Effect of Wellbore Storage on Pulse-Test Pressure Response

1975 ◽  
Vol 27 (06) ◽  
pp. 707-709 ◽  
Author(s):  
M. Prats ◽  
J.B. Scott
Keyword(s):  
Pressure Response ◽  
Pulse Test ◽  
Wellbore Storage ◽  
Test Pressure

A Method To Account for Afterflow at the Pulsing Well During Pulse Tests

1983 ◽  
Vol 23 (03) ◽  
pp. 519-520
Author(s):  
Hubert Winston
Keyword(s):  
Computer Simulations ◽  
Flow Rate ◽  
Storage Capacity ◽  
Pulse Length ◽  
Test Area ◽  
Pilot Test ◽  
Test Results ◽  
Pulse Test ◽  
Wellbore Storage ◽  
And Storage

Abstract The nature of wellbore storage is such that afterflow during a pulse test can affect the reservoir pressure performance and can lead to the calculation of erroneous performance and can lead to the calculation of erroneous values for formation transmissibility and storage. This is most likely to occur when the wells of interest are close together or when after flow persists for a long time relative to the pulse length. This article describes a technique that was developed to account for the effects of after flow at the pulsing well during pulse testing of a small production pilot. The technique is not general because it requires that a computer-generated simulation of each pulse test be made. An application of the method is given. Introduction In carrying out a pulse test, we introduce a pressure disturbance into a reservoir by alternately increasing and decreasing the flow rate at the pulsing well in a known manner. The pressure at the responding well is monitored, and, if the wells are in pressure communication, the pressure distrubance eventually will affect the pressure at the responding well. Since the form and the duration of the flow, rate disturbance are known, and since the mathematics that describe the pressure behavior of fluid-beefing reservoirs are well understood, the pulse test pressure response can be predicted. Several methods are available to calculate values for formation transmissibility and storage within a pulse-tested reservoir. Although all real reservoirs are heterogeneous, the models for deriving these techniques assume that the reservoir is ideal. When the wells of interest are far apart or when the duration of after flow is short relative to the pulse length, the effects of wellbore storage on the pulse test results will be slight. If, on the other hand, the pulsing well and the responding well are close together or if after flow persists for a tong time, the effects of wellbore storage on the pulse test results may be substantial. The work described here began during the analysis phase of a series of pulse tests that were run in a small phase of a series of pulse tests that were run in a small pilot test area. Computer simulations of the tests showed pilot test area. Computer simulations of the tests showed that the method of Mondragon and Menzie would not compensate adequately for the strong effects of after flow on test results. Description of the Method Since a series of injection/falloff tests had been run in the pilot area, it was possible to obtain values for the ratio of formation transmissibility to the wellbore storage capacity, /F, at each well by type-curve matching techniques. Using this parameter, we can determine the after flow vs. time profiles that would occur during the pulsing-well shut-in periods and incorporate them into a computer simulation of each pulse test. A typical pulsing well-flow profile showing after flow during the shut-in period is profile showing after flow during the shut-in period is illustrated in Fig. 1. Given that the pulsing wells were observed to go on vacuum soon after shut-in and given that the wellbore storage capacity for these wells during the on-vacuum condition should be approximately two orders of magnitude larger than it would be during injection SPEJ p. 519

An Analytical Study of Interference in Composite Reservoirs

1985 ◽  
Vol 25 (02) ◽  
pp. 281-290 ◽  
Author(s):  
Abdurrahman Satman
Keyword(s):  
Pressure Drop ◽  
Composite System ◽  
Pressure Response ◽  
Oil Field ◽  
Observation Well ◽  
Wellbore Storage ◽  
Interference Test ◽  
Interference Tests ◽  
Inner Region ◽  
Observation Wells

