An Investigation of Wellbore Storage and Skin Effect in Unsteady Liquid Flow: II. Finite Difference Treatment

1970 ◽  
Vol 10 (03) ◽  
pp. 291-297 ◽  
Author(s):  
Robert A. Wattenbarger ◽  
H.J. Ramey
Keyword(s):  
Differential Equation ◽  
Skin Effect ◽  
Annular Region ◽  
Curve Matching ◽  
Type Curve ◽  
Flow Rates ◽  
Flow Capacity ◽  
Wellbore Storage ◽  
Straight Line ◽  
Short Time

Abstract An investigation of the effect of wellbore storage and skin effect on transient flow was conducted using a finite-difference solution to the basic partial differential equation. The concept of skin partial differential equation. The concept of skin effect was generalized to include a composite annular region adjacent to the wellbore (a composite reservoir). The numerical solutions were compared with analytical solutions for cases with the usual steady-state skin effect. It was found that the solutions for a finite-capacity skin effect compared closely with analytical solutions at short times (wellbore storage controlled) and at long times after the usual straight line was reached. For intermediate times, presence of a unite-capacity skin effect caused significant departures from the infinitesimal skin solutions. Two straight lines occurred on the drawdown plot for cases of large radius of damage. The first had a slope characteristic of the flow, capacity of the damaged region; the second straight line had a slope characteristic of the flow capacity of the undamaged region. Results are presented both in tabular form and as log-log plots of dimensionless pressures vs dimensionless times. The log-log pressures vs dimensionless times. The log-log plot may be used in a type-curve matching plot may be used in a type-curve matching procedure to analyze short-time (before normal procedure to analyze short-time (before normal straight line) well-test data. Introduction Skin effect was defined by van Everdingen and Hurst as being an impediment to flow that is caused by an infinitesimally thin damaged region around the wellbore. The additional pressure drop through this skin is proportional to the wellbore flow rate and behaves as though flow through the skin were steady-state. Wellbore storage is caused by having a moving liquid level in a wellbore, or by simply having a volume of compressible fluid stored in the wellbore. When surface flow rates change abruptly, wellbore storage causes a time lag in formation flow rates and a corresponding damped pressure response. A recent study was made to determine the combined effects of infinitesimally thin skin and wellbore storage. Analytical methods were used along with numerical integration of a Laplace transformation inversion integral. Tabular and graphical results were presented for various cases. It was recognized during the study that this representation of skin was oversimplified; that skin effect should be thought of as a result of formation damage or improvement to a finite region adjacent to the wellbore. It was suggested that a skin effect could arise physical in a number of ways. One simple example physical in a number of ways. One simple example would be to assume that an annular volume adjacent to the wellbore is reduced uniformly to a lower permeability than the original value. This would be similar to the composite reservoir problem. Perhaps a better example would be to problem. Perhaps a better example would be to assume that the permeability increases continuously from a low value at the wellbore to a constant value in the undamaged reservoir. In either case, the damaged region would have a finite storage capacity and would lead to transient behavior within the skin region. A negative skin effect could arise from an increase in permeability within an annular region adjacent to the wellbore. This might physically result from acidizing. But it is believed that cases of more practical importance are those in which negative skin effects are caused by hydraulic fracturing. A high-permeability fracture communicating with the wellbore gives the appearance of a negative skin effect. For the purposes of this study, it was decided to represent a skin effect, either positive or negative as an annular region adjacent to the wellbore with either decreased or increased permeability. permeability. SPEJ P. 291

An Investigation of Wellbore Storage and Skin Effect in Unsteady Liquid Flow: I. Analytical Treatment

1970 ◽  
Vol 10 (03) ◽  
pp. 279-290 ◽  
Author(s):  
Ram G. Agarwal ◽  
Rafi Al-Hussainy ◽  
H.J. Ramey
Keyword(s):  
Skin Effect ◽  
Initial Period ◽  
Outer Boundary ◽  
Well Test ◽  
Time Data ◽  
Wellbore Storage ◽  
Straight Line ◽  
Pan American ◽  
Well Tests ◽  
Short Time

