliminate turbulence and slippage in two-phase .flow tests. A correction method is presented which can be used to calculate the true two-phase laminar flow relative permeability characteristic even though furbulence and slippage exist. .INTRODUCTION It is customary to make use of Darcy's law and modifications of this law, together with laboratory data on formation core samples to predict the performance of producing reservoirs. Such predictions are based on an assumption that fluid flow is in the laminar or streamline region for the laboratory test. It was the purpose of this inves- tigation to determine the extent to which turbulent flow may occur in laboratory fluid flow tests on hetero-geneous porosity limestones. Considering that turbulent flow conditions might exist in some laboratory fluid flow tests, additional emphasis was placed on the development of a method to correct for turbulence when laminar flow conditions could not be attained. FLUID FLOW CONCEPTS FOR POROUS MEDIA The Influence of Pore Geometry on Fluid Flow One of the more important factors influencing fluid flow in porous media is the geometry of the pore space which includes such characteristics of the pores as size, shape, distribution, roughness, uniformity, etc. In general, oil- and gas-producing formations can be divided into two broad types on the basis of pore geometry. One has been called sandstone-type porosity media, which is characterized by a small range in pore size, uniformity in shape of the pores, smooth pore surfaces and a regular and uniform distribution of pores. The other type has been called heterogeneous porosity media and is usually limited to the dolomites and limestones. This type is characterized by a wide variation in the size, shape, and distribution of the pores and rough, irregular pore surfaces. It is therefore apparent that conditions are much more favorable for turbulent flow* in heterogeneous-type porosity media than in sandstone-type porosity media. Interrelationship Between Turbulence and Gas Slippage In studying the problem of turbulent flow in laboratory tests on porous media, it is necessary to be aware of the interrelationship between slippage and turbulence for gas flow. As a result of slippage or the Klinken-berg effecta, apparent perrneabilities to gas are greater than the true value because there is no stationary layer of gas in contact with the walls of the flow channels. Gas slippage decreases as the mean free path of the gas molecules decreases. Since the mean free path of any gas decreases with increasing density, increases in static pressure result in lower apparent gas permeabilities. However, a reduction in gas permeability can also be due to turbulence. Therefore, in studying only turbulent flow in porous media, it is necessary to hold gas density, and slippage, constant or to reduce slippage to a negligible value by operating at high static pressures. Presentation of Laminar and Turbulent Flow Data A graphical relationship between permeability and a pseudo-Reynolds number, N,, will be used to show the two types of fluid flow, i.e., laminar and turbulent. The usual graphical method for such a description has been the use of friction factor-Reynolds number charts4. On such a logarithmic diagram, the laminar region appears as a straight line having a slope of 45 degrees. As the friction factor decreases and the Reynolds number increases, the turbulent region is reached and appears as a deviation from the 45-degree slope line. However, in petroleum engineering literature resistance of por-

By R. C. Hassinger, D. V. von Rosenberg

Transverse dispersion has received considerably less treatment in the literature than has longitudinal dispersion. Different methods for determining transverse dispersion coefficients have been used in different investigations, and the results obtained have not been consistent enough to permit accurate generalizations as to the effect of various physical parameters on the magnitude of these coefficients. A numerical solution to the differential equation describing transverse dispersion in the absence of longitudinal dispersion was obtained to enable one to calculate the dispersion coefficient from experimental results. The more general dispersion equation including longitudinal dispersion also was solved numerically to give quantitative limits of a dimensionless group within which the assumption of negligible longitudinal dispersion is justified. Possible experimental procedures were examined, and one utilizing a cylindrical packed column was chosen for the determination of transverse dispersion coefficients. Values of these coefficients were determined for a system of two miscible organic fluids of equal density and viscosity, for two sizes of packing material over a wide range of flow rates in the laminar regime. The dispersion coefficient was found to decrease, for a constant value of the product of packing size and interstitial velocity, as the size of the packing material particles increased. INTRODUCTION Longitudinal dispersion has received extensive treatment in the literature, and consequently is better understood than its orthogonal counterpart, transverse dispersion. Many mathematical models of dispersion processes assume that transverse dispersion is rapid enough to damp out any radial** concentration gradients and therefore may be neglected. Laboratory and production results, however, indicate that this is a poor assumption.l,2 Various experimental procedures for determining transverse dispersion coefficients have been used in previous investigations, but the results have generally been expressed by similar correlations. The transverse dispersion coefficients obtained, however, have often varied considerably for given values of the correlation parameters. We feel that further experimental determinations of transverse dispersion coefficients will help alleviate some of the inconsistencies in these empirical correlations. One assumption implicit in all previous investigations is that of negligible longitudinal dispersion in the experimental system. An attempt to justify this assumption often is made using intuitive reasoning, but it is apparent that this reasoning must break down as the condition of zero flow rate is approached. A mathematical examination of the equations describing the system yields physical limits outside of which the assumption of negligible longitudinal dispersion is invalid. BACKGROUND In a porous medium, the "effective molecular diffusivity" De is less than the molecular diffusivity D measured in the absence of a porous medium, due to the tortuous path which a diffusing molecule must travel. Various authors3-5 have reported values of the ratio De/D in the range of 0.6 to 0.7. When there is fluid flow within the porous medium, mass transfer occurs by convective dispersion as well as by molecular diffusion. These are separate phenomena and can be treated as such on a microscopic scale. However, the mathematical complexity is such that only extremely simple geometries could be considered, and the results hardly would be applicable to the complex geometries existent in actual porous media. A more