Satman, Abdurrahman; SPE; Technical U. of Istanbul Abstract This paper discusses the interference test in composite reservoirs. The composite model considers all important parameters of interest: the hydraulic diffusivity, the mobility ratio, the distance to the radial discontinuity, the distance between wells, the wellbore storage, and skin effect at the active well. Type curves expressed as a function of proper combinations of these parameters are presented. Introduction Interference tests are widely used to estimate the reservoir properties. An interference test is a multiwell test that requires at least one active well, either a producer or injector, and at least one observation well. During the test, pressure effects caused by the active well are measured at the shut-in observation wells. Basic techniques for analyzing interference tests in uniform systems are discussed in Ref. 1. Usually, type-curve matching is the preferred technique for analyzing the pressure data from the test. Early interference test studies assumed that the storage capacity of the active well and the skin region around the sandface have a negligible effect on the observation well response. Recently, investigators have focused on wellbore storage and skin effects. Tongpenyai and Raghavan presented a new solution for analyzing the pressure response at the presented a new solution for analyzing the pressure response at the observation well, which took into account the effects of wellbore storage and skin at both the active and the observation wells. They produced type curves expressed as a function of exp(2S) products, the ( / ) ratios, and ( / ) to correlate the pressure response at the observation well. Composite systems are encountered in a wide variety of reservoir situations. In a composite system, there is a circular inner region with fluid and rock properties different from those in the outer region. Such a system can occur in hydrocarbon reservoirs and geothermal reservoirs. The injection of fluids during EOR processes can cause the development of fluid banks around the injection wells. This would be true in the case of a in-situ combustion or a steamflood. In a geothermal reservoir, pressure reduction in the vicinity of the well may cause the phase boundaries. A producing well completed in the center of a circular hot zone surrounded by producing well completed in the center of a circular hot zone surrounded by a concentric cooler water region is also a composite system. During the early to late 1960's, there was great interest in the composite reservoir flow problem. Hurst discussed the "sands in series" problem. He presented the formulas to describe the pressure behavior of problem. He presented the formulas to describe the pressure behavior of the unsteady-state flow phenomenon for fluid movement through two sands in series in a radial configuration, with each sand of different permeability. Mortada studied the interference pressure drop for oil fields located in a nonuniform extensive aquifer comprising two regions of different properties. He presented an expression for the interference pressure drop properties. He presented an expression for the interference pressure drop in an oil field resulting from a constant rate of water influx in another oil field. Loucks and Guerrero presented a qualitative discussion of pressure drop characteristics in composite reservoirs. Ramey and Rowan and pressure drop characteristics in composite reservoirs. Ramey and Rowan and Clegg developed approximate solutions. Refs. 11 through 13 also discuss composite reservoir systems and present either analytical or numerical solutions. Composite system model solutions have been used to determine some critical parameters during the application of EOR processes. The formation of a fluid bank around the injection well makes the reservoir a composite system. Van Poollen and Kazemi discussed how to determine the mean distance to the radial discontinuity in an in-situ combustion project. Refs. 16 and 17 discuss the effect of radial discontinuity in interpretation of pressure falloff tests in reservoirs with fluid banks. Sosa et al. examined the effect of relative permeability and mobility ratio on falloff behavior in reservoirs with water banks. The presence of different temperature zones in nonisothermal reservoirs may resemble permeability boundaries during well testing. Mangold et al. presented a numerical study of a thermal discontinuity in well test analysis. Their results indicated that nonisothermal influence could be detected and accounted for by tests of sufficient duration with suitably placed observation wells. Horne et al. indicated the possibility of determining compressibility and permeability contrasts across the phase boundaries in geothermal reservoirs. The most recent study of well test analysis in composite reservoirs was by Eggenschwiler, Satman et al. Their studies presented a very general composite system model. The problem was solved analytically by using the Laplace transformation with numerical inversion. The solution concerned the transient flow of a slightly compressible fluid in a porous medium during injection or falloff for a single well confined in concentric regions of differing mobilities and hydraulic diffusivities. The system assumed both wellbore storage and a skin effect. Their results indicated that a pseudosteady-state pressure response exists in the transition region between the inner region and outer region semilog straight lines. This response is drawn on a Cartesian vs. plot, the slope of which is used to estimate the bulk volume of the inner region. SPEJ p. 281

The Influence of Heterogeneities on Well Test Pressure Response - A Sensitivity Analysis

1996 ◽  
Vol 4 (01) ◽  
pp. 67-72 ◽  
Author(s):  
G.B. Savioli ◽  
M.S. Bidner ◽  
P.M. Jacovkis
Keyword(s):  
Sensitivity Analysis ◽  
Pressure Response ◽  
Well Test ◽  
Test Pressure

The Influence of Vertical Fractures Intercepting Active and Observation Wells on Interference Tests

1982 ◽  
Vol 22 (06) ◽  
pp. 933-944 ◽  
Author(s):  
Naelah A. Mousli ◽  
Rajagopal Raghavan ◽  
Heber Cinco-Ley ◽  
Fernando Samaniego-V.
Keyword(s):  
Test Data ◽  
A Priori ◽  
Pressure Response ◽  
Fracture Plane ◽  
Observation Well ◽  
Compass Orientation ◽  
Vertical Fracture ◽  
Wellbore Storage ◽  
Interference Test ◽  
Observation Wells

