Society of Petroleum Engineers Journal

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ISSN : 0197-7520
Published by: Society of Petroleum Engineers (SPE) (10.2118)
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James C. Frauenthal, Roland B. Di Franco,
Society of Petroleum Engineers Journal, Volume 25, pp 902-908; https://doi.org/10.2118/11593-pa

Abstract:
A generalization of upstream weighting is proposed as a method for reducing grid-orientation effects in reservoir simulation. For the two sample problems studied,. a piston-flow waterflood and a realistic gas injection, the piston-flow waterflood and a realistic gas injection, the grid-orientation effect was almost completely eliminated. The new generalized upstream weighting (GUW) method is particularly attractive because it is fast and accurate, and particularly attractive because it is fast and accurate, and can be added easily to an existing simulator that uses upstream weighting. Introduction The grid-orientation effect is a well-known phenomenon in finite-difference reservoir simulation. Numerical results are highly dependent on the orientation of the finite-difference grid imposed on the model. In practice it occurs whenever one has a strongly adverse mobility ratio. This happens when one tries to push a viscous oil with a highly mobile fluid, such as steam or hydrocarbon gas. This paper presents a technique for reducing grid-orientation effects that is fast, flexible, and easily added to an existing simulator. A good survey of the research in this area was recently published. With this in mind, we will give an published. With this in mind, we will give an idiosyncratic interpretation of some of the techniques suggested by others. The main numerical difficulty in petroleum reservoir simulation is largely a consequence of the need to estimate individual phase mobilities halfway between finite-difference gridpoints. Because averaging the values from adjacent gridpoints is numerically unstable, the midgridpoint typically is assigned the value at the next upstream point. The idea of looking upstream for information point. The idea of looking upstream for information is found throughout much of computational fluid dynamics. Many improvements on one-point upstream weighting have been proposed in the reservoir simulation literature. The principal attractions of these techniques are that they can be interchanged easily within existing computer codes and do not add significantly to computation time. We found that the upstream weighting procedures have a common feature. If the midgridpoint in procedures have a common feature. If the midgridpoint in question lies, for example, on a grid line in the x direction, these techniques consider only other points on this same grid line in the extrapolation/interpolation process. A second body of literature developed around the idea of using a nine-point (instead of the standard five-point) finite-difference scheme to represent two-dimensional (2D) second derivatives. Because the nine-point scheme is a weighted superposition of two 5-point grids with a common center point and a 45 * relative rotation, the procedure averages away the grid-orientation effect to some extent without explaining it. Nevertheless, the nine-point grid schemes include one attractive feature absent from the upstream schemes: the weighting parameter can be tuned to improve the quality of the results. parameter can be tuned to improve the quality of the results. Perhaps the biggest fault of these procedures is that they Perhaps the biggest fault of these procedures is that they do not extend easily to three dimensions. The widening of the matrix bandwidth also increases the computation time. Our proposed technique is a modification of a procedure used successfully in the convective-heat transfer literature. It amounts to a generalization of one-point upstream weighting, accomplished by the introduction of mobility values from nearby points that lie in the true upstream direction rather than along a single grid line. This is explained in more detail in the next section. Note that the technique requires very little computer time. In fact, because most reservoir simulators use an automatic timestep adjustment, the improved stability of the technique, relative to standard upstream procedures, allows larger timesteps to be taken. Also, two adjustable parameters that permit the grid-orientation effect to be almost parameters that permit the grid-orientation effect to be almost completely eliminated are introduced. Finally, because the procedure works well with the standard five-point finite-difference representation of 2D second derivatives, it generates easily to three dimensions and is completely compatible with most reservoir simulators. Governing Equations The conservation equations for multiphase fluid flow in porous media are well known. However, the porous media are well known. However, the equations for three-phase flow are listed below for completeness. The continuity equations are as follows. SPEJ P. 902
Christine Ehlig-Economides, Michael J. Economides
Society of Petroleum Engineers Journal, Volume 25, pp 839-847; https://doi.org/10.2118/12520-pa

Abstract:
Prominent examples of linear flow behavior in-the well test Prominent examples of linear flow behavior in-the well test literature describe flow within or to a fracture penetrated by a producing well. The characteristic pressure transients generally producing well. The characteristic pressure transients generally are exhibited in the early portion of a well test and are followed by infinite-acting radial flow behavior and/or boundary effects. In contrast, if a formation is of a predominantly linear shape, linear flow is expected to develop in late time. In this paper, analyses of interference, drawdown, and buildup tests that are applicable to linear flow systems are described theoretically and illustrated by practical examples. The necessary equations for the analyses are provided for testing oil, gas, and geothermal steam wells. In elongated linear flow systems, the pressure transient behavior associated with linear flow occurs late in the drawdown or buildup test. The type curves provided in this work show that this pressure behavior is distinguishable from conventional well tests, pressure behavior is distinguishable from conventional well tests, particularly in interference tests. particularly in interference tests. Introduction Interest in linear flow geometry was limited for a long time to water influx applications. Miller I provided solutions for pressure distributions in semi-infinite- or finite-length linear pressure distributions in semi-infinite- or finite-length linear aquifers assuming water influx into the oil zone at a constant flow rate. Ehlig-Economides et al. 2 and Ehlig-Economides and Economides recently developed methods for analyzing geothermal well tests in a predominantly linear flow system. This work was motivated by the presence of parallel linear faults that are predominant in geothermal regions, such as the one shown in Fig. 1. Methods for interference analysis and for drawdown testing of geothermal steam wells were presented. Linear flow geometry currently is cited as a fairly common occurrence in low-permeability gas fields. Kohlhaas et al. provided a case study of linear flow behavior for a gas well completed in a channel-like reservoir and equations for analyzing the linear flow portion of drawdown and buildup tests. Stright and Gordon examined rate-decline behavior in gas wells in the Piceance basin in northwest Colorado that exhibited apparent linear flow behavior. In one case, the well penetrated a fracture in a low-permeability marine sand in which a number of long, natural fractures were present and appeared to be related to extensive faulting in the area. In another case, the well was completed in a long, narrow sand body shown by outcrops in the same area. A recent paper by Nutakki and Mattar provided solutions for drawdown vs. time for linear flow geometry. The solutions are identical to the work done by Ehlig-Economides and Economides for geothermal steam wells. However, the method of analysis, which made use of a "pseudoskin" factor, was distinctly different. In this paper, the previous methods of interference and drawdown analysis for geothermal wells in a linear flow system are reintroduced with additional coefficients for oil- and gas-well testing. In another paper, the drawdown behavior of fractured wells in the predominantly linear flow system is presented in detail. Theory In Fig. 1, the geological map from a geothermal region shows linear faults running parallel for several hundred feet. If the regional faults provide impermeable boundaries to flow, then a particular well may drain a volume best described as a long, narrow particular well may drain a volume best described as a long, narrow channel. In Fig. 2, schematics of several types of depositional environments show possible oil- and gas-reservoir geometries that would result in predominantly linear flow. These formations, which generally are long, narrow shapes, may be the results of river meander point bars, oxbow lakes, river channels, or tectonic breccias. The model used for this work employs the diffusivity equation, which requires assumptions concerning the formation and fluid properties, such as homogeneous and isotropic formation, horizontal monophasic Darcy flow, fluid of small and constant compressibility, and constant viscosity. The boundary conditions and appropriate dimensionless variables are defined separately for interference analysis and for drawdown/buildup analysis. Interference Analysis For interference analysis, the active well is located at the center of a rectangular cylinder of infinite length and is approximated by a planar source, as depicted in Fig. 3. The cross section of the cylinder is assumed to be a rectangle with height h and width b. The planar source boundary condition for the linear flow model is analogous to the vertical line source for horizontal radial flow. For drawdown analysis, a model incorporating wellbore storage and skin is required, as will be discussed later in this paper. SPEJ P. 839
Jeffrey A. Joseph, Leonard F. Koederitz
Society of Petroleum Engineers Journal, Volume 25, pp 804-822; https://doi.org/10.2118/12950-pa

Abstract:
This paper presents short-time interpretation methods for radial-spherical (or radial-hemispherical) flow in homogeneous and isotropic reservoirs inclusive of wellbore storage, wellbore phase redistribution, and damage skin effects. New dimensionless groups are introduced to facilitate the classic transformation from radial flow in the sphere to linear flow in the rod. Analytical expressions, type curves (in log-log and semilog format), and tabulated solutions are presented, both in terms of pressure and rate, for all flow problems considered. A new empirical equation to estimate the duration of wellbore and near-wellbore effects under spherical flow is also proposed. Introduction The majority of the reported research on unsteady-state flow theory applicable to well testing usually assumes a cylindrical (typically a radial-cylindrical) flow profile because this condition is valid for many test situations. Certain well tests, however, are better modeled by assuming a spherical flow symmetry (e.g., wireline formation testing, vertical interference testing, and perhaps even some tests conducted in wellbores that do not fully penetrate the productive horizon or are selectively penetrate the productive horizon or are selectively completed). Plugged perforations or blockage of a large part of an openhole interval may also promote spherical flow. Numerous solutions are available in the literature for almost every conceivable cylindrical flow problem; unfortunately, the companion spherical problem has not received as much attention, and comparatively few papers have been published on this topic. papers have been published on this topic. The most common inner boundary condition in well test analysis is that of a constant production rate. But with the advent of downhole tools capable of the simultaneous measurement of pressures