Well-test Analysis Research Articles

Ekofisk Field Reservoir Characterization: Mapping Permeability Through Facies and Fracture Intensity

Summary The development of a strategy for the detailed three-dimensional (3D) description of permeability was a key ingredient of the recent reservoir characterization study of the Ekofisk field. Because the ultimate objective of this characterization effort was the construction of a new full-field 3D reservoir flow model, permeability and its heterogeneity received special focus. Permeability has a tremendous influence on history matching of reservoir fluid flow models and, in turn, reservoir-management decisions. This is particularly true in a mature, waterflooded field such as Ekofisk. The Ekofisk field is a high-porosity, low-matrix permeability naturally fractured chalk. Fluid-flow characteristics of the reservoir are largely governed by the distribution, orientation, and interconnectivity of the natural-fracture system. To honor this mechanism, an algorithm was developed based on the log linear relationship between fracture spacing (intensity) data from core and well-test effective permeability. To capture the intrinsic heterogeneity and complex nature of Ekofisk field, the basic relationship between fracture intensity and permeability was modified to incorporate variations associated with (1) chalk facies (2) fracture type; (3) porosity; (4) structural location; (5) structural curvature; and (6) silica content. To calibrate the algorithm, permeability determined from distributing total well-test flow capacity (kh) based on production log contribution was used as a tuning parameter. As a final step, geostatistical techniques were used to ensure that permeabilities derived from the algorithm matched those obtained from well-test analysis.

Reservoir Description by Well-Test Analysis by Use of Cyclic Flow-Rate Variation

Summary This work investigates the possibility of characterizing the permeability distribution in areally heterogeneous reservoirs through the interpretation of pressure response to cyclic flow-rate variations. We formulated a mathematical model for the pressure behavior caused by sinusoidal flow rates in reservoirs with continuously and smoothly varying radial-permeability distributions. The solution is obtained by the application of a regular perturbation analysis, and a correlation between the radius of cyclic influence and the frequency of a sinusoidal flow rate is developed. The analytical perturbation solution allows a qualitative assessment of the effects of areal reservoir heterogeneities on the pressure response either at the active well or at an observation well. Because the perturbation method results in only an approximate solution, we propose a quantitative method to describe the permeability distribution based on the fully correct multicomposite radial reservoir model. The permeability in each zone of the equivalent reservoir is estimated by using a nonlinear regression procedure. The frequency correlation may be used to design pulse-test flowrate schedules so that an optimum result can be achieved in terms of parameter estimation. We investigated several factors affecting the quality and the uncertainty in the estimated permeability distribution, along with examples including a variety of geometric and permeability distribution configurations. These factors include the type of test (constant-rate drawdown or pulse test) and reservoir configuration. In particular, we found the frequency of flow-rate changes and the point in the system at which to measure and interpret the pressure data to be important.

An investigation of constant-pressure gas well testing influenced by high-velocity flow

This paper presents the results of a study of transient pressure analysis of gas flow under either constant bottom-hole pressure conditions or the constant wellhead pressure conditions. The effects of formation damage, wellbore storage and high-velocity flow are included in the model. The analysis of simulated well tests showed that the interpretation methods used for liquid flow are generally accurate when the m( p) is used. For these conditions, a graph of 1/ q D vs. log t D presents gradually lower values of 1.1513 as the value of p wf decreases: for pressure buildup conditions, a graph of m D(1, Δ t a D )/ q D(Δ t a D = 0) vs. ( t a D + Δ t a D )/Δ t a D shows values of this slope within 1% of the 1.1513 value. However, when high-velocity flow influences constant pressure production tests, the slope can yield errors up to 13%. This upper limit occurs when the formation has a relatively ‘high’ permeability (around 1 mD) and the rate performance test is affected by high-velocity flow. It was found that pressure buildup tests are superior to rate performance tests because high-velocity flow does not affect the slope of the straight line portion of the buildup curve. Derivative analysis of simulated buildup tests showed that the skin factor is considerably miscalculated when the high-velocity flow effect is significant. This problem could lead to errors in the calculation of the skin factor, s, up to 300%.