Abstract This paper reviews pressure behavior at an observation well intercepted by a vertical fracture. The active well was assumed either unfractured or intercepted by a fracture parallel to the fracture at the observation well. We show that a vertical fracture at the observation well has a significant influence on the pressure response at that well, and therefore wellbore conditions at the observation well must be considered. New type curves presented can be used to determine the compass orientation of the fracture plane at the observation well. Conditions are delineated under which the fracture at the observation well may influence an interference test. This information should be useful in designing and analyzing tests. The pressure response curve at the observation well has no characteristic features that will reveal the existence of a fracture. The existence of the fracture would have to be known a priori or from independent measurements such as single-well tests. Introduction In this work, we examine interference test data for the influence of a vertical fracture located at the observation well. All studies on the subject of interference testing have been directed toward understanding the effects of reservoir heterogeneity or wellbore conditions at the active (flowing) well. Several correspondents suggested our study because many field tests are conducted when the observation well is fractured. They also indicated that it is not uncommon for both wells (active and observation) to be fractured. To the best of our knowledge, this is the first study to examine the influence of a vertical fracture at the observation well on interference test data. Two conditions at the active well are examined: an active well that is unfractured (plane radial flow) and an active well that intercepts a vertical fracture parallel to the fracture at the observation well. The parameters of interest include effects of the distance between the two wells, compass orientation of the fracture plane with respect to the line joining the two wellbores, and the ratio of the fracture lengths at the active and observation wells if both wells are fractured. The results given here should enable the analystto interpret the pressure response at the fractured observation well.to interpret the pressure response when both the active and the observation wells are fracturedto design tests to account for the existence of a fracture at one or both wells, andto determine quantitatively the orientation and/or length of the fracture at an observation well. We also show that one should not assume a priori that the effect of a fracture on the observation well response will be similar to that of a concentric skin region around the wellbore-i.e., idealizations to incorporate the existence of the fracture, such as the effective wellbore radius concept, may not be applicable. Mathematical Model and Assumptions In this study, we consider the flow of a slightly compressible fluid of constant viscosity in a uniform and homogeneous porous medium of infinite extent. Fluid is produced at a constant surface rate at the active well. Wellbore storage effects are assumed negligible because the main objective of our work is to demonstrate the influence of the fractures. However, note that wellbore storage effects may mask the early-time response at the observation well. Refs. 1 and 2 discuss the influence of wellbore storage on interference test data. We obtained the solutions to the problems considered here by the method of sources and sinks. The fracture at the observation well was assumed to be a plane source of infinite conductivity. SPEJ P. 933^

Pulse Tests and Other Early Transient Pressure Analyses for In-Situ Estimation of Vertical Permeability

1974 ◽  
Vol 14 (01) ◽  
pp. 75-90 ◽  
Author(s):  
George J. Hirasaki
Keyword(s):  
Pressure Response ◽  
Gravity Drainage ◽  
Transient Pressure ◽  
Type Curve ◽  
Pulse Test ◽  
Recovery Processes ◽  
Vertical Permeability ◽  
Constant Rate ◽  
Rate Test