Jan 1, 1969

By P. van Meurs, C. van der Poel

From observations of the linear displacement of oil by water from a porous medium as visualized in transparent models, new insight into the mechanism of vircous fingering, as occurring in the case of unfavorable oil-water viscosity ratios, has been obtained. A mathematical description of the observed phenomena leads to formulas. expressing both oil production and pressure drop across the formation as a func-tion of cumulative water injection with the oil-water viscosity ratio as a parameter. Theoretical results are compared with those obtained from scaled laboratory experiments in sand-filled rubes in which water was injected at the one end and production was obtained from the other end. In the second part of the paper the same principles are used to calculate a more realistic production scheme in which production of oil and water is obtained from wells regularly distributed over the field. Results show satisfactory agreement with production data of an actual oil field. Application of the theory is extremely simple as only a limited number of readily available parameters have to be known and results are presented in an analytical form. INTRODUCTION When oil is displaced from a porous medium by water having a viscosity lower than the oil. the oil-water interface is essentially unstable and has the tendency to break up into what are called "fingers" or "streamers". This Viscous fingering has been noted before by Engelberts and Klinkenberg' and has recently been demonstrated in transparent models by van Meurs-. It is highly questionable whether it is at all possible to perform relative permeability measurements In the laboratory reproducing the same distribution of water and oil in the cores as Present in practice. Therefore, we based our descriptive theory on an idealized model which was "tailored" to the fingering mechanism as observed in transparent models under scaled conditions. This approach was the more attractive, as a highly simplified model had already yielded an adequate description of the process. Though we are aware our theoretical approach can be extended in several ways, it is given here in its simplest form to explain the fundamental principles and to avoid complicated formulas. SIMPLEST CASE OF A LINEAR DRIVE Observations and Theoretical Model In Fig. 1 a series of photographs shows how water penetrates into a formation saturated with an oil which is considerably more viscous than the water. The technique for obtaining these photographs, using transparent models, has already been described?. The fingers can be clearly observed and are seen to be mainly parallel to the flow direction. Note that the contours of these fingers are not smooth but show protrusions of water enclosing oil pockets.

By J. G. Richardson, J. W. Graham

The purpose of this paper is to present the results of theoretical and experimental studies of water imbibition. The imbibition processes are involved in recovery of oil from stratified and fractured-matrix formations in natural water drives and water flooding. An understanding of the role of inhibition in implementing the recovery of oil from such formations is deemed essential to proper control of these reservoirs to achieve maximum recovery. The theoretical studies involved development of the differential equations which describe the spontaneous imbibition of water by an oil-saturated rock. The dependence of the rate of water intake by the rock on the permeability, interfacial tension, contact angles, fluid viscosities and fluid saturatiorls is discussed. A few experiments were performed using core samples to determine the effects of core length and presence of a free gas suturation. The role of water imbibition in recovery of oil from a fractured-matrix reservoir by water flooding was investigated by use of a laboratory model. This model was scaled to represent one element of a frac-tured-matrix formation. Water floods were made at various rates with several fracture widths. Interpretations were made of the behavior expected in a system containing many matrix blocks. The presence of a free gas sntu.ration was found to reduce the rate of water imbibition. In the reservoir prototype of the fractured-matrix model, water imbibition rather than direct displacement by water was the dominant mechanism in the recovery of oil at low rates. INTRODUCTION Imbibition may be defined as the spontaneous taking up of a liquid by a porous solid. The spontaneous process of imbibition occurs when the fuid-filled solid is immersed or brought in contact with another fluid which preferentially wets the solid. In the process of wetting and flowing into the solid, the imbibing fluid displaces the non-wetting resident fluid. Common examples of this phenomenon are dry bricks soaking up water and expelling air, a blotter soaking up ink and expelling air and reservoir rock soaking up water and expelling oil. As increasingly better lithological descriptions have been made of the characteristics of petroleum-bearing formations, it has become obvious that imbibition phenomena which were once considered laboratory curiosities are of practical importance. For instance, in reservoirs composed of water-wet sand strata of different permeability in intimate contact, the tendency of water to channel through the more permeable stratum is offset by the tendency for water to imbibe into the tight sand and expel oil into the coarse sand. Also, in fractured-matrix formations the tendency of water to channel through the fractures is offset by water-wet matrix blocks. As some imbibition of the water into the of the largest fields in the world are fractured-matrix reservoirs, it has become increasingly important to understand all the factors involved in the imbibition process. Examples of fractured-matrix reservoirs are the Spraberry field in West Texas which produces from a fractured sandstone', the giant Kirkuk field in Iran', the Dukhan field in Qatar, Persian Gulf2, and the Masjid-I-Sula-main and the Haft-Kel fields in Southwestern Iran, which produce from fissured limestone3. Research into recovery of oil from fractured-matrix formations was stimulated by the rapid decline of oil productivity of wells in the Spraberry formation. One result of this research was the water imbibition process developed by the Atlantic Refining Co.4 Another idea was that much of the Spraberry oil could be recovered by conventional water-flooding procedures5. Subsequently, pilot floods were conducted in this field to test the feasibility of these ideas. It was felt that an understanding of the role played by imbibition processes in displacement of oil from a fractured-matrix reservoir could not be obtained from field data alone because of the many complicating factors and uncertainties involved. Therefore, theoretical and laboratory studies were undertaken to provide this understanding. Study of the equations which describe the linear, countercurrent imbibition process provided an insight into the role of various factors in the process, such as the permeability of rock and inter-facial tension. In addition to the theoretical studies, imbibition experiments were conducted with core samples to determine the effect on the rate of imbibition of such variables as core length and free gas saturation. The principal experimental studies were conducted by water flooding a scaled model of an clement of a frac-tu red-matrix reservoir to evaluate