Pressure Behavior in Finite Channel-Levee Complexes

Summary In a channelized environment, the overbank facies (levees, crevasse-splays) have poorer reservoir qualities than the channel itself. In this type of environment, the geometry of this two-feature complex, together with its permeability contrast, influences the pressure transient response. The pressure behavior of this kind of reservoir has been computed for well-test analysis purposes. Our geometric model comprises a main channel bounded laterally with finite or infinite width levees. It is conceptualized as a composite linear strip reservoir with different mobilities and diffusivities. The length of the whole system also can be either finite or infinite. The solution uses a time-space Laplace transform and a spatial Fourier transform already used by Ambastha,1 Butler,2 and Kuchuk.3 Moreover, our model adds lateral limits by no-flux boundary conditions and longitudinal limits by superposition of image wells or by using a finite Fourier transform. This paper exhibits specific features of the type curves generated for the model. The influence of the levees and of the permeability ratio between channel and levees on the derivative signature is discussed. Hints are given for diagnostic purposes and parameter estimation. Fieldcase buildup analyses show the applicability of the approach.

Well-Test Analysis for Naturally Fractured Reservoirs

Well testing provides a powerful tool to detect and to evaluate heterogeneities in naturally fractured reservoirs (NFR`s). Experience has shown that this type of reservoir may display behavior that consists of a variety of flow models. This paper presents a discussion of the applications and limitations of pressure-transient tests in the evaluation of NFR`s.

Well-Test Analysis for Naturally Fractured Reservoirs

Well-Test Analysis for Naturally Fractured Reservoirs

Discrimination Between Reservoir Models in Well-Test Analysis

Summary In well-test analysis with nonlinear regression, discrimination between candidate reservoir models is a key procedure. Graphical analysis now performs this step, with the pressure derivative plot and confidence intervals used to select an adequate model. Human bias may influence the selection by graphical analysis, however, and the result may vary according to the interpreters. Confidence intervals can give a quantitative evaluation of model discrimination, but it sometimes provides inappropriate results. We propose a new quantitative method, the sequential predictive probability method, to discriminate between candidate reservoir models. This method is based on Bayesian inference, in which all information about the reservoir model and, subsequently, the reservoir parameters deduced from well-test data, is expressed in terms of probability and is regarded as a direct extension of the idea of confidence intervals. This method gives a unified measure of model discrimination. We demonstrate the applications of this method to synthetic and actual field well-test data.

The Method of Sources and Sinks—A Perspective

Abstract Professor Henry J. Ramey once remarked that he wished he had devoted more time to the study of recovery problems but that the intellectual challenges of issues in well-test analysis were much too enticing. Among his myriad interests, the method of sources and sinks had a special place. Undoubtedly, his early work in thermal recovery1 served as a spark for his "deep affection" for the method of sources and sinks. This communication is a bird's-eye-view of this subject as it pertains to well-test analysis. I hope that this note will spark an interest in this topic for those unfamiliar with this method of solving partial differential equations and at the same time provide additional insights to those familiar with this topic. The examples considered here have been chosen with two perspectives. First, given the nature of this contribution, they serve a historical purpose. Second, they address some issues that need to be highlighted.

