Adsorbed water on the rock surfaces in vapor-dominated geothermal fields has long been thought to provide a major source of fluid within the reservoir. Over the past several years, the Stanford Geothermal Program has conducted a series of experimental, theoretical and numerical investigations into the phenomena of water adsorption in geothermal systems, and their effects on reservoir performance. The results and conclusions of the most recent studies will be summarized in this paper. It has been found through these studies that the amount of (liquid) water adsorbed in vapor-dominated geothermal fields is very considerable, even at pressures well below the boiling point pressure. Adsorbed water represents the major fraction of fluid stored in the reservoir and can he the most important source. Reservoir performance forecasts are strongly governed by amount, and the rate of release of adsorbed water. Based on the experimental results it can be inferred that water adsorbs more easily during reinjection than it subsequently is able to desorb, which results in a reduction in the efficacy of reinjection. Introduction In simple terms, a vapor-dominated geothermal reservoir consists of porous or fractured rock, with the interstitial spaces filled predominantly with steam. However, a more complete understanding of the behavior of this type of reservoir requires a more sophisticated description than this. The "adsorption" process is a combination of the mechanisms of physical adsorption and capillary condensation. Due to these processes, water molecules are stored on the surfaces of the pore spaces in a state that is more like that of a liquid than that of a vapor. This is true even if the thermodynamic conditions are such that liquid water could not exist in a free space. The consequence of the adsorption phenomenon is that water exists in the pore space of a vapor-dominated geothermal reservoir, even though the steam present in large fractures and voids may be superheated. The large surface area of a porous material and the large density difference between the liquid and vapor states of water mean that the mass of liquid constitutes the major component of fluid storage, even though it is only vapor that flows to the wells. The performance of a vapor-dominated geothermal reservoir is governed strongly by the effects of adsorption. The adsorbed liquid phase represents most of the fluid in the reservoir, and sustains production beyond what might be expected for a reservoir filled only with vapor. While this is a very beneficial effect, adsorption complicates the analysis of the reservoir since the adsorbed water is "invisible" to the reservoir engineer. The useful life and sustainable production capacity of the reservoir is dependent on the quantity of adsorbed water in place, yet this quantity can be measured only indirectly. Furthermore, the of reinjection into a vapor-dominated reservoir is also influenced by adsorption. Hence, proper design and implementation of a reinjection scheme must take proper account of the adsorption phenomena. Over past several years, the Stanford Geothermal Program has conducted a number of investigations into the properties of adsorption and its effect on geothermal production and injection. The results of these studies will be summarized in the following sections. Separate issues to be discussed are: (1) What is adsorption? ( 2 ) How much adsorption occurs in geothermal reservoirs'! (3) What are the properties of adsorbed water in geothermal rocks? (4) How does adsorption affect production and injection? What is Physical adsorption is caused mainly by Van der Waals attractive forces, including the dispersion force. In addition, there will be electrostatic forces if either the adsorbent or the adsorbate is polar in nature. The process is similar to condensation of vapor molecules onto a liquid phase of the same composition. The major characteristics of physical adsorption can be summarized as follows (Satterfield, 1980: Ruthven, 1984): Physical adsorption is an exothermic process so the amount of gas physically adsorbed at constant pressure always decreases monotonically as temperature is increased. The average heat of physical adsorption for the formation of a monolayer usually exceeds that of liquefaction, but seldom by more than a factor of about two. Physical adsorption requires no activation energy and therefore can occur nearly as fast as molecules strike a surface. The process is reversible and equilibrium is established very rapidly unless diffusion through a fine porous structure limits the process. hysteresis is caused by geometric effects in that the specific curvature in contact with the vapor at a specified relative pressure as vapor pressure is increased is different from that as the vapor pressure is decreased. In a porous material, adsorption and capillary condensation are two closely related processes, they both cause the vapor to condense onto the solid. They are related in such a way that adsorption is a precursor of capillary condensation. The physical processes of adsorption in porous materials can he divided into three steps: (1) submonolayer adsorption, (2) multilayer adsorption with transition to (3) capillary condensation. The pressure range at which the transition from multilayer adsorption to capillary condensation occurs depends on the structure of the material. If the material is microporous, the pore space will be filled up (commonly termed as volume before multilayer adsorption is developed. In larger multilayers of adsorbed water form as pressure increases. At a certain pressure, capillary condensation commences in the small pores. As the pressure is progressively increased, wider and wider pores are filled while multilayer adsorption is simultaneously taking place.