By P. E. Baker

An experimental study of heat flow in steam flooding was carried out with steam displacing water in a plane-radial fluid-flow model. Temperature distributions in the model reservoir, overburden, and substratum were measured at frequent intervals during flooding by means of a fixed array of thermocouples. Heat losses to overburden and substratum and the division of heat between the steam and hot-water zones in the reservoir were calculated from the temperature data by performing numerical integrations over the appropriate volumes. Temperature profiles and heat distribution results are presented. Some results were (1) the fraction of injected heat that is lost to overburden and substratum, when expressed as a function of time, did not depend on injection rate; (2) a significant portion of the injected heat was contained in the hot-water zone ahead of and underlying the steam front in the reservoir. The division of heat between the steam and hot-water zones did depend on injection rate; and (3) considerable gravity override was observed. The experimental results are compared with those of several published theoretical studies of heat transfer in hot-fluid injection; approximate agreement on heat losses is found with some of the most idealized theories. A valid comparison cannot be made in regard to steam us hot-water zone; basic interpretation of the hot-water zone, in terms of a vertical steam front, is clouded by gravity override in the experiments. INTRODUCTION The experimental study reported here primarily concerns two problems of heat transfer in steam flooding that have economic and engineering importance. These are (1) the fraction of injected heat lost to the overburden and substratum, and (2) the division of the remaining heat between a zone containing steam and a zone of hot water at lower-than-boiling temperature. The volume of the steamed region, which has a direct effect on oil recovery, can be calculated readily from these results. Several valuable theoretical studies have been published on this problem, but no experimental tests of the theories have previously appeared. Tests were needed because the effects of the necessary simplifications in the theories could not be determined otherwise. The basic, untested theoretical problem is the effect of "decoupling" heat and mass transfer, and the resulting inability to include the effects of heat transfer and condensation on fluid flow. The theoretical problem solved so far has been a heat transfer problem in which fluid is present as a heat carrier and flows in a stipulated manner, either linear or plane-radial. The simplifications that have sometimes been made in regard to thermal conductivity by, for example, Marx and Langenheim,l Lauwerier2 and Thomas3 apparently do not have an important effect on heat loss calculations, although the results of the different methods disagree to a certain extent, as shown by Spillette4 and by Ramey.5 A recent paper by the author6 compared the results of experiments in hot-water flooding with several theoretical results and showed a rather poor agreement. It will be seen that the experimental heat loss results for steam flooding, however, show acceptable agreement. These comparisons are discussed in a later section. EXPERIMENTAL APPARATUS AND PROCEDURE The system studied was one in which a sand pack, initially water saturated and at a uniform temperature, was flooded with steam at a constant rate and temperature. The temperature distribution in the "reservoir" and adjacent "strata" was measured with an array of thermocouples, and heat losses were determined from these measurements. The sand pack contained no oil because the only concern of the experiments was heat flow, and it was important to have the flow pattern as simple