Abstract Formation vertical permeability is often the dominant influence in water or gas coning into a well, in gravity drainage of high-relief reservoirs, and in interlayer crossflow in secondary recovery projects. The advantages of either conducting a projects. The advantages of either conducting a pulse test or analyzing the early transient pressure pulse test or analyzing the early transient pressure response of a constant-rate test compared with previous techniques are simplicity of interpretation, previous techniques are simplicity of interpretation, short duration of test, and minimum interference from conditions some distance from the test well. The pulse test has a further advantage over the constant-rate test in that the rate does not have to be kept constant during the short flow period.Presented are the development of the theory and the curves of the dimensionless response time used in interpreting field data obtained by these techniques. The vertical permeability is determined with the pulse test from the time to the maximum pressure response and with the constant-rate test pressure response and with the constant-rate test from the extrapolated time to zero pressure response from the inflection point.Applications of the techniques to layered systems and to an oil zone with underlying water are demonstrated with results of numerical simulations. The vertical-permeability pulse test has been used to estimate the vertical permeability of a low-permeability zone in the Fahud field, Oman. Introduction The formation vertical permeability is often a dominant influence in reservoir recovery processes with vertical fluid flow such as water or gas coning, gravity drainage of high-relief reservoirs, the rising steam process, and displacement by water or gas in a heterogeneous formation. How reliably numerical reservoir simulators can predict the recovery performance of these processes depends upon how performance of these processes depends upon how accurately the significant reservoir parameters are estimated. Furthermore, in simulating a reservoir in two dimensions, the validity of the assumption of vertical equilibrium is based on the value of the vertical permeability.With the previously mentioned recovery processes, the reservoir cannot be modeled as a homogeneous reservoir with a single fluid. A well that has fluid coning or that is producing by gravity drainage will often have a fluid contact intersecting the well and thus dividing the reservoir into zones of differing mobility and compressibility. Reservoir stratification on a microscopic scale will result in a vertical permeability that is less than the horizontal permeability that is less than the horizontal permeability; but stratification on a macroscopic permeability; but stratification on a macroscopic scale will divide the reservoir into zones of differing permeabilities. Thus the design and interpretation permeabilities. Thus the design and interpretation of a vertical-permeability test for most practical reservoir situations will require that the reservoir zonation be represented.Transient pressure techniques for estimating in-situ vertical permeability have been introduced by Burns and by Prats. Both techniques require injection or production at a constant rate from a short perforated interval and measurement of the pressure response at another perforated interval pressure response at another perforated interval that is isolated from the first by a packer. The interpretation technique of Burns required a computer-generated type curve or a single-phase numerical reservoir simulator. This type-curve approach is applicable for an anisotropic, homogeneous, infinite reservoir model, and the numerical simulator with a regression analysis program is needed for finite or layered reservoir models. The technique presented by Prats did not require a computer program because the result of the analysis was presented on a single graph. The horizontal and vertical permeabilities could be estimated from the slope and the intercept of the pressure response and, the appropriate value from the graph. The method of Prats was based on an infinite, anisotropic, Prats was based on an infinite, anisotropic, homogeneous reservoir model.The pulse test and early transient analysis techniques presented here were developed to provide a simple means of interpretation for layered provide a simple means of interpretation for layered systems. Some advantages are thatno computer program is requiredlayered reservoirs can be program is requiredlayered reservoirs can be represented;test duration is shorter than for previous methods; andthere is less interference previous methods; andthere is less interference from reservoir conditions some distance from the test well. SPEJ P. 75

Pulse-Test Response of a Two-Zone Reservoir

1970 ◽  
Vol 10 (03) ◽  
pp. 245-256 ◽  
Author(s):  
E.G. Woods
Keyword(s):  
Flow Rate ◽  
Single Layer ◽  
Pressure Response ◽  
Test Results ◽  
Well Test ◽  
Reservoir Model ◽  
Reservoir Properties ◽  
Pulse Test ◽  
Pulse Testing ◽  
Single Well

Woods, E.G., Member AIME, Esso Production Research Co., Houston, Tex. Abstract A mathematical investigation of pressure response of two-zone reservoirs indicates apparent transmissibility (kh/ ) obtained by pulse testing is always equal to or greater than the total transmissibility of the zones, and that apparent storage (phi ch) is always equal to or less than the total storage of the zones. These apparent zone properties approach total properties as vertical fluid communication between zones increases. The presence of non uniform wellbore damage in the zones alters the division of flow between zones, and consequently, alters their apparent transmissibility ratio. In the absence of wellbore damage. the flow-rate ratio is a good estimator of the transmissibility ratio of the zones. A procedure is proposed for advantageously using differences in reservoir properties determined by single-well tests and pulse tests to describe flow properties of two-zone reservoirs. A numerical properties of two-zone reservoirs. A numerical example is included. Introduction Pulse tests, interference tests, and single-well pressure buildup or drawdown tests have been used pressure buildup or drawdown tests have been used to estimate reservoir properties. These pressure transient tests are normally analyzed with mathematical models which assume that the reservoir is a homogeneous single layer. Various techniques for analyzing single-well test data to obtain information about the properties of layered reservoirs have been shown by others to have limited applicability. This mathematical study was undertaken to determine what errors could be caused by interpreting pulse tests (in a multizone reservoir) with a single-layer model. Pulse testing is based on the measurement and interpretation of a pressure response in one well to a transient pressure disturbance introduced by varying flow rate at an adjacent well. The measured pressure response is usually a few hundredths of a pressure response is usually a few hundredths of a pound per square inch. Pulse-test terminology is pound per square inch. Pulse-test terminology is shown in Fig. 1; Johnson et al. give a complete description of pulse testing. Measured at the wellhead or in the wellbore, pressure response is a function of reservoir pressure response is a function of reservoir transmissibility (T=kh/mu) and diffusivity (n = k/phi cmu) in the region between the two wells; from these two quantities reservoir storage ( = /n=phi ch) can be derived. The analysis presented here discusses additional reservoir information made available by pulse testing and shows that single-well test and pulse-test results can be combined to give more information about a two-zone reservoir than either type of test alone. Also, procedures are given for estimating the magnitude of error if test results of a two-one reservoir are interpreted with the assumption that it is a one-zone, vertically homogeneous, reservoir. Discussions of theoretical work, field data requirements, interpretation procedure, and a numerical example follow. Details of the mathematical model are given in the Appendix. THEORETICAL STUDY - TWO-ZONE MODEL Reservoir Model - Assumptions and Boundary Conditions A reservoir model consisting of two zones penetrated by two wells, each of which is completed in both zones was assumed (Fig. 2). SPEJ p. 245