The quantification of the amount of water retained in geothermal reservoir rocks allows a more realistic estimation of reserves for vapor-dominated geothermal reservoirs. If the measured desorption isotherm resembles the production characteristics of a geothermal system, understanding of the adsorption/desorption hysteresis will aid the design of reinjection processes.Adsorption/desorption isotherms of both nitrogen and water vapor on Berea sandstone and a graywacke sample from The Geysers well NEGU-17 were measured, Water vapor adsorption was determined at temperatures of 80, 100, 120 and 130 degrees C. Some measurements were also conducted in the presence of added clay. Hysteresis was observed for both nitrogen and water adsorption. However, the behaviors differ in the two cases, indicating the presence of different mechanisms for nitrogen and water adsorption, The observed hysteresis for nitrogen is likely to be caused by structural heterogeneity. However, for water, the situation is more complicated. Apart from structural heterogeneity, chemical interaction of water with the rock surface and changes in the structure of the rock during adsorption are possible sources of contribution to the observed hysteresis. The surface area of the two rock samples was determined from nitrogen adsorption isotherms. The Frenkel-Halsey-Hill (FHH) equation was found to fit the water adsorption isotherms reasonably well.At low relative pressures. adsorption is the dominant process in water retention in the rock samples studied; at higher pressures, capillary condensation is more important. However, there is no clear distinction between these two phenomena.

The measurement of the quantity of adsorbed water on geothermal reservoir rocks allows a more realistic estimation of reserves for vapor-dominated geothermal reservoirs. This study measured adsorptioddesorption isotherms of water vapor on rock samples from Calpine Co.'s well MLM-3, both core fragments and well cuttings from Coldwater Creek steamfield and a number of well cuttings from well Prati State 12, Northwest Geysers steam field. Surface areas of these rock samples were measured using nitrogen adsorption at 77K. The results of these measurements suggest that surface area is a crucial factor in determining the amount of water adsorption. Analysis of the water adsorption data indicates that adsorption is the dominant phenomena in the matrix of the reservoir rock at relative pressures below 0.8. Depending on the structure of the rock, capillary condensation contributes considerably to the total water retention at relative pressure between 0.8 and 1.0. However, there is no clear distinction between adsorption and capillary condensation and it is difficult in the experiments to determine when complete saturation occurs. A significant result of these experiments was the demonstration that well cuttings show adsorption characteristics very much like those obtained from core fragments. This should allow further adsorption measurements to bemore » made more extensively and at lower cost.« less

Experimental isotherms of water vapor adsorption/desorption on three geothermal reservoir rock samples have been measured at temperatures of 80, 100, 120 and 140°C. Initial surface status of the sample was found to influence the amount of water adsorbed. At low relative pressures, adsorption is the dominant process of water retention onto the rock samples. Adsorption/desorption hysteresis was observed to exist over the whole pressure range at all temperatures. Similar observations were made for all three samples. The results of this study suggest that adsorption is important in storing water in geothermal reservoir rocks not only in itself, but also in inducing capillary condensation.

This study presents drawdown and buildup pressure derivative type-curves for a well producing at a constant rate from the center of a finite, circular reservoir. Early time response (wellbore storage and skin effects) is correlated by C{sub D}e{sup 2s}, and late time response (outer boundary effects) by r{sup 2}{sub eD}/C{sub D}. The outer boundary may be closed, or at a constant pressure. Design relations are developed for the time to the beginning and the end of infinite-acting radial flow. Producing time effects on buildup responses are also discussed.