Jan 1, 1970

By N. L. Hancox

Previous researchers have used the cutting and rejoining model to represent a porous body when attempting to place Archie's law on a theoretical basis and calculate rock permeabilities (F = Ø-m, where F = formation factor, = - porosity and m = a constant). In using the model, a porous solid is assumed to consist of sections with parallel sides containing straight. continuous pores of total porosity 4 (pore to total volume or, for a homogeneous body, pore to total area). The joining of pores at an interface between two sections is assumed to be random which results in a common pore area Ø2. This reduced area Ø2 is then taken as that area which limits electrical conduction or fluid flow in the body. Agreement between experimental results and results calculated using a model is not always good Because of this, various modifications of the model are presented — for instance, the random nature of the joining is questioned. Formation factor measurements on specially constructed porous specimens are described in this paper. it is concluded that the common pore area limits flow completely only if sections containing straight pores are very thin, and that, in most natural materials, the common pore area at an interface must be greater than that given by random joining. However, the model is still useful in permeability calculations, provided that the fractional area limiting flow is determined from formation factor measurements. INTRODUCTION Two important properties of porous media are permeability k, which describes the ease with which a fluid can flow through a porous medium, and formation factor F, defined as the ratio of the resistivity of a saturated specimen to the resistivity of the saturating liquid which describes the electrical properties of the saturated material. k is defined by Darcy's law,l k= µqL/P Ae . . . . . . . . . . . . . . . [1] where µ = liquid viscosity, q = flow rate, L = length of specimen, p = pressure across the specimen and = - the effective area over which flow occurs, F is given experimentally by Archie's law,2 F = Ø-m ,..............(2) where 4 is porosity defined as the pore to total volume or, for a homogeneous body, the pore to total area; and m lies between 1.3 for loose sand and 2 for cemented sand. Consider a porous body of total cross-sectional area A and length L, saturated with a liquid of resistivity R and with an effective area for conduction of Ae. Then, from the definition of F given previously, F=A/Ae , ................(3) or, from Eqs. 2 and 3, Ae = A Øm ..............(4) Thus, in any attempt to calculate k or F, some assumptions must be made concerning the pore structure of the body and a value derived for A,. To determine Ae, Childs and George3 and Wyllie and Gardner4 suggested an elementary statistical representation often referred to as the cutting and rejoining model of a porous body. The body is assumed to be composed of two or more parallel-sided sections of porosity 4, containing straight, continuous pores with a common pore area of Ø2 at an interface between two sections. The value is given by a random joining of the pores in either section. Two such sections,

Jan 1, 1969

By R. E. Gilchrist, R. F. Nielsen

When a gas is displaced by mother in a porous medium, and there is a relative immobile liquid present. there is a transition zone in which the gas composition varies from essentially that of the original gas to that of the injected gas. The change in extent of this zone with time may be governed by a mixing process in the direction of flow and by the rate of establishment of gas-liquid equilibrium, if the gases are appreciably soluble in the liquid. The relative importance of these two factors in deterri~ining the growth of the transition zone is discussed, with appropriate equations and experimental data. INTRODUCTION The various solution methods of oil recovery involve a transfer of the components of a mixture, whether within a single phase or between a liquid and gas. The similarity of a natural porous medium to systems used in separation and chromatographic processes makes it seem reasonable that certain concepts used by chemical engineers in "mass transfer" might be applicable to petroleum reservoirs. One approach, the HETP (height equivalent to a theoretical plate), involves a distance or length of time over which equilibrium might be con. sidered as established. Another approach involves direct use of a rate of mixing or rate of establishment of equilibrium. The latter approach has been preferred in relation to production problems. DISCUSSION AND PROCEDURE When a gas or liquid in a porous medium is displaced by one of different composition but miscible with it there will be set up a transition zone in which the composition varies from cssentially that of the original fluid to essentially that of the injected fluid. If the fluid being displaced is a gas, and there is a relatively immobile liquid present, the transition zone may be