and flow rates, this idealized inner boundary condition has been refined and more sophisticated models have been proposed. Therefore, similar methods must be developed for spherical flow analysis, especially for short-time interpretations. This general problem has recently been addressed elsewhere. Theory The fundamental linear partial differential equation (PDE) describing fluid flow in an infinite medium characterized by a radial-spherical symmetry is (1) The assumptions incorporated into this diffusion equation are similar to those imposed on the radial-cylindrical diffusivity equation and are discussed at length in Ref. 9. In solving Eq. 1, the classic approach is illustrated by Carslaw and Jaeger (later used by Chatas, and Brigham et al.). According to Carslaw and Jaeger, mapping b=pr will always reduce the problem of radial flow in the sphere (Eq. 1) to an equivalent problem of linear flow in the rod for which general solutions are usually known. (For example, see Ref. 17 for particular solutions in petroleum applications.) Note that in this study, we assumed that the medium is spherically isotropic; hence k in Eq. 1 is the constant spherical permeability. This assumption, however, does not preclude analysis in systems possessing simple anisotropy (i.e., uniform but unequal horizontal and vertical permeability components). In this case, k as used in this paper should be replaced by k, an equivalent or average (but constant) spherical permeability. Chatas presented a suitable expression (his Eq. 10) obtained presented a suitable expression (his Eq. 10) obtained from a volume integral. It is desirable to transform Eq. 1 to a nondimensional form, thereby rendering its applicability universal. The following new, dimensionless groups accomplish this and have the added feature that solutions are obtained directly in terms of the dimensionless pressure drop, PD, not the usual b (or bD) groups. ......................(2) .......................(3) .........................(4) The quantity rsw is an equivalent or pseudospherical wellbore radius used to represent the actual cylindrical sink (or source) of radius rw. SPEJ p. 804
J. Geertsma
Society of Petroleum Engineers Journal, Volume 25, pp 848-856; https://doi.org/10.2118/8073-pa

Abstract:
Elementary borehole- and perforation-stability problems in friable clastic formations for unrestricted fluid flow between reservoir rock and underground opening are treated on the basis of linear poroelastic theory. Thermal stress effects caused by a temperature difference between reservoir and borehole fluids can be predicted from the mathematical similarity of poro- and thermoelasticity. A tension-failure condition applies for the prediction of hydraulic fracture initiation in a formation around injection wells. The resulting equations are partially well-known. Similarly, a uniaxial compression-failure condition should predict perforation failure leading to sand influx in production wells. The major difference between these situations is that, at sufficient depth of burial, the tensile strength of a friable rock mass has only a minor effect on the fracturing pressure level, but the actual value of the compressive strength plays a crucial role in the prediction of sand-influx conditions. Practical suggestions for resolving the latter are given. Introduction This paper discusses borehole- and perforation-stability problems as encountered in friable sandstone formations that have in common free fluid flow between a reservoir and an underground opening. Such a condition prevailsduring fluid production through either casing perforations or open hole andduring injection of fluids into a reservoir for pressure maintenance, gas conservation, tertiary oil recovery, or well stimulation. In the absence of a membrane (such as a filter cake) at the rock/hole interface, the effective stress normal to the rock surface is zero. Rock failure can result either in tension during fluid injection or in compression during fluid production. Because one of the principal effective stresses (the radial stress) is zero and the effect of the intermediate principal effective stress is small, failure is of either the unconfined tension or compression type. Rock failure resulting from fluid production from friable sandstones causes sand-particle influx. Failure caused by fluid injection means either planned or unintentional formation fracturing. The production technologist has to foresee such failure conditions as a function of changes in the stress regime with time. He has to start with a best possible estimate of the initial in-situ state of stress. On the basis of log data and core sample analysis, relevant rock deformation and strength properties must be determined next. Finally, an estimate of changes in the stress field resulting from prolonged production or injection must be made. Problem Areas Formation Particle Influx in Production Wells. Although significant improvements have been made in well-completion techniques aimed at sand-particle retention by both gravel packing and sand consolidation, straightforward production through casing perforations is the preferred production method because of minimum costs and maximum usage of well-flow potential. Moreoever, gravel packing long intervals of strongly deviated holes remains a difficult, expensive operation to perform, while sand consolidation processes for oil wells at temperatures above 75 degrees C [167 degrees F] are not available commercially. Friable formation sands i.e., formations that have some strength of their own-do not necessarily present a sand-influx problem initially. Sand production may develop gradually in time, once total drawdown increases and/or water breakthrough occurs. Deviated boreholes may encounter less favorable stress concentrations around perforations than vertical holes. All in all, it is necessary to predict the sand-influx potential of a well as soon as possible after drilling to serve as a basis for a completion policy. A perforation pattern that both results in production from only the more competent zones and