ABSTRACT Pilot in-situ combustion oil recovery operations began in the South Belridge Field in 1963, and commercial operations began on a 164-acre area in 1964. This operation ended in 1986 when an air compressor failed. South Belridge oil in place of a third of billion barrels of oil with an estimated 8 percent recovery inspired interest in thermal oil recovery in 1947. This study presents results of 22 years of commercial in-situ combustion at South Belridge. Although continuous steam injection is the most important thermal oil recovery operation in South Belridge, in-situ combustion offers opportunity for extending thermal operations in other fields far beyond bounds appropriate for steam injection. Results at South Belridge for both commercial steam injection and in-situ combustion have been published. Steam injection is among the best in California, and in-situ combustion is considered average for California conditions. At South Belridge, the surface energy requirement per barrel of oil produced by in-situ combustion was about one fifth that required for steam drive. The pounds of flue gas generated per barrel of oil recovery from in-situ combustion was about half that required for steam drive. Emulsions were produced by in-situ combustion, but posed no special problems. Well failures for in-situ combustion were similar to those for steam drive once old (pre-1964) completions were replaced. The ratio of cum. inj. air to cum. prod. oil was 3.7 MCF/BBL, about a third of the design ratio. In-situ combustion offers an efficient extension of thermal enhanced oil recovery to deep, high-pressure, low-oil-reactivity formations.

This paper presents new analytical solutions for the dimensionless pressure drop or cumulative influx for nonhomogeneous aquifers whose thickness, permeability-viscosity ratio, or porosity-compressibility vary linearly with distance. These solutions apply to one-dimensional linear flow conditions with finite aquifer size. The inner boundary condition may be either constant rate or constant pressure. The outer boundary may be either closed, or at constant pressure. The solutions presented in this paper contain homogeneous aquifer solutions as limiting cases. Thus, this study extends the state-of-the-art of analytical aquifer modelling.Based on this study, a nonhomogeneous aquifer behaves as a homogeneous aquifer at early times. At late times, pseudosteady or steady-state behaviour is observed, depending on the outer boundary condition. But the dimensionless time to late-time state is dependent on the type and severity of the property variation. Limiting solutions at early and late times are presented for each case.

ABSTRACT Usually, well tests from enhanced oil recovery projects, such as steam injection, in-situ combustion, and CO2 flooding projects, are analyzed using a radial, two-region composite reservoir model. However, a three-region model may be more appropriate in many cases. An analytical solution for the transient pressure response of a well in a radial, three-region reservoir is available. But a detailed study of the transient pressure and/or pressure derivative response of a well in a three-region reservoir has not been presented in the literature. Using an analytical solution, this study establishes the ratio of the intermediate region radius to the inner region radius as a correlating parameter for the transient pressure derivative responses for a three-region reservoir. Additional four parameters are related to the mobilities and the storativities of different regions. This study shows that the deviation time method would result in an estimate for the inner region radius, if the effects of the mobilities and the storativities of the inner and the intermediate regions are not balanced in a way to produce an incorrect deviation time. Analytical expressions for the effective porosity-compressibility product and mobility are developed for the analysis of pressure transient data by the pseudosteady state (PSS) method. The PSS method would result in an estimate of the combined volume of the inner and the intermediate regions, if an effective porosity-compressibility value is used to analyze the pseudosteady data. However, at times, the development of an apparent pseudosteady state may yield an overestimated volume. An idea about the development of an apparent pseudosteady state may be obtained by calculating the effective dimensionless time corresponding to the time to start of an approximately constant Cartesian slope for the pressure transient data in question.