Agarwal, Ram G., Pan American Petroleum Corp. Tulsa, Okla., Pan American Petroleum Corp. Tulsa, Okla., Al-Hussainy, Rafi, Junior Members AIME, Mobil Research and Development Corp., Dallas, Tex., Ramey Jr., H.J., Member AIME, Stanford U. Stanford, Calif. Abstract Due to the cost of extended pressure-drawdownor buildup well tests and the possibility of acquisitionof additional information from well tests, the moderntrend has been toward development of well-testanalysis methods pertinent for short-time data."Short-time" data may be defined as pressureinformation obtained prior to the usual straight-lineportion of a well test. For some time there has been portion of a well test. For some time there has been a general belief that the factors affecting short-timedata are too complex for meaningful interpretations. Among these factors are wellbore storage, variousskin effects such as perforations, partial penetration, fractures of various types, the effect of a finiteformation thickness, and non-Darcy flow. A numberof recent publications have dealt with short-timewell-test analysis. The purpose of this paper isto present a fundamental study of the importance ofwellbore storage with a skin effect to short-timetransient flow. Results indicate that properinterpretations of short-time well-test data can bemade under favorable circumstances. Upon starting a test, well pressures appearcontrolled by wellbore storage entirely, and datacannot be interpreted to yield formation flowcapacity or skin effect. Data can be interpreted toyield the wellbore storage constant, however. Afteran initial period, a transition from wellbore storagecontrol to the usual straight line takes place. Dataobtained during this period can be interpreted toobtain formation flow capacity and skin effect incertain cases. One important result is that thesteady-state skin effect concept is invalid at veryshort times. Another important result is that thetime required to reach the usual straight line isnormally not affected significantly by a finite skineffect. Introduction Many practical factors favor short-duration welltesting. These include loss of revenue during shut-in, costs involved in measuring drawdown or buildupdata for extended periods, and limited availabilityof bottomhole-pressure bombs where it is necessaryto survey large numbers of wells. on the other hand, reservoir engineers are well aware of the desirabilityof running long-duration tests. The result is usuallya compromise, and not necessarily a satisfactoryone. This situation is a common dilemma for thefield engineers who must specify the details of specialwell tests and annual surveys, and interpret theresults. For this reason, much effort has been givento the analysis of short-time tests. The term"short-time" is used herein to indicate eitherdrawdown or buildup tests run for a period of timeinsufficient to reach the usual straight-line portions. Drawdown data taken before the traditional straight-lineportion are ever used in analysis of oil or gas portion are ever used in analysis of oil or gas well performance. Well files often contain well-testdata that were abandoned when it was realized thatthe straight line had not been reached. This situationis particularly odd when it is realized that earlydata are used commonly in other technologies whichemploy similar, or analogous, transient test. It is the objective of this study to investigatetechniques which may be used to interpret informationobtained form well tests at times prior to the normalstraight-line period. THEORY The problem to be considered is the classic oneof flow of a slightly compressible (small pressuregradients) fluid in an ideal radial flow system. Thatis, flow is perfectly radial to a well of radius rwin an isotropic medium, and gravitational forces areneglected. We will consider that the medium isinfinite in extent, since interest is focused on timesshort enough for outer boundary effects not to befelt at the well. SPEJ p. 279

Pressure Analysis for Fractured Wells

1972 ◽  
Author(s):  
Alain C. Gringarten ◽  
Henry J. Ramey ◽  
R. Raghavan
Keyword(s):  
Skin Effect ◽  
Time Pressure ◽  
Physical Nature ◽  
Well Testing ◽  
Well Test ◽  
Time Data ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Straight Line ◽  
Short Time

INTRODUCTION During the last few years, there has been an explosion of information in the field of well test analysis. Because of increased physical understanding of transient fluid flow, the entire pressure history of a well test can be analyzed, not just long-time data as in conventional analysis.! It is now often possible to specify the time of beginning of the correct semilog straight line and determine whether the correct straight line has been properly identified. It is also possible to identify wellbore storage effects and the nature of wellbore stimulation as to permeability improvement, or fracturing, and perform quantitative analyses of these effects. These benefits were brought about in the main by attempts to understand the short-time pressure data from well testing, data which were often classified as too complex for analysis. One recent study of short-time pressure behavior2 showed that it was important to specify the physical nature of the stimulation in consideration of stimulated well behavior. That is, statement of the van Everdingen-Hurst infinitesimal skin effect as negative was not sufficient to define short-time well behavior. For instance, acidized {but not acid fraced) and hydraulically fractured wells did not necessarily have the same behavior at early times, even though they might possess the same value of negative skin effect.

scholarly journals A New Method for the Evaluation of Well Rehabilitation from the Early Portion of a Pumping Test

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 744
Author(s):  
Daniel Kahuda ◽  
Pavel Pech
Keyword(s):  
Skin Effect ◽  
Pumping Test ◽  
Real Space ◽  
New Method ◽  
Maximum Slope ◽  
Skin Factor ◽  
Wellbore Storage ◽  
Straight Line ◽  
Early Portion ◽  
Well Rehabilitation

This study analyzes the unsteady groundwater flow to a real well (with wellbore storage and the skin effect) that fully penetrates the confined aquifer. The well is located within an infinite system, so the effect of boundaries is not considered. The Laplace-domain solution for a partial differential equation is used to describe the unsteady radial flow to a well. The real space solution is obtained by means of the numerical inversion of the Laplace transform using the Stehfest algorithm 368. When wellbore storage and the skin effect dominate pumping test data and testing is conducted for long enough, two semilogarithmic straight lines are normally obtained. The first straight line can be identified readily as the line of the maximum slope. The correlation of the dimensionless drawdown for the intersection time of this first straight line, with the log time axis as a function of the dimensionless wellbore storage and the skin factor, is shown. This paper presents a new method for evaluating the skin factor from the early portion of a pumping test. This method can be used to evaluate the skin factor when the well-known Cooper–Jacob semilogarithmic method cannot be used due to the second straight line not being achieved in the semilogarithmic graph drawdown vs. the log time. A field example is presented to evaluate the well rehabilitation in Veselí nad Lužnicí by means of the new correlation.