enables delivery of the required well production capacity could be implemented. Formation Fracturing Around Injection Wells. A familiar type of formation failure is fracturing in tension around injection wells. Formation fracturing always occurs when the injection pressure surpasses the formation breakdown pressurei.e., the fluid pressure that brings the hoop stress around the opening in a tension equal to the tensile strength. Once initiated at or below this pressure level (because the formation may contain natural fractures), fracturing proceeds while the injection pressure surpasses the least principal in-situ total stress. The instantaneous shut-in pressure recorded during or after a fracturing job provides the best value of the least principal total stress component. The in-situ state of stress is not necessarily a constant during the production life of a reservoir. Changes both in reservoir pressure and in temperature adjacent to a well affect the local stress field in the formation. The effect of reservoir pressure variations on formation fracturing potential is well-known. Breckels and van Eekelen explicitly account for this effect. It is less recognized that in deeper formations cooling of the borehole surroundings by injection of liquids at near-surface temperature causes reservoir-rock shrinkage, leading to a reduction in both fracture initiation and propagation pressure. SPEJ P. 848^
O. Glaso
Society of Petroleum Engineers Journal, Volume 25, pp 927-934; https://doi.org/10.2118/12893-pa

Abstract:
This paper presents a generalized correlation for predicting the minimum miscibility pressure (MMP) required for predicting the minimum miscibility pressure (MMP) required for multicontact miscible displacement of reservoir fluids by hydrocarbon, CO2, or N2 gas. The equations are derived from graphical correlations given by Benham et al. and give MMP as a function of reservoir temperature, C7+ molecular weight of the oil, mole percent methane in the injection gas, and the molecular weight of the intermediates (C2 through C6) in the gas. CO2 and N2 are represented in the current correlation by "equivalent" methane/propane- and methane/ethane-mixture injection gases, respectively. The study shows that for hydrocarbon systems, paraffinicity has an effect on MMP. In the equations, the C7+ paraffinicity has an effect on MMP. In the equations, the C7+ molecular weight of the oil is corrected to a K factor of 11.95, thereby accounting for varying paraffinicity. An additional temperature effect on N2 MMP is related to the API gravity of the oil. The N2 correlation, however, is not tested against measured MMP data other than those used to develop the equation and should be used with care. A correlation that accounts for the additional effect on CO2 MMP caused by the presence of intermediate components in the reservoir oil is presented. Predicted MMP's from the correlations developed are compared to experimental slim-tube displacement data from the literature and from our displacement tests on North Sea gas/oil systems. These displacement tests have been performed with a packed slim tube, where the effect of viscous fingering is reduced to a minimum. Introduction Multicontact miscibility is represented most easily with a ternary diagram, where the composition of the driving or displaced fluid is altered. This is obtained by vaporization of light hydrocarbon components into a driving gas or by condensation of hydrocarbon components from a driving gas into the reservoir oil. Miscibility between reservoir oils and hydrocarbon gases is achieved either by vaporization or by condensing-gas-drive mechanism, depending on the reservoir oil and injection-gas composition. With N2 and CO2, miscibility is obtained by vaporization, but with CO2, miscibility usually is achieved at lower pressure because CO2 extracts much higher-molecular-weight hydrocarbons from the reservoir oil than N2 gas. The prediction of miscibility conditions from ternary diagrams is based on experimentally determined or calculated gas and liquid compositions of a reservoir-oil/injection-gas mixture. The experimental gas and liquid equilibrium data are not easy to obtain and are often time-consuming to determine, especially near the plait point. The method for calculating gas and liquid data with point. The method for calculating gas and liquid data with equations of state to predict miscibility relies largely on gas and liquid compositions near the plait-point region. It is generally accepted that such data may not be sufficiently accurate. Flow experiments offer the most reliable method to determine the pressure required for miscibility with CO2, N 2, and hydrocarbon gas. The slim-tube method has been most widely used to determine miscibility. Different experimental procedures and interpretation criteria, however, have ted to different definitions of miscibility and have caused considerable confusion. The limitation of the slim-tube test and the problems associated with miscible displacement in porous media have been described by several authors. Phase behavior and mechanisms of miscible flooding with CO2, N2, and hydrocarbon gas have also been described by several authors. Correlations for predicting MMP have been proposed by a number of investigators and are important tools in the selection of potential reservoirs for gas miscible flooding. Therefore, the correlations must be as accurate as possible. Several CO2 MMP correlations have been published, but none of these can be used with enough published, but none of these can be used with enough confidence for final project design. They are useful, however, for screening and preliminary work. Correlations on CO2 miscible flooding have shown temperature to be the most important parameter but they disagree regarding the effect of oil type (e.g., C7+ properties of the oil). Compared with CO2 miscible flooding, very little has been published on high-pressure hydrocarbon gas miscible flooding. A recent publication gives a correlation for predicting MMP with lean hydrocarbon gases and nitrogen. In 1960, Benham et al. presented empirical curves that can estimate miscibility conditions for reservoir oils that are displaced by rich gas within a pressure range of 1,500 to 3,000 psia [10.34 to 20.68 MPa]. They assumed a limiting tie line (at the critical composition on a ternary diagram) parallel to the C1–C7+ axis and estimated mole percent methane in the injection gas from calculated percent methane in the injection gas from calculated critical points with pressure, temperature, molecular weights of C2 through C4 in the gas, and the C5+ molecular weight of the oil as variables. From Benham et al.'s data, the proposed equations have been derived for predicting MMP. SPEJ P. 927