By R. I. Lahring, C. G. Inks

A surfactant waterflood, using a block copolymer of ethylene and propylene oxide (PLURONIC L64*), wa., started in 1956 in Kansas to determine the commercial feasibility of such a process. The production formation was the Bartlesville sand at a depth of 1,400 ft. Leares in the test area had attained both primary and secondary production peaks, and were on a normal decline when the tests were initiated. The injection wells were taking water at a reasonable pressure and none of the operating conditions were particularly unusual. The leases were selected primarily because of normal operating conditions, and not because of any serious problems demanding remedie>,. Oil production and water injection data were recorded during the 10-year test period, and their compilation indicates that the surfactant resulted in an increase of about 9 percent in secondary oil production. Other benefits derived from the surfactant injection were lower injection pressure that resulted in reduced power consumption and reduced erosion of the pumps; and lower calcium scale buildup. These fringe benefits more than offset the cost of the surfactant used. Introduction During the past several decades, considerable research has been carried out on secondary recovery of crude oil that remains in the producing formation despite the most efficient, current primary production practices. Methods are constantly sought of increasing recovery of oil, while at the same time improving the economic efficiency of operations. One method that has received intensive study over the years is the use of a surfactant as a waterflood additive. Laboratory tests show conclusively that dilute solutions of surfactants remove considerably more oil from uncon-solidated sand cores than does water alone.'- The loss of surfactant by adsorption at solid-liquid interfaces has caused serious doubt that surfactants can be used economically as waterflooding additives. This is especially true with anionic and cationic surfactants, and to a lesser extent with nonionic surfactants. This work was undertaken to determine the effectiveness in increasing oil production by injecting water containing small quantities of a nonionic surfactant. The surfactant selected was PLURONIC L64*, a block copolymer based on ethylene and propylene oxide, having the following structure The selection of the test site, a typical shoe-string sandstone type of field located at Batesville pool, Toronto District of Woodson County, Kans., was made because of its normal primary and secondary recovery operating conditions, and not because of any serious operating problems. When the tests were begun, the field was experiencing the customary post-peak production decline of a waterflood. Using for the tests a field that was on a normal production decline, while maintaining constant all variables other than the addition of the surfactant. was of varamount importance if success or failure was to be attributed to a particular cause. It was reasoned that if a surfactant was added to the injection waters and nothing else was done to influence the oil production or injection of water, the effects of the surfactant on the flood could be determined precisely. Production History The first well in the tested field was drilled in 1935. Gas repressurization began immediately, but it was not until Aug., 1938, that the major portion of the field was developed. During the period of repressurization, 1,700 MMcf of gas was injected. As can be seen from the curves of Fig. 1, the production peak from gas injection was attained in 1937 and a normal production decline followed. Early in 1942, water injection wells were drilled and injection of water Was initiated. The amount of water injected increased as more injection wells were drilled until a peak injection rate of 2,700 BID was reached in

Jan 1, 1969

By O. C. Holbrook, George G. Bernard

A new theoretical treatment has been obtained for the behavior of pattern waterflood injection wells when closed in. Two cases are treated: Case I where oil and water are assumed to have the same properties, and Case 2 where they arc different. In applying the method, one plots log (p — p,) vs closed-in time, where p is well-bore pressure at any tims and p, is static pressure. The value of p. is determined by trial and error as that value which makes the plot linear at large time. A value for the permeability-thickness product can be determined from the intercept of this linear part, and a value of the skin factor from the injection pressure at time of closing in. Application of the method to data from water floods at three fields seems to give reasonable results. For the case of unit mobility ratio, it is proved that this new method should give the same value for permeability-thickness product as the conventional pressure build-up method. In addition, the new method gives correct values for static pressure, whereas the conventional method does not, often indicating negative static pressures. The new method may be used in cases where the surface pressure persists after closing in as well as in cases where it does not. INTRODUCTION It is of considerable interest and importance to be able to determine the characteristics of the reservoir in an area surrounding a water injection well. Thus, if we can determine early in the life of an injection well that there is a considerable "skin effect", remedial measures can be started before a full-scale pattern flood begins. Similarly, if it can be shown that a gradual buildup of skin effect is occurring with time, measures to free the water of plugging material can be taken. Determination of static pressure in the water-injection well may show that the water is entering a thief zone and not the desired reservoir. Finally, determination of the permeability of the sand around the injection well will allow estimation of the future relation between injection pressure and rate. It should be possible to determine average reservoir permeability, skin effect and static pressure from pressure fall-off data. However, at the time we began work on this subject, it was thought that no adequate theory on which to base such determinations' was available. According to the conventional method which considers the reservoir to be filled with one fluid of small compressibility (see Van Everdingen, Joers2, and Nowak2), shut-in pressure is plotted vs log where is injection time, and At is closed-in time. The physical significance of injection time, may well be questioned in this case, since in a reservoir completely filled with a single fluid (as required by this theory) and with input and output rates equal, the pressure behavior after an initial transient is independent of t,. Attempts by our Tulsa area to use this theory led to negative values of static pressure in most cases. Because of these limitations of the method discussed above, it was decided to attempt to develop a new theory of pressure behavior in water injection wells, one which would apply when there is a gas saturation, as is so often the case in water floods. In the following treatment the assumptions and basic equations are given first, then the method of application of the equations. A complete example is given to clarify details of application. All difficult mathematics has been placed in the appendices so that the reader can follow the text without difficulty. However, if he wishes only to apply the results without knowing the basis for them, he can learn how to do this from reading only the sections entitled "Plotting of Experimental Results" and "Example." ASSUMPTIONS AND BASIC EQUATIONS Statement of Problem It will be assumed that a horizontal layer of constant thickness contains in its pore system a mixture of oil, gas and water. While water is being injected into this pore- system through a well at constant rate, an oil bank is built up, gas being expelled from the space taken by the oil as shown in Fig. 1. The saturations within each