Distinguished Author Series articles are general, descriptiverepresentations that summarize the state of the art in an area of technology bydescribing recent developments for readers who are not specialists in thetopics discussed. Written by individuals recognized as experts in the area, these articles provide key references to more definitive work and presentspecific details only to illustrate the technology. Purpose: to informthe general readership of recent advances in various areas of petroleumengineering. Abstract The decade of the eighties produced important findings in well testanalysis. However, the large number of new and sometimes competitive methodsalso has produced confusion. The main objective of this paper is to considerthe current state of practical well test analysis methods. Often new studiesproduce conclusions that time proves incomplete or partly untrue. The storagelog type curve was initially presented as a method to analyze shorttime data. This was later found to be impossible. But the diagnose tic value of thelog-log curves was far more important than shorttime analysis. Then later thederivative was added to the type curve and one conclusion was that Hornercurved were no longer necessary and that short time analysis was now possible. Neither conclusion is entirely correct, yet the diagnostic value of thederivative remains. Another major development was computer aidedinterpretation. The computer was necessary to differentiate data, and of greathelp in preparing the large number of graph required for modern interpretation. An important breakthrough resulted with development of nonlinear regression forspecific models and the ability to consider rate variation. Results of aninterpretation could be used to simulate the test data and a comparison ofsimulation and field data made. The regression coefficient or confidence limitprovided a quantitative measure of the agreement of field data with the modelchosen. Results may also be used to determine where a correct straightlinecould be on a Homer buildup graph. This procedure proven that it is verydifficult to find a Horner straightline slope with the precision previuslythought possible. Widespread use of electronic pressure gauges and computerdata acquisition has created net problems for a well test analyst. A newproblem revealed by type curve analysis is presented. Introduction A 1976 study reviewed important findings of the previous decade and stressedpractical applications of new methods not described in the originalpublications. At that time. three log-log versions of the storage and skinproblem had appeared, and several type curves for fractured wells had beenpresented. Many well test analysts threw up their hands at the proliferation oftype curves. The 1976 study concluded that a major advantage of the log-logtype curve was that it was usually possible to identify the flow model and findthe start of a semilog straightline for the appropriate model. It wasrecommended that a Horner straightline should still be used as the final basisof analysis where possible. The 1976 study pointed out problems with fracturetype curves (short apparent fracture lengths for large jobs), and otherexisting worries on selection of an appropriate type curve. One major advantageof the understanding that new methods brought was that it was possible tocorrect bad test data and fill in missing data in many cases. Since 1976, problems identified in that study have been solved. and true breakthroughspresented. The purpose of this study is to present useful practical methods forwell test analysis and design. Important new information includes selection ofan industry standard storage type curve. development of derivative methods, solution of the finite fracture conductivity problem. and development ofcomputer aided interpretation and design. STORAGE TYPE CURVE The traditional engineering dilemma is two methods to solve a problem whichyield different answers. Well test analysis is replete with this problem. Papers often say something like the data was analyzed by the Smith methodyielding 20 md, the Jones method yielding 2 darcies, and the von Schultz typecurve yielding 0.15 md. The average is …" Remarkably, the three differentmethods are usually different graphs of the same solution. The second well testanalysis monograph by R. C. Earlougher, Jr. was published in 1977, but thelog-log type curves described for the first time in an SPE monograph wereconsidered controversial by the SPE Board of Directors. An early SPE Boarddecision was not to publish full-scale log-log type curves as this wouldindicate SPE approval of log-log type curves, or a particular type curve. Fortunately, this decision was reversed. Gringarten et al. ended thecontroversy over the best form of the wellbore storage and skin effect typecurve in 1978. Their type curve of the log of dimensionless pressure vs the logof tD/CD with CD exp 2s as a parameter has become the industry standard. Theiroriginal type curve combined radial flow and fracture flow results andindicated the effect of producing time on buildings. It was a remarkableimprovement which caught immediate acceptance. So one problem identified inref. 1 was solved.

Discussion on air/brine drainage capillary pressure curves and permeability values for sandstone samples

ABSTRACT The effects of the unswept zone mobility (kh/µ) on steam inject1v1ty were Investigated. Six falloff tests were run in a steamflood near Maricopa, California. The tests were analyzed using the radial composite model with the aid of the Barua-Horne and the Kappa Saphir well test analysis software packages. Computer aided matching of the radial composite model with steam injection well falloff data provided remarkable agreement between field data and model simulation. It was possible to find skin, well bore storage, steam zone mobility and compressibility, and the mobility and compressibility of the zone ahead of the steam front. Low mobility ahead of the steam zone was found to limit steam injectivity in several field cases.

Abstract The Dykstra-Parsons approach for computing the vertical coverage of a waterflood has been modified in order to estimate the vertical coverage for an in situ combustion process. The modified approach for combustion ignores the effect of gravity forces in determining burn thickness. It simply assumes that the burn moves to the top of the pay zone. Burn thickness is then shown to be dependent upon the reservoir permeability variation, the mobility ratio of the injected gas (containing oxidant) to the combustion gas, initial reservoir temperature and the combustion temperature. The model was successfully applied to field core data from the Fosterton Northwest combustion project, using spreadsheet software on a personal computer. An average 31 percent burn thickness determined from the model, compared favourably with a field-observed value of 34 percent which was determined by post-burn coring. The model performance was improved by using multiple pseudo-permeability variations for the core data, instead of a single variation value, as is often used when applying the Dykstra-Parsons model.