A.R. Hasan, C.S. Kabir
Society of Petroleum Engineers Journal, Volume 25, pp 823-838; https://doi.org/10.2118/11580-pa

Abstract:
The use of the acoustic well sounding (AWS) technique to determine bottomhole pressure (BHP) requires an estimate of the gas-void fraction (f.) in the liquid column of a pumping well annulus. Three correlations relating the annular superficial gas velocity to fg are available for saturated oil columns. These correlations were developed by Godbey and Dimon, Podio et al., and Gilbert as reported by Gipson and Swaim. Use of these correlations for determining the BHP, either flowing or shut in, involves a stepwise numerical integration often performed by a computer. This work addresses three aspects of estimating the BHP from AWS data:estimation of the superficial gas velocity,development of analytical solutions for a single-step BHP calculation, andcomparison and interpretation of the predicted BHP's by use of the three correlations for the field examples. A mathematical model, based on the principle of mass balance of the annular. gas phase, is used to determine the superficial gas velocity. This model rigorously accounts for the time-dependent pressure, volume, and the gas deviation factor in the liquid-free annulus. Analytical solutions are obtained for both the Godbey-Dimon and Podio et al. correlations to calculate the BHP in a single step. These analytical solutions provide a significant improvement over the numerical stepwise integration technique, because a hand-held calculator can be used for the BHP calculations. The field examples studied indicate that both the pumping liquid column height and the superficial gas velocity pumping liquid column height and the superficial gas velocity play a key role in estimating the gas void fraction-an play a key role in estimating the gas void fraction-an essential element in calculating the BHP. We observe that only the early-time shut-in pressures are affected by the presence of gas bubbles in the liquid column. Because the presence of gas bubbles in the liquid column. Because the bottomhole flowing pressure (BHFP) is dependent on the correlation used to predict the fg, both skin and productivity index calculations are affected. Estimation of the productivity index calculations are affected. Estimation of the permeability/thickness product and the static reservoir permeability/thickness product and the static reservoir pressure, however, are independent of the fg correlation pressure, however, are independent of the fg correlation used. Introduction The majority of the oil wells in North America are on some form of artificial lift system. Brown gives a comprehensive review of these artificial lift systems. Typically, the oil is lifted up the tubing string while the gas is vented through the annulus to avoid gas-locking the pump. Sucker-rod (beam) pumps are the most popular and pump. Sucker-rod (beam) pumps are the most popular and widely used lift system in the industry. The process of gas venting through the annular liquid column (oil and/or water) has a profound effect on the liquid density. Because knowledge of the gas-lightened liquid column is the key to a meaningful BHP (flowing and/or shut in) estimation, a better understanding of the physical process is essential, so we explored the relevant physical process is essential, so we explored the relevant works available in the literature to provide an overview of the state of the art for estimating BHP's in sucker-rod pumping wells. pumping wells. A knowledge of the BHFP (pf) is an essential element in predicting a well's productivity index (J) and its inflow performance relationship (IPR). This information is instrumental in proper artificial lift design. A pressure buildup test conducted on a pumping well can provide an array of valuable information-such as permeability/thickness product, skin, and static reservoir pressure. The last piece of information is necessary for a meaningful J estimation. We will examine the methods available that permit estimation of pwf and subsequent shut-in pressures, pws, for a buildup analysis. Because of the mechanical constraints, a subsurface pressure recorder normally cannot be run down the pressure recorder normally cannot be run down the tubing string to monitor the in-situ pressure in a sucker-rod pump. After the pump and rods have been pulled, pump. After the pump and rods have been pulled, however a recorder can be run downhole to record pressures in the conventional mariner. This method has several problems. First, a rig is needed to pull the pump and rods and problems. First, a rig is needed to pull the pump and rods and rerun them following the test. The cost of the test may be prohibitive, especially for marginal wells. Second, the early-time data, including the p is lost because of the very nature of the operation. Permanent downhole recorders are used sometimes to monitor pressures in key wells of a field in certain cases. Because of their permanent nature, the recorders have a very limited application. Nind described several other alternatives-such as depression of the annular liquid column and two methods involving the use of a dynamometer. These methods are time-consuming and have other limitations. They are capable of estimating only the pf, and, consequently, have no application in pressure buildup testing. The use of AWS with an echometer has been a very popular method for estimating both the flowing and popular method for estimating both the flowing and shut-in pressures in pumping wells. Thomas et al. and McCoy describe the principle of the method. SPEJ P. 823