By S. C. Jones, J. A. Davis

This paper describes displacement mechanisms of micel-lur solution slugs, displuced by a thickened water "mobility buffer", in a glass micromodel and in consolidated Berea sandstone cores. Colored motion pictures, taken through a microscope, recorded interactions on a pore-to-pore bash in the micromodel. Production and differential pressure data from consolidated cores previously waterflooded to residua1 oil saturation revealed displacement mechani.sm.s macroscopically. Oil is displaced miscibly, while interstitia1 water is displaced immiscibly by the injected micellar. solution slug. Part of this water is dispersed and carried near the lead ing edge of the .slug, and some may remain as a residual saturation. Thickened water displaces any residual water. It also emulsifies with the. slug material, thereby displacing it. The displacement sequence forms banks of oil and water with relatively constant fractional flows, saturations, and mobilities. The mobility of oil and water flowing ahead of the .slug defines .slug viscosity required for stable displacement. Equations are presented that describe. several aspecis of the displacement flow behavior: oil breakthrough, oil cut during production of the stabilized bank, breakthrough of banked water and the resulting decreased fractional flow of oil, fluid mobilities, etc. Breakthroughs, calculated from the equations, are compared with experimental data. Slugs of micellar sollution, ranging from 1 to 5 percent PV, produced unusually high oil recoveries (up to 100 percent) in previously waterflooded consolidated cores. Investigation of the effect of mobility buffer size on oil recovery indicated that recovery is reduced in 3-in. X 4-ft cores for mobility buffer sizes .smaller than 50 percent of the pore volume. Introduction A new oil recovery process,* conceived in 1962, utilizes a slug of micellar solution' that has sufficient viscosity to avoid an unfavorable mobility ratio with respect to the oil and water it displaces. These micellar solutions are composed of hydrocarbons, water, and surfactants, and may contain electrolytes and co-surfactants. The micellar solution is displaced by a "mobility buffer". The mobility buffer is a bank of reduced-mobility fluid, preferably an aqueous polymer solution. The entire system is displaced by unthickened water. This paper describes some of the microscopic and macroscopic displacement mechanisms observed during laboratory development of the fluids for a potential field test. Microscopic phenomena were observed photographically in a specially constructed glass flow model and macroscopic data were taken from constant rate, tertiary displacements conducted in Berea sandstone cores. Qualitative Description of Micellar Solution Flooding This section qualitatively describes displacement mechanisms that occur when a slug of micellar solution is injected into a previously waterflooded core. The slug completely removes oil from the portion of core it contacts, and banks oil in the process. The oil saturation in this bank and the flowing WOR reach definite, fixed values that are determined by water and oil mobilities and slug characteristics. This zone of constant WOR and oil saturation will be called "stabilized oil bank" in the following discussion. When this stabilized bank reaches the outlet end of the core, the oil cut jumps from zero to a constant value equal to the fractional flow of oil. Saline water has little or no solubility in the slug. Because of this. the slug displaces in-place brine immiscibly. During slug injection, most of the brine is displaced ahead of the slug, some is carried along in the leading portion of the slug, and part of the brine may become immobile. The immobile, residual brine is later miscibly displaced by thickened water. Displacement of all the oil and only part of the water during slug injection results in a higher fractional flow of oil ahead of the slug than occurs when all the water is displaced after injection of thickened water is begun. The slug spontaneously emulsifies fresh (low-salt content) water. By emulsification, the slug can become infinitely diluted, and hence totally displaced, by thickened water. Fluid saturations in the core are shown schematically in Fig. 1. Parts A and B show conditions before and after the start of the thickened-water injection, respectively. Since thickened water displaces any residual brine by-