Summary Computation of miscible displacement performance requires an estimate of the amount of mixing in the reservoir. Dispersion coefficients measured from displacements in laboratory cores are often used to compute reservoir performance. This paper considers interpretation of effluent flowing concentration data obtained from heterogeneous cores by use of the Coats-Smith, porous-sphere, and transverse-matrix-diffusion heterogeneous models. Analytical solutions to the three heterogeneous models are presented in Laplace space. Approximate solutions for short- and long-time effluent flowing concentrations, developed from simplification of the Laplace transformation solution, are used to develop practical methods of interpreting effluent concentration data to determine model parameters. Criteria for design of laboratory experiments based on these results are suggested.

Abstract A radial composite reservoir model is used to analyze well-tests from a variety of enhanced oil recovery projects, geothermal reservoirs, and acidization projects. A composite reservoir is made up of two or more regions. Each region has its own rock and fluid properties. Also, dynamic phenomena, such as phase changes and multi-phase 1ow effects in a region near the front, can cause a sharp pressure drop at the front. Such a sharp pressure drop is modelled as a thin skin at the front in this study. An analytical solution for the transient pressure behaviour of a well in a two-region composite reservoir with a skin at the front is obtained using the Laplace transformation. Analysis shows that a thin skin at the front can explain a short duration pseudo-steady state corresponding to the inner swept volume for small mobility and storativity contrasts. The effects of is skin at the front are similar, to the effects of storativity ratio. Thus, neglecting a thin skin at the font can cause large errors in parameter estimation using a type-curve matching method. Also, graphical correlations are presented for the time to rile end of pseudo-steady state behaviour corresponding to the inner swept volume with a skin at the front. Such correlations should help in selecting a proper pseudo-steady Cartesian straight line for data analysis. Introduction Figure 1 shows a schematic diagram of a two-region, radial composite reservoir. The inner and outer regions of a composite reservoir have different, but uniform rock and fluid properties, and are separated by a discontinuity. The distance R is the front (or discontinuity) radius, which is an important parameter sought from well tests in composite reservoirs. Eggenschwiler et al.(I) presented an analytical solution in Laplace space for the transient pressure behaviour of a well producing (or injecting) at a constant rate from (or into) a two-region, radial infinite composite reservoir. Horne et a(2) extended them Eggenschwiler et a, solution to finite composite reservoirs. This study considers transient pressure derivative behaviour of a well in a two-region, composite reservoir with an infinitesimally thin skin at the front. The effects of a thin skin at the front on the transient pressure and pressure derivative behaviour of a well in a composite reservoir is considered important because a thin skin at the front may be a practical approach to model the following physical situations:vapourization at the discontinuity while injecting cold water in a hot geothermal reservoir;condensation at the steam front such as in steam injection projects;cases where a transition region is apparent. For in situ combustion cases, Onyekonwu(3) observed a transition region.Pressure profiles presented in Figures 6.8 and 6.11 of Reference 3 suggest that the system may be modeled as a two-region reservoir with a thin skin at the discontinuity; andsimulated CO2 flooding results show that from 600;0 or the over-all pressure- drop occurs in a small region around the front(4).

SummaryBecause a reservoir undergoing a thermal recovery process is typically idealized as a composite reservoir, this study develops new design and interpretation equations by investigating pressure-derivative behavior of a well in a two-zone, radial, infinite or finite composite reservoir. Accurate design equations help establish the test duration required to observe a particular feature in well test data and thus the applicability of an interpretation method to determine front radius, or swept volume.This study shows that the dimensionless time to the end of the first semilog line (deviation time) based on front radius is a constant. The deviation-time method may be used if wellbore storage does not mask the first semilog line. Design equations for the time of the beginning of the second semilog line and the time to observe outer-boundary effects show that the intersection-time method is not suitable for thermal recovery well test analysis. Correlations developed for the end of pseudosteady-state behavior of the swept region should help select the correct Cartesian line to calculate swept volume. This paper also presents derivative type curves applicable for all front radii, with mobility and storativity ratios as parameters for infinitely large composite reservoirs. For closed and constant-pressure outer boundaries, the ratio of outer boundary to front radius is the third parameter.