Itzhak Rosenbaum
Society of Petroleum Engineers Journal, Volume 25, pp 886-892; https://doi.org/10.2118/11920-pa

Abstract:
1.0 Introduction On September 1, 1981 the "Memorandum of Agreement between the Government of Canada and the Government of Alberta relating to Energy Pricing and Taxation" was signed. The Energy Agreement contains very complex oil and gas regulations. The purpose of this study is to provide an easy procedure by which Engineers and Corporate Planners could easily determine the economic limit for non-EOR projects in Alberta. The economic limit in this study is defined as the minimum average daily oil production rate needed to break-even on a Before and/or After Income Tax basis. The study utilizes the current, effective January 1, 1983, Canadian Oil and Gas taxes and royalties. The procedure to determine the economic limit is independent of the current taxes and royalty rates and thus can be used at any period of time. The economic limit can be expressed by an easy to use set of equations. These equations are developed in the appendices. The values of the constants in the equations are determined by the tax rates, royalty factors, operating costs and wellhead price. Once the constants are calculated for a given project, it is then very simple to calculate the economic limit as well as perform sensitivity analysis for that project. These equations can be used in both the planning stages as well as in every day use in the area office. The operating costs used in this study are completely arbitrary. They are not representative of any particular field or project. The intent of this paper is to develop and easy method by which a project can be evaluated. paper is to develop and easy method by which a project can be evaluated. It is not the intent of this paper to comment on the economics of any particular project in Alberta. particular project in Alberta. Both single well as well as unit's or project's economic limit can be evaluated by the method outlined below. In calculating the unit's or project's royalty rate an average monthly oil production rate per producer project's royalty rate an average monthly oil production rate per producer must be used.
A.T. Watson, P.D. Kerig, R.W. Otter
Society of Petroleum Engineers Journal, Volume 25, pp 909-916; https://doi.org/10.2118/12585-pa

Abstract:
Homogeneous core samples are needed for EOR experiments. We have devised a simple test for detecting the presence of nonuniformities in cores. The test consists of presence of nonuniformities in cores. The test consists of measuring the pressure drop across the core during a two-phase immiscible displacement experiment. We show that for a constant injection rate, the pressure drop will be linear with time provided that the core is homogeneous. In situations for which the initial section of the core is homogeneous, but the properties are not uniform in a latter section of the core, the location of the position where the rock properties fast change may be approximately determined. The effect of heterogeneities on the pressure-drop profile is demonstrated with analytical solutions and profile is demonstrated with analytical solutions and laboratory experiments. Introduction Core samples are used routinely for EOR or relative permeability experiments. For such experiments, selection permeability experiments. For such experiments, selection of a homogeneous core sample is necessary. Visual inspection of the core is not sufficient to ensure homogeneity. Often, vugs or shale barriers may be present, which may invalidate experimental results. In this paper, a simple test to detect the presence of core heterogeneities is devised. The scale of heterogeneities considered corresponds to the usual macroscopic description of porous medium properties. The properties of a porous medium (e.g., the properties. The properties of a porous medium (e.g., the porosity and permeability) at any particular location refer porosity and permeability) at any particular location refer to average quantities for some appropriate (small) representative volume element. In this way, each (locally averaged) property is defined at every point within the medium, the collection of which defines the representation of each property as a function of position. If each macroscopic property has the same value at all positions, the medium is said to be homogeneous. Otherwise, the medium is heterogeneous. A more complete discussion of macroscopic properties and heterogeneities can be found in Refs. 1 through 3. The macroscopic scale is a natural one to use for core selection because attempts to model coreflood experiments or to estimate properties of the porous medium on the basis of measured flow data generally will use mathematical models that use macroscopic properties. A homogeneous core sample is necessary for the experimental determination of relative permeabilities from displacement experiments. Explicit methods for estimating relative permeabilities from displacement data are based on the permeabilities from displacement data are based on the Buckley-Leverett model, in which the core is assumed to be homogeneous. The absolute permeability generally is determined from a single-phase flow experiment and thus represents an average value for the entire core. If the core is not homogeneous, so that the absolute permeability takes on different values in different locations permeability takes on different values in different locations in the core, errors will appear in the relative permeability estimates. Although the magnitude of the errors will depend on many factors, a macroscopically homogeneous sample is always preferred. Note that heterogeneities may also be defined on a microscopic scale. A porous medium that is macroscopically homogeneous may be microscopically heterogeneous. In fact, this typically would be the case because few real porous media structures