Fast-Fourier-Transform-Based Deconvolution for Interpretation of Pressure Transient Test Data Dominated by Wellbore Storage

2005 ◽  
Vol 8 (03) ◽  
pp. 224-239 ◽  
Author(s):  
Yueming Cheng ◽  
W. John Lee ◽  
Duane A. McVay
Keyword(s):  
Laplace Transform ◽  
Early Time ◽  
Pressure Response ◽  
Pressure Data ◽  
Reservoir System ◽  
Wellbore Storage ◽  
Constant Rate ◽  
Storage Effects ◽  
Pressure Transient Test ◽  
Deconvolution Techniques

Summary We present a deconvolution technique based on a fast-Fourier-transform (FFT)algorithm. With the new technique, we can deconvolve "noisy" pressure and rate data from drawdown and buildup tests dominated by wellbore storage. The wellbore-storage coefficient can be variable in the general case. In cases with no rate measurements, we use a "blind" deconvolution method to restore the pressure response free of wellbore-storage effects. Our technique detects the afterflow/unloading rate function with Fourier analysis of the observed pressure data. The technique can unveil the early-time behavior of a reservoir system masked by wellbore-storage effects, and it thus provides a powerful tool to improve pressure-transient-test interpretation. It has the advantages of suppressing the noise in the measured data, handling the problem of variable wellbore storage, and deconvolving the pressure data without rate measurement. We demonstrate the applicability of the method with a variety of synthetic and actual field cases for both oil and gas wells. Some of the actual cases include measured sandface rates (which we use only for reference purposes), and others do not. Although this paper is focused on deconvolution of pressure-transient-test data during a specific drawdown/buildup period corresponding to an abrupt change of surface flow rate, the deconvolution method itself is very general and can be extended readily to interpret multirate test data. Introduction In conventional well-test analysis, the pressure response to constant-rate production is essential information that presents the distinct characteristics for a specific type of reservoir system. However, in many cases, it is difficult to acquire sufficient constant-rate pressure-response data. The recorded early-time pressure data are often hidden by wellbore storage(variable sandface rates). In some cases, outer-boundary effects may appear before wellbore-storage effects disappear. Therefore, it is often imperative to restore the early-time pressure response in the absence of wellbore-storage effects to provide a confident well-test interpretation. Deconvolution is a technique used to convert measured pressure and sandface rate data into the constant-rate pressure response of the reservoir. In other words, deconvolution provides the pressure response of a well/reservoir system free of wellbore-storage effects, as if the well were producing at a constant rate. Once the deconvolved pressure is obtained, conventional interpretation methods can be used for reservoir system identification and parameter estimation. However, mathematically, deconvolution is a highly unstable inverse problem because small errors in the data can result in large uncertainties in the deconvolution solution. In the past 40 years, a variety of deconvolution techniques have been proposed in petroleum engineering, such as direct algorithms, constrained deconvolution techniques, and Laplace-transform-based methods, but their application was limited largely because of instability problems. Direct deconvolution is known as a highly unstable procedure. To reduce solution oscillation, various forms of smoothness constraints have been imposed on the solution. Coats et al. presented a linear programming method with sign constraints on the pressure response and its derivatives. Kuchuk et al. used similar constraints and developed a constrained linear least-squares method. Baygun et al. proposed different smoothness constraints to combine with least-squares estimation. The constraints were an autocorrelation constraint on the logarithmic derivative of pressure solution and an energy constraint on the change of logarithmic derivative. Efforts also were made to perform deconvolution in the Laplace domain. Kuchuk and Ayestaran developed a Laplace-transform-based method using exponential and polynomial approximations to measured sandface rate and pressure data, respectively. Methods presented by Roumboutsos and Stewart and Fair and Simmons used piecewise linear approximations to rate and pressure data. All the Laplace-transform-based methods used the Stehfest algorithm to invert the results in the Laplace domain back to the time domain. Although the above methods may give a reasonable pressure solution at a low level of measurement noise, the deconvolution results can become unstable and uninterpretable when the level of noise increases. Furthermore, existing deconvolution techniques require simultaneous measurement of both wellbore pressure and sandface rate. However, it is not always possible to measure rate in actual well testing. Existing techniques are, in general, not suitable for applications without sandface rate measurement.

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