Interference Testing In a Two-region Composite Reservoir With a Frontal Skin

Abstract A two-region composite reservoir model is used to analyze well-test data from a variety of enhanced oil recovery projects, geothermal reservoir, and acidization projects. Dynamic phenomena, such as phase changes and multi-phase flow effects in a region near the front, can cause a sharp pressure drop at the front. Such a sharp pressure drop can be modeled as a thin frontal skin. This study considers interference testing in a two-region composite reservoir with a thin frontal skin. Wellbore storage and skin at the active well are also included in the analytical solution to the problem. Correlating parameters are established in the presence of a frontal skin for type-curve marching analysis of interference data from such reservoirs. Our results indicate that for an observation well in the inner region surrounding the wellbore, the effects of storativity ratio (i.e. Φc, ratio) and frontal skin on interference tests are similar. Thus, frontal skin cannot be estimated independently of storativity ratio from an interference test on an observation well in the inner region. However, interference test data collected at an observation well located in the outer region beyond the front helps estimate storarivity ratio and frontal skin independently of each other. The information presented in this paper should be useful in obtaining a consistent analysis of well tests conducted in composite reservoir situations. Introduction This study considers interference pressure and pressure derivative responses in a two-region composite reservoir with an infinitesimally thin skin at the discontinuity. The observation well may be located in any region. Figure 1 shows a schematic diagram of a radial, two-region composite reservoir with an observation well located in the outer region (region 2) at a distance a from the active well. Region 1 (inner region) extends to a radius R, and a thin skin sr may occur at the discontinuity. Ambastha and Ramey(1) presented an analytical solution for transient pressure behavior at any point in a reservoir depicted by Figure 1. Their analytical solution as presented in the Appendix of this paper has been used to investigate interference test analysis in a radial, two-region composite reservoir with a frontal skin. All results presented in this study are for an infinite reservoir. FIGURE 1: Two-region composite reservoir. (Available in full paper) Correlating Parameters Satman(2) presented an study of interference responses in radial, two region infinite composite reservoir. He did not consider the effects of a thin skin at the discontinuity. He correlated transient interference pressure responses using CD/aD, CDe2s, a/R, M and F as correlating parameters. He defined dimensionless pressure and time using the properties in the outer region, and considered the interference pressure responses for the observation wells located in the outer region only. This study also considers the same correlating parameters as used by Satman(2). A thin skin at the discontinuity, Sr is an additional correlating parameter, Figure 2 through 7 verify the selected correlating parameters under different conditions. Figure 2 through 7 are for M = 10 and Fs = 100. TABLE 1: Parameters used to generate responses shown on Figures 3, 6 and 7. (Available in full paper)

Well-Test Analysis in Solution-Gas-Drive Systems for Fractured Reservoirs

Summary This study examines issues pertaining to two-phase (oil and gas) transient flow in fractured reservoirs. Dual-porosity and dual-permeability models are examined. Pressure, saturation, and flowing GOR behaviors are noted, and the influence of communication on these behaviors is documented. Methods to compute saturation as a function of pressure for the fracture and matrix systems are presented.

Analysis of Transient-Pressure Response of Horizontal Wells in Bounded Reservoirs

Summary The main purpose of this paper is to present analysis methods for transient-pressure response of horizontal wells in bounded reservoirs. Several lateral-boundary models are examined, and detailed explanations of possible derivative responses are given. New, generalized diagnostic rules and well-test analysis procedures are provided. Practical issues are discussed at length.

Well-Test-Model Recognition With Laplace Space

Summary This study presents a mathematical background that justifies a new use of Laplace space in well-test analysis. It enables us to perform the whole parameter identification (CD S, k, h, etc.) in Laplace space or at least gives us a powerful tool to treat pressure data to recognize the model to use for parameter identification in real space. It shows how the Laplace transform of pressure can be plotted with exactly the same behavior as the real pressure function so that the plots keep their familiar shape. The coefficients of the dimensionless parameters also remain the same, which enables us to display a new set of characteristic and easily understandable type curves in Laplace space. The mathematical background also sheds light on use of the Laplace transform to deconvolute flow rates by modifications of earlier techniques that were extremely sensitive to noise in the data. The Laplace-space approach provides an entirely new way of examining and understanding well-test results. It has been applied successfully to noisy, simulated data and real field data where conventional interpretation could not illuminate ambiguities.

Fibrous Illite Controls Productivity in Frontier Gas Sandstones, Moxa Arch, Wyoming

Summary Core, log, and well-test analyses from two wells recently completed in the Frontier sandstone in the Moxa Arch area of Wyoming revealed that fibrous illite severely reduced gas productivity. In this study area, presence of fibrous illite currently cannot be predicted and effects can be recognized only through laboratory tests on preserved cores.

Advances in Practical Well-Test Analysis (includes associated paper 26134 )

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.