are microscopically homogeneous. In this paper, we develop a test for detecting the presence of macroscopic heterogeneities in core samples. presence of macroscopic heterogeneities in core samples. The test is conducted by displacing the fluid that initially saturates the porous medium with a second fluid that is immiscible with the displaced fluid. The pressure drop across the core is recorded up to the time of breakthrough of the displacing fluid. The test is based on the observation that, with a constant injection rate and incompressible fluids, the pressure drop will be linear with time provided that the core is homogeneous. It is also shown provided that the core is homogeneous. It is also shown that, if the porosity and permeability for a heterogeneous core may be approximated as functions of the longitudinal spatial dimension, the pressure drop will be linear with time provided that the region in which both fluid phases are flowing simultaneously has uniform properties. The detection of heterogeneities by this method is discussed and illustrated with analytical solutions for the displacement process and with laboratory experimental data. Theory We consider here a displacement experiment with two incompressible fluids. Initially, the core is saturated with one fluid and the other fluid is injected at one end. For example, if the core initially contains only oil or air, water might be injected at one end. The core could contain the irreducible saturation of the displacing fluid initially, although this is not experimentally convenient and is not necessary for conducting the test. The pressure drop across the core is recorded through the time of breakthrough of the displacing fluid at the core outlet. SPEJ P. 909
T.G. Monger
Society of Petroleum Engineers Journal, Volume 25, pp 865-874; https://doi.org/10.2118/12708-pa

Abstract:
This paper investigates the role of oil aromaticity in miscability development and in the deposition of heavy hydrocarbons during CO2, flooding. The results of phase equilibrium measurements, compositional studies, sandpack displacements, and consolidated corefloods are presented. Reservoir oil from the Brookhaven field and presented. Reservoir oil from the Brookhaven field and synthetic oils that model natural oil phase behavior are examined. Phase compositional analyses Of CO2/synthetic-oil mixtures in static PVT tests demonstrate that increased oil aromaticity correlates with improved hydrocarbon extraction into a CO2-rich phase. The results of tertiary corefloods performed with the synthetic oils show that CO2-flood oil displacement efficiency is also improved for the oil with higher aromatic content. These oil aromaticity influences are favorable. Reservoir oil experiments show that a significant deposition of aromatic hydrocarbon material occurs when CO2, contacts highly asphaltic crude. Solid-phase formation was observed in phase equilibrium and displacement studies and led to severe plugging during linear flow through Berea cores. It is unclear how this solid phase will affect oil recovery on a reservoir scale. Introduction Several reports suggest that oil aromaticity affects the CO2, displacement process of reservoir oil. Henry and Metcalfe noted the absence of multiple-liquid phase generation in displacement tests performed with a crude oil of low aromatic content. Holm and Josendal showed that when a highly paraffinic oil was enriched with aromatics, the slim-tube minimum miscibility pressure (MMP) decreased and oil recovery improved. Qualitative differences in the phase behavior of two crudes with contrasting aromatic contents prompted the suggestion by Monger and Khakoo that increased oil aromaticity correlates with improved hydrocarbon extraction into a CO2-rich phase. Clementz discussed how the adsorption of petroleum heavy ends, like the condensed aromatic ring structures found in asphaltenes, can alter rock properties. Laboratory studies have shown that improved oil properties. Laboratory studies have shown that improved oil recoveries in tertiary CO2 displacements benefited from changes in wetting behavior apparently, induced by asphaltene adsorption. Tuttle noted that CO2, appears to reduce asphaltene solubility and can cause rigid film formation. In these respects, oil aromaticity may also account for phase-behavior/oil-recovery synergism. Asphaltene deposition, though not a problem during primary and secondary recovery operations, was primary and secondary recovery operations, was reported in the Little Creek CO2 -injection pilot in Mississippi. Wettability alteration from asphaltene precipitation appears to have explained the results of low residual oil at high water-alternating-gas ratios in the Little Knife CO2, flood minitest in North Dakota. This paper provides detailed laboratory data from phase equilibrium measurements, compositional studies. sandpack displacements, and consolidated corefloods that illuminate the role of aromatics in miscibility development and in solid-phase formation during CO2 - flooding. The results for synthetic oils that model crude-oil behavior suggest that CO2-flood performance will benefit from increased oil aromaticity. The interpretation of reservoir oil results is more difficult. The precipitation of highly aromatic hydrocarbon material is observed when CO2, contacts Brookhaven crude. One purpose of this paper is to examine the variables that influence asphaltene precipitation. Near the wellbore, solid-phase formation might precipitation. Near the wellbore, solid-phase formation might reduce injectivity or impair production rates. Perhaps in other regions of the reservoir, altered permeability and/or wettability caused by solid-phase deposition might improve the ability of CO2, to contact oil. Additional work is needed to determine which potential benefits of oil aromaticity are significant on the reservoir scale. Advances in computer-implemented equations of state are making the prediction of CO2,/hydrocarbon phase behavior easier and more reliable. When an equation of state with CO2/reservoir-oil mixtures is used, an important