Summary A new method of drawdown-pressure test analysis is proposed that takes into consideration the non-Darcian flow as well as the skin and borehole-storage effects. Two new correlations obtained from numerically simulated drawdown tests are used and the method of application is illustrated. The drawdown-pressure results of a synthetic numerically simulated test are used to recalculate the a priori known reservoir skin and permeability. A comparison between the obtained and the "true" reservoir skin and permeability shows an excellent agreement when the proposed method is applied. Drawdown-pressure analysis of the given examples with the conventional method shows errors > 5 % in the calculated permeability and > 50% in the calculated skin factor.

ABSTRACT A radial, composite reservoir idealization is used to analyze falloff tests from enhanced oil recovery projects such as thermal recovery, and CO2 flooding. Swept volume (or front radius) is a primary parameter to monitor the progress of a project. A falloff test is an inexpensive way to obtain an estimate of swept volume (or front radius). Either deviation time from a semi-log line corresponding to the inner region mobility, or a short duration pseudosteady state behavior corresponding to the inner region swept volume, or type-curve matching may be used to analyze the data. Any of these methods would produce an inaccurate estimate for swept volume (or front radius), if injection time is short. To the best of our knowledge, injection time effects on falloff responses for a well in a composite reservoir have not been presented in the literature. Using an analytical solution, this study establishes dimensionless injection time based on front radius as a correlating parameter for falloff responses for all front radii. Effects of short injection time on the accuracy of the methods to estimate swept volume (or front radius) are discussed. If injection time effects are ignored, the pseudosteady state method may overestimate swept volume by an order of magnitude. For short injection times, model selection (a two-region vs. a three-region model) for type-curve matching can be difficult. Finally, a correlation is presented for the magnitude of injection time to analyze falloff data using an injectivity type-curve.

Summary This paper describes the behavior of a naturally fractured reservoir when a well is producing through a vertical fracture with uniform flux or infinite conductivity. The reservoir model is a double-porosity medium, and both pseudo-steady-state and transient-interporosity-flow models are studied. The derivative vs. time for each solution is shown, and an analysis method for matching field data to such a model is presented. This study combines a reservoir and a well model, both of which have been extensively studied separately. Included are a quick review of the main characteristics of these models and the methods used to solve the problems. At the end of the study, a general method is suggested to extend models with constant boundary conditions—e.g., homogeneous and double-porosity cases.

Summary The pressure response of a double-porosity reservoir to a slug test in a fully penetrating well with wellbore storage and skin is presented. Pseudosteady-state matrix flow and transient matrix flow with and without matrix skin are considered. Three kinds of type curves are discussed: early-time log-log, intermediate-time semilog, and late-time log-log. Pressure distribution around the active well and the prospects of interference slug testing are considered. The early-time response of the slug test depends on the presence of wellbore skin; hence, two kinds of early-time type curves are presented. When the active well has wellbore skin, the early-time correlating parameter is the product of the skin and the dimensionless storage, resulting in a new log-log type curve. When wellbore skin is not present, the early-time response is proportional to the square root of time with dimensionless storage as the correlating parameter. The intermediate-time semilog type curves are applicable when wellbore skin is not present, or CDe2S>104. The double-porosity effects are significant in the late-time log-log format, but the flat portion of the pressure response occurs at dimensionless pressures less than 0.01. The radius of investigation of the slug test in a double-porosity system is also examined with and without wellbore skin at the active well. Interference responses and pressure profiles are presented. Although the presence of wellbore skin reduces the magnitude of the dimensionless pressure responses at observation wells, the detectable radius of investigation does not significantly depend on wellbore skin. Interference slug testing in a double-porosity system requires high-precision pressure-recording tools in the observation wells because the double-porosity effects occur at small dimensionless pressures. Transient matrix flow without matrix skin reduces the double-porosity effects and limits the use of type curves for determining λ and ω. The slug-test double-porosity effects in a reservoir with transient matrix flow with fracture skin and pseudosteady-state matrix flow are similar.