An Improved Regression Algorithm for Automated Well-Test Analysis

Summary Automated well-test analysis is a familiar technique, but the procedure still depends on the speed and robustness of the regression algorithms used. We examine a modification of the Cholesky factorization (CF) method for the solution of nonlinear-parameter-estimation problems and show that this modification is a very beneficial adaptation of the Gauss-Newton method. The new algorithm, the modified Gauss-Cholesky (MGC) method, is more robust under unfavorable conditions than two of the most reliable existing algorithms [the Gauss-Marquardt (GM) and the Newton-Barua (NB) methods]. This robustness seems to depend on the algorithm's ability to control the rapid change of ill-defined parameters and not on computational singularity or higher-order representation.

Treating-Pressure Analysis in the Bakken Formation

Summary The Bakken formation is an oil-producing interval in the Williston basin. Usually, commercial Bakken wells are linked to an anisotropic natural fracture network. Hydraulic fracturing treatments have been used extensively in vertical wells and to a limited extent in horizontal wells. In this paper, bottomhole treating pressures (BHTP's) are analyzed to improve understanding of hydraulic fracture propagation in the Bakken. Introduction The Bakken formation produces oil over a wide area in the Williston basin. Bakken sediments were deposited in the early Mississippian/late Devonian and consist of upper and lower black shales and a middle carbonate/siltstone interval.1 The Bakken formation is confined by the carbonates, shales, and sands of the Lodgepole (upper) and Three Forks (lower) formations. These bounding zones are productive locally. In most areas of the Williston basin, matrix permeability in Bakken reservoirs in very low (<0.1 md). Oil is produced through an anisotropic natural fracture set, and the fractures seem to trend normal to the minimum horizontal stress.2 Hydraulic fracturing treatments are used extensively in vertical Bakken wells to improve well productivity.3 Normally, 50,000 to 150,000 gal of gelled Bakken lease oil is used as the fracturing fluid.4 A variety of proppant types and concentrations have been used, in volumes ranging from 80,000 to 500,000 lbm. Usually post-treatment well-test analysis shows that the apparent conductive (propped) fracture half-length is <100 ft,5 regardless of the fracturing technique used. A hydraulic fracture simulator6 indicates that propped half-lengths range from 300 to 600 ft. The discrepancy between well-test and simulator results suggests that hydraulic fractures trend in the Bakken.2 When this happens, a propped fracture affects well productivity by circumventing formation damage (e.g., plugged natural fractures) and by linking into on-trend natural fractures missed by the wellbore. In horizontal wells, fracture treatments may improve well productivity of bypassing wellbore damage and by mitigating vertical permeability anisotropy (i.e., layering effects).2,7 Analyzing bottomhole pressure (BHP) during a fracture treatment helps to determine how the hydraulic fracture is propagating. Analyzing surface pressure or BHP immediately after a fracture treatments helps to determine the fracturing fluid-loss rate and the dimensions of the hydraulic fracture.8-15 This information can be used to refine the job design for future treatments in the evaluated zone. The principles of BHTP analysis are based on the relationship between fracturing fluid pressure and the elastic deformation of rock at the fracture walls; formation rock properties must be known to use this technique. The primary focus of this paper is to analyze BHTP and supplementary data from a variety of wells in an effort to understand the nature of fracture propagation in the Bakken formation. Topics covered in this paper include the mechanical properties of the gross Bakken interval, the fracture-height growth, the effect of fracturing fluid viscosity and proppant addition on net treating pressure, the use of the G-function plot to estimate the fracturing fluid-loss rate, and the effect of perforation restriction on BHTP and how to remove this restriction. Rock Properties and Fracture-Height Growth The elastic properties of rock (i.e., Young's modulus, E, and Poisson's ratio, µ) affect hydraulic fracture propagation. Young's modulus is the stress/strain ratio for uniaxial stress16; it is a measure of rock stiffness that affects hydraulic fracture width and net fracture pressure (i.e., BHTP minus fracture closure pressure). Poisson's ratio is the ratio of lateral expansion to longitudinal contraction for uniaxial stress. This property, along with pore pressure, determines the amount of vertical overburden stress that is applied horizontally to rock layers. Poisson's ratio is directly proportional to the minimum in-situ horizontal stress, sHmin, as expressed by17 Equation 1 where sV=vertical or overburden stress, a=poroelastic constant that varies between 0 and 1, pp=pore pressure, and s=tectonic stress.