consideration is the characterization of the heavy hydrocarbon components. One characterization method that appears to match the experimental data accurately in the critical point region for rich-gas/reservoir-oil mixtures is based on assigning separate paraffinic, aromatic, and naphthenic cuts. An additional aim of this study is to provide experimental data in assisting similar modeling provide experimental data in assisting similar modeling efforts for CO2/reservoir-oil mixtures. Experimental phase equilibrium data for mixtures containing CO2, and phase equilibrium data for mixtures containing CO2, and heavy hydrocarbons, particularly aromatics, are scarce. The behavior of multicomponent CO2,/hydrocarbon systems is not readily deduced from the phase equilibria of binary or ternary systems. Materials and Methods Phase Equilibrium Studies. A schematic diagram of the Phase Equilibrium Studies. A schematic diagram of the apparatus used in the phase-behavior experiments appears in Fig. 1. A detailed description of the equipment, procedures, chemicals, and analytical methods used is given procedures, chemicals, and analytical methods used is given in Ref. 10. SPEJ P. 865
S. E. Halfman, M. J. Lippmann, J. A. Gilreath
Society of Petroleum Engineers Journal, Volume 25, pp 793-803; https://doi.org/10.2118/12739-pa

Abstract:
The Cerro Prieto geothermal field is located in Baja California, Mexico, in the, Salton Trough-a rift basin filled mainly with Colorado River sediments. A comprehensive wireline log analysis was undertaken as part of a multidisciplinary study of this geothermal system. It establishedthe physical properties of the various sedimentary units;the depositional environment and hydrothermal alteration of the units;the location, attitude, and displacement of faults; andthe subsurface circulation of the geothermal fluids. Presented are the methodology that was used and the application of the results to further exploration and development of this high-temperature geothermal resource. Introduction The liquid-dominated Cerro Prieto geothermal field is located in the sediment-filled Mexicali Valley of Baja California, Mexico, about 20 miles [30 km] south of the U.S. border (Fig. 1). More than 100 deep exploration and development wells have been drilled in the area (Fig. 2), a few reaching crystalline basement. Analysis of the vast amount of data collected from these wells has given us a good understanding of the geologic characteristics of this high-temperature (up to 680F [360C]) geothermal resource. The exploration effort at Cerro Prieto is summarized in an earlier paper. paper. The purpose of this paper is to discuss the wireline log analysis that led tothe development of geologic and hydrogeologic models of the field,an understanding of the depositional environment of some of the sedimentary units identified in the subsurface, andthe identification of postdepositional changes in these units. These studies have postdepositional changes in these units. These studies have allowed us to determine the variations in porosity, permeability, thickness, and lateral continuity of the permeable (and less permeable) layers in the system-crucial parameters for the design permeable) layers in the system-crucial parameters for the design of drilling and completion of new wells and for the development of a reservoir management plan. Geologic Setting and Recent History of the Area The Mexicali Valley is part of the Salton Trough, an actively developing structural depression that resulted from tectonic activity that has created a series of spreading centers and transform faults that link the East Pacific Rise to the San Andreas fault system. The Cerro Prieto field is associated with one of these spreading centers, where the crust is being pulled apart by right-lateral strikeslip movement along the Cerro Prieto and Imperial faults (Fig. 3). During the early Pliocene, the current configuration of the Gulf of California began to develop by major crustal extension, which split Baja California from the Mexican mainland. At that time, the waters of the Gulf of California extended northward to about the Salton Sea area. The progradation of the Colorado River delta into the Cerro Prieto area began in the mid- to late Pliocene. The southwesterly advance of the delta was essentially complete by the late Pliocene. This resulted in the conversion of the Salton basin to a nonmarine depositional basin. By the mid-Pleistocene, the marine connection between the Gulf of California to the south and the Imperial Valley to the north was severed. Geologic and Hydrogeologic Models of Cerro Prieto The subsurface stratigraphy at Cerro Prieto is characterized by vertical and lateral variations in lithofacies. The lithologic column consists ofan upper part of unconsolidated and semiconsolidated sediments (Unit A) that is mainly sands, silts, and clays, anda lower part of consolidated sediments (Unit B) that is mainly sandstones and part of consolidated sediments (Unit B) that is mainly sandstones and shales. The hydrothermal alteration of the deeper layers and the existence of hydrothermal mineral zonation around the reservoir have been documented by careful mineralogic studies of well cuttings and cores and by analysis of wireline well logs. Following the general approach of Lyons and van de Kamp, Halfman et al. used wireline and lithologic log data to delineate and to classify the lithologic sequences penetrated by the wells into three lithofacies groups: sandstone, sandy shale, and shale (Figs. 4 and 5A). The sandstone beds basicallyare thick, permeable, and well-defined (with some interbedded shales) in the sandstone group,are thinner and less permeable (with a higher percentage of intercalated shales) in the sandy-shale group, andare even thinner ( less than 10 ft [ less than 3 m]) in the shale group (e.g., Fig. 4). The main geophysical logs used to develop this model include gamma ray (GR), spontaneous potential (SP), deep induction (ILD), and compensated formation density (RHOB). JPT P. 793
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