Jan 1, 1969

By D. O. Wyble

Five water-driver fields, for which pressure predictions had been made within a few years after discovery, were re-studied when four to five years of additional pressure and production data became available. It was fortnd that forecasts of the pressure in water-dri~fe reservoirs may be subject to considerable unccrtainty. Predictions car be erroneous when there is insufficient presswe history to define the cllaracteristics of the aquifer, and when there are errors in the pressure, production or geologic data. INTRODUCTION The efficient operation of an oil or gas reservoir requires that the important characteristics of the reservoir be determined soon after its discovery. It is especially desirable to evaluate the pressure-production relationship quickly, for this relationship provides a basis for deducing the type of production mechanism that is operative, and for making pressure predictions. The pressure predictions, in turn, provide a basis for calculating efficient rates of production, determining whether water or gas should be injected, etc. The importance of pressure prediction is such that forecasts should be made as accurate as possible, and the limits of error well defined. Historically, pressure forecasts for some fields have proved very accurate, while for others the forecasts were so erroneous that they resulted in the adoption of wrong, or at best, unnecessary production practices. Pressure predictions made for water-drive fields are especially subject to error. Accurate forecasting for these fields requires that much be known not only about the reservoir proper but about the adjacent water-filled rock as well. The water-containing rock, or aquifer, may extend for many miles, and often there is only meager data regarding its thickness, permeability and porosity. Much of the information must be inferred from the previous pressure behavior of the reservoir. A brief pressure history may provide little information about the characteristics of the aquifer. Hence, pressure predictions made early in the life of water-drive fields can be incorrect. The work described in this paper was done to determine the degree of reliability which can be expected of pressure predictions made within a few years after water-drive fields are discovered. Five fields, for which the original pressure predictions had been based on less than seven years' history, were re-examined with the aid of four to five years of additional pressure data. Where the predictions were inaccurate, the reasons for failure were ascertained. The studies were accomplished by use of the electric reservoir analyzer.' The analyzer was first adjusted to repeat the original pressure-production match using the same values for the various parameters as were used in the original study. Then, the actual production rates experienced during the time elapsed since the initial study were set into the analyzer, and the pressure behavior indicated by the machine for this period was compared with that which actually OCcurred. Where the pressure profile traced out by the analyzer deviated from the observed field behavior, the analyzer was readjusted to obtain a better over-all match. The old and the new solutions were compared to determine the reasons for any differences. COMPARISON OF PREDICTED RESERVOIR PRESSURE BEHAVIOR WITH ACTUAL PERFORMANCE Field A The original pressure-production match is entirely adequate as evidenced by the pressure match of the field's history subsequent to Jan., 1952 (see Fig. 1)'.

By L. Yarborough, L. R. Smith

This paper presents results of a laboratory study of retrograde condensate recovery by revaporization into dry injection gas. Flow tests were performed in 10.6-ft long sand packs at 100F and 1,500 psi. In three runs methane revaporized the liquid from a n-pentane-methane mixture in the presence of immobile water. TWO of these tests were water-wet, and the third was totally oil-wet. In the three runs n-pentane recovery was complete after 2.5 hydrocarbon PV of injection. There was no significant performance difference between the two wettability extremes. In a fourth experiment, a methane-hydrogen sulfide mixture revaporized a synthetic light, sour condensate. No water saturation was present. Equilibrium compositions and volumetric data were obtained for the four-component condensate. The heavy component, n-beptane, was removed after 6 PV production. Comparison of the effluent fluid compositions with known equilibrium data shows that the flowing fluid was equilibrium vapor and that the mixing zone between equilibrium vapor and dry injection gas was short. Data indicated that complete recovery of retrograde liquid occurred after it was contacted by a sufficient quantity of dry gas. INTRODUCTION When pressure declines below the fluid dew point in a gas condensate reservoir, a liquid phase forms. In this process, referred to as retrograde condensation, the quantity of liquid formed is frequently small enough that the liquid is not a flowing phase. To prevent loss of valuable retrograde liquids, the process of dry gas cycling has been employed for several years as a more or less standard practice. In this procedure the reservoir pressure is maintained above the fluid dew point so that the liquid components may be produced as vapor and then separated at the surface. Although full pressure maintenance by gas cycling seems ideal in terms of preventing liquids loss, several factors can reduce the atuactiveness of such an operation. From a study of a condensate reservoir in Alberta, Canada, Havlena et a1.1 con-cluded that cycling under conditions of declining pressure leads to economic advantages and to a high recovery of hydrocarbon liquids. This study considered effects of volumetric sweep efficiency, retrograde behavior of the original wet gas and revaporization characteristics of the retrograde liquid when contacted by dry gas. The first major work concerning revaporization of liquid in a gas condensate system is that of Standing et a1.2 Calculations based upon the PVT behavior of a recombined gas condensate fluid indicated that all retrograde liquid can be recovered if it is contacted by a sufficient quantity of dry gas. The paper considered the effect of variable permeability upon the recovery of retrograde liquid. Standing et al. concluded that recovery of heavier components in the retrograde liquid is greatest if reservoir pressure is allowed to decline below the dew point prior to dry gas injection. Since the work of Standing et al., several laboratory studies have been reported which show that recovery of hydrocarbon liquids by vaporization into dry injected gas can contribute to increased recovery above that obtained by ordinary production practices. Vaporization from retrograde condensate,3 conventional oil4-7 and volatile oil8 reservoirs has been considered. There is little work that deals with revaporization recovery from condensate reservoirs. This study demonstrates that vapor-liquid equilibrium exists when a dry gas is injected into a porous medium containing retrograde condensate; investigates the effect of wettability on revaporization of retrograde condensate; and provides an indication of the amount of dry gas necessary to