Expected Developments in Transient Testing

Summary. This paper discusses the developments expected in six areas of pressure-transient testing during the next 50 to 10 years (advances in measurements, new models, computer-aided analysis, integration with other reservoirdescription methods, standardization, and new testing methods). Its purpose is to stimulate discussion purpose is to stimulate discussion among those working in well-test analysis about the developments needed in this area of technology. Introduction Transient tests are used in all areas of petroleum engineering to provide useful petroleum engineering to provide useful information about the well/reservoir system. For example, they can be used to evaluate the types of fluids discovered and the potential of wildcats and development wells by drilstem tests; to estimate the completion efficiency after perforating, gravel packing, or fracturing of a well; to monitor the changes in reservoir pressures and wellbore skin throughout the well's life; to determine the communication among several wells by interference and pulse test s; to provide information about injection wells through step-rate and falloff tests; and to play an important role as one of the reservoir-description methods. Transient testing is a rigourous, reliable, and relatively well-understood tool of the trade. Use of transient information is widespread for several reasons.They provide information needed to manage oil and gas reservoirs (e.g. permeability, reservoir pressure, and effective permeability, reservoir pressure, and effective fracture length).They are relatively simple to run (in some cases, we need only a surface pressure gauge and a valve). pressure gauge and a valve).The results from these tests are not tool-dependent (i.e., we don't need different interpretation methods for pressure gauges from different manufacturers if their accuracy, precision, and resolution are in the same range).Interpretation models are available in the literature (probably because several of these models were developed at academic institutions and service companies). From time to time, papers that summarize the state of the art of discuss the use of current technology are presented. This paper looks to the future. It points out areas paper looks to the future. It points out areas where technical advances are needed to solve existing problems in reservoir description and management. Areas of expected development were determined on the basis of the current st ate of technology and the forces that most likely will dictate the directions of the work. Although transient testing is considered to be a "mature" area of reservoir engineering, it is still is one of the most active areas of interest in research, development, and field operations. The high level of activity is expected to continue because (1) several technical problems have not been solved (e.g., rigorous analyses of tests in hetergeneous formations or reservoirs undergoing secondary or tertiary recovery are needed); (2) computer and communication developments have provided more capabilities to transfer, to process, and to analyze data; (3) the industry is becoming aware of the benefits of comprehensive reservoir description, which requires integration of several characterization methods where transient testing is proving to be a key element; and (4) results from work in this area have been successful in the past. Therefore, it is likely that resources will be allocated to develop the needed technology. The key word describing the expected developments is "evolution" . While a revolutionary development is could occur, it is more likely that small, steady steps will contribute to well-test-analysis development in the next few years. Advances in Measurements Flow rate and pressure are the two parameters monitored and used in well testing. parameters monitored and used in well testing. Flow rate originally was used as the controlling variable and pressure response was measured vs. time. The name "pressure-transient analysis: reflects this procedure. The flow rate usually was changed at the surface. The pressure response was measured either at the surface or downhole. Now, either flow rate or pressure is used as the controlling variable, and the response of the other parameter is measured (we have not only PD vs. tD type curves, but also 1/qD vs. tD type curves). Thus, "well-test analysis" is a more appropriate name than pressure-transient analysis. Analysis pressure-transient analysis. Analysis methods that use the transient behavior of the flow rate and pressure simultaneously also are available. Nevertheless, more tests are run by changing the flow rate at the surface and measuring the bottomhole-pressure (BHP) response vs. time. JPT P. 898

Well-Test Analysis Following a Closed-Fracture Acidizing Treatment

Summary A new model representing fluid flow in a reservoir treated with closed-fracture acidizing (CFA) is presented. The model is characterized by a low-conductivity fracture (representing the closed fracture) and highly conductive wormholes (owing to acid flow). Application of the model to pressure-transient data analysis following a CFA treatment is presented through a field example.

Framework for Constructing Clastic Reservoir Simulation Models

Summary. This paper surveys practical methods for reservoir modeling. To eliminate unnecessary jargon and to promote synergy, a simple classification system of sand-body architecture is proposed that helps relate geology to fluid flow. Guidelines are given for treating reservoir heterogeneities and upscaling properties to gridblock-scale averages. Introduction The main objective of this paper is to give guidelines for the preparation of simulation input for clastic reservoirs. Reservoir simulation efforts range from material-balance-type analysis to very detailed 3D simulation with as many as 50,000 gridblocks. Early simulation efforts attempted to estimate the drive mechanism and recovery efficiency for a given development scheme and to present preliminary ideas on well position, spacing, and the completion interval. In a fairly simple reservoir, about five wells may supply sufficient data for a 3D simulation, and radial models around these wells can provide useful insight into the relationship between core permeability measurements and actual regional permeability distribution. This will require geological modeling and can extend to modeling of sedimentary structure. For successful detailed 3D simulation, a reservoir geological model and an excellent understanding of the permeability distribution and continuity are necessary. Reservoir Heterogeneities The main difficulty in geological modeling is to take proper account of the various largeto small-scale heterogeneities. These can be conveniently subdivided into seven basic types ranging from large-scale faults, external and internal sand-body characteristics, to microscopic features, with fractures as the seventh class. Each type of heterogeneity influences fluid flow and hence sweep and recovery efficiencies (Table 1). In this paper, we focus on the modeling of reservoir architecture and permeability within genetic sand-body units. Faults and fractures can be very important in reservoir modeling, but these types have been discussed recently in some excellent books and papers. Thus, in this paper, the discussion is restricted to some remarks on major features and influences with references to useful literature. Sealing faults constitute no-flow boundaries in simulation models and therefore often form the grid boundaries. Thus, major faults tend to have a strong influence on grid orientation. Faults that are semisealing or nonsealing can be incorporated into modern simulators by inserting special gridblock connections with estimated transmissibilities. Transient pressure testing can be carried out to arrive at realistic tmnsmissibilities of fault zones. Small-scale fractures are difficult to incorporate into models. Tight cemented fractures can be detected on borehole-wall imaging logs or in cores. They may reduce permeability significantly and occasionally may cause severe small-scale compartmentalization of the reservoir. Well testing will reveal the degree of reservoir deterioration caused by the tight fractures. Open fractures are comparatively rare in most clastic reservoirs. In tight sandstones, they may play an important role, especially in gas reservoirs. Reservoir simulation of these so-called dual-porosity reservoirs is difficult because of the problem of quantifying the degree of capillary contacts across fractures. A recent paper presents methods to model block-to-block interaction. Welltest analysis can show the presence of an open-fracture system, but the results may be ambiguous because certain layered systems have a pressure response similar to dualporosity reservoirs. For this reason, one generally has to carry out core studies to analyze the natural fracture system and the fracture spacing. General Approach to Reservoir Modeling Any scheme for geological reservoir modeling starts with a data base from which one first derives a depositional model through a core/log facies analysis (Fig. 1). Regional information is usually a major help, not only in reaching conclusions, but also in planning the data acquisition. With the facies model and the facies pattern identified in each well, a correlation can be attempted. At this stage, one needs a statistical data base of the geometry of each sand- or shale-body type detailed seismics may be of use, especially if high-quality 3D surveys are available. The detail of the correlation that can be obtained is a function of well spacing and reservoir complexity. If the well spacing is large or if the reservoir architecture is very complex, a detailed, deterministic correlation may not be possible. In that case, we can apply statistical methods to develop likely configurations of the reservoir architecture. JPT P. 1248⁁

Well-Test Analysis for Solution-Gas-Drive Reservoirs: Part 3—A Unified Treatment of the Pressure-Squared Method

Summary This work considers the analysis of radial-flow, well-test pressure data under multiphase flow conditions. We show that drawdown- and buildup-pressure data can be analyzed to obtain estimates of effective permeability and the skin factor with a semilog plot of pressure squared vs. time. It is shown that the liquid Matthews-Brons-Hazebroek (MBH) functions can be used to obtain an approximate estimate of average reservoir pressure. A theoretical explanation for a semilog analysis method based on the pressure-squared method is presented.