Jan 1, 1969

By J. L. Huitt, IM. L. Slusser, E. E. Glenn, M. L. Slusser

This paper is concerned with: (1) an analysis and interpretation of the filtration characteristics of drilling muds on filter paper, and (2) an interpretation of early stage "filtration" on consolidated synthetic porous media, herein referred to as the "surge loss" period. It is shown that water-loss data can be plotted so as to disclose the existence of a surge period, a non-uni-form cake thickness period, and a constant pressure filtration period. The same periods occur during exposure of consolidated porous media to muds. The data on consolidated porous media indicate that: (1) mud particles bridge pores inside porous media during the surge period, and (2) "filter cake" build-up inside porous media occurs during subsequent filtration. The data also show that the surge loss increases with sample permeability and with pressure differential. INTRODUCTION The phenomenon of mud filtrate invasion into porous sands of a drilling well has been recognized for many years.1,2,3,4 Part of API Code 29 is concerned with the filtration testing of a drilling mud to yield data on this subject. In a number of investigations "plastering properties" of muds were studied,5,6,7,8 "plastering" apparently meaning cake forming properties. In such studies the characteristics (thickness, permeability, and toughness) of the cake and the rate at which the liquid phase of the mud was separated from the solids (filtration rate through the cake, commonly referred to as water loss) were measured or at least considered. From the standpoint of its effect on well productivity, filtrate invasion into "clean" water-wet pay sands (i.e., those containing no clay minerals) may not necessarily be a serious problem. An increase in water saturation in the zone immediately around the wellbore would cause loss of oil permeability. However, in such a system, much of this water may be removed by oil production. If filtration occurs into "dirty" sands (i.e., those containing appreciable clay minerals), clay swelling or other mechanisms may cause losses in oil permeability which cannot be overcome by oil production.'.' The phenomenon of mud particle invasion into the pay sand of a drilling well was considered to be a possible serious factor in the early days of rotary drilling. Opinions varied as to whether drilling fluids "mudded up" and "sealed" oil sands. In 1932 Rubel,9 Gill,10 and Parsons," in separate papers, presented differences of opinion together with some laboratory and field data concerning loss of oil production caused by drilling fluid invasion into pay zones. These papers, and the discussions, furnish a large background on this subject and indicate the very clear thinking of many men at a time when petroleum production technology was in its infancy. Jones and Babson,6 and Silent,' experimentally found that the depth to which mud particles invaded water-saturated sand packs was small (no greater than 1/16 in). Arn-quist12 in 1937 observed loss of water permeability due to invasion of mud particles into water-saturated, consolidated, sandstone samples. Williams and Cannon5 studied the filtra-tion properties of drilling muds and mentioned "sludge" which penetrated a short distance into the water-saturated filtering medium (sand pack). Byck5 concluded that formation permeability had no effect on the plas-

Jan 1, 1958

By C. S. Matthews, H. C. Lefkovits

The performance of depletion-type reservoirs at the stage in which the gas is at such low pressure that gravity is essentially the sole driving force has been investigated both theoretically and by use of scaled models. A simple theory is developed which completely explains the scaled model experiments. It also agrees with some field data. When the range of production rates to be considered is less than 25, the theory predicts that the production rate decline curve for homogeneous reservoirs in which there is a free surface will be of the hyperbolic type with n = 2: The theory gives a physical significance to the parameter y. INTRODUCTION This investigation was undertaken to determine a method for prediction of performance of reservoirs where gravity is the sole driving agent. Depletion-type reservoirs fall into this category after the pressure has fallen to some low value. Some examples of this type are found at Healdton ('Oklahoma), Oklahoma City (Oklahoma), Midway-Sunset (California), and East Coalinga (California). Generally the production rate per unit thickness is quite low in such reservoirs, with the conse- quence that this stage is sometimes called the stripper stage. However, per well production rates may be of the order of 50 B/D because of the considerable sand thickness open in some of the reservoirs. In the past, predictions of behavior of such reservoirs have been based on empirical extrapolation of the rate of production to the economic limit. Difficulties arise when new wells are drilled in the field or when production is artificially curtailed, since in such cases the decline rate of individual wells or leases changes and no clear trend can be detected. It was hoped that the present study would lead to improved methods for evaluation of such reservoirs. The study was initiated by building a scaled model for a particular field and by running a number of experiments on this model. Later a simple theory was developed which explained the laboratory results completely. The theory led, as shown below, to a hyperbolic-type decline equation which had been used previously' in a completely empirical manner. THEORY The General Case The problem to be treated here is the following: We are given a homogeneous cylindrical porous reservoir with exterior radius r, wellbore radius r., and height h,, containing, from the bottom up to a height hit oil, some gas, and interstitial water (see Fig. 1 A). The portion of the reservoir between K, and h, is filled with gas at low pressure, with residual oil, and with interstitial water. If at a time t = 0, the level of the oil in the wellbore is lowered to a height h,, what is the production rate from the reservoir at a time to The configuration within the reservoir at some instant

Jan 1, 1957