Decline Curve Analysis Using Type Curves for Two-Porosity Systems

1981 ◽  
Vol 21 (03) ◽  
pp. 354-362 ◽  
Author(s):  
Giovanni Da Prat ◽  
Heber Cinco-Ley ◽  
Henry Ramey
Keyword(s):  
Fluid Flow ◽  
Flow Rate ◽  
Skin Effect ◽  
Curve Analysis ◽  
Fractured Reservoir ◽  
Type Curve ◽  
Decline Curve Analysis ◽  
Decline Curve ◽  
Wellbore Storage ◽  
Naturally Fractured

Abstract Constant producing pressure solutions that define declining production rates with time for a naturally fractured reservoir are presented. The solutions for the dimensionless flow rate are based on a model presented by Warren and Root. The model was extended to include constant producing pressure in both infinite and finite systems. The results obtained for a finite no-flow outer boundary are new and surprising. It was found that the flow rate shows a rapid decline initially, becomes nearly constant for a period, and then a final decline in rat,- takes place.A striking result of the present study is that ignoring the presence of a constant flow rate period in a type-curve match can lead to erroneous estimates of the dimensionless outer radius of a reservoir. An example is presented to illustrate the method of type-curve matching for a naturally fractured system. Introduction Naturally fractured reservoirs consist of heterogeneous porous media where the openings (fissures and fractures) vary considerably in size. Fractures and openings of large size form vugs and interconnected channel, whereas the tine cracks form block systems which are the main body of the reservoir (Fig. 1). The porous blocks store most of the fluid in the reservoir and are often of low permeability, whereas the fractures have a low storage capacity and high permeability. Most of the fluid flow will occur through the fissures with the blocks acting as fluid sources. Even though the volumetric average permeability in a naturally fractured system is low, such systems often exhibit an effective permeability that is higher than the block matrix permeability, and behave differently from ordinary homogeneous media. These systems have been studied extensively in the petroleum literature. One of the first such studies was published by Pirson in 1953. In 1959, Pollard presented one of the first pressure transient models available for interpretation of well test data from two-porosity systems. The most complete analysis of transient flow in two-porosity systems was presented in 1960 by Barenblatt and Zheltov. The Warren and Root study in 1963 is considered the forerunner of modern interpretation of two-porosity systems. Their paper has been the subject of study by many authors. The behavior of fractured systems has long been a topic of controversy Many authors have indicated that the graphical technique proposed by Pollard in 1959 is susceptible to error caused by approximations in the mathematical model. Nevertheless, the Pollard method still is used. The most complete study of two-porosity systems appears to be the Mavor and Cinco-Ley study in 1979. This study considers wellbore storage and skin effect, and also considers production, both at constant rate and at constant pressure. However, little information is presented concerning the effect of the size of the system on pressure buildup behavior.Although decline curve analysis is widely used, methods specific to two-porosity fractured systems do not appear to be available. It is the objective of this paper to produce and study decline curve analysis for a naturally fractured reservoir. The Warren and Root model was chosen as the basis for this work. Partial Differential Equations The basic partial differential equations for fluid flow in a two-porosity system were presented by Warren and Root in 1963. The model was extended by Mavor and Cinco-Ley to include wellbore storage and skin effect. SPEJ P. 354^

Analysis of Short Transient Tests Affected by Changing Wellbore Storage

1998 ◽  
Vol 1 (03) ◽  
pp. 261-267 ◽  
Author(s):  
M. Vasquez-Cruz ◽  
R. Camacho-Velazquez
Keyword(s):  
Exponential Function ◽  
Radial Flow ◽  
Error Function ◽  
Early Time ◽  
Curve Matching ◽  
Well Test ◽  
Flow Conditions ◽  
Type Curve ◽  
Wellbore Storage ◽  
Matching Procedure

Abstract It is well known that wellbore storage and phase redistribution have a direct influence over well testing data, mainly on those recorded at early times of the test. After this early time period, such influence disappears, and the pressure response is dominated by the reservoir and the skin zone properties. However, sometimes the effects of wellbore dynamics last long enough as to completely disguise the reservoir response. The above situation frequently constrains the use of some analysis procedures such as type curve matching, especially if the test did not last long enough as to reach radial flow conditions. In this way, some tests are uninterpretable because of the duration of these wellbore effects. Using as a basis two classical models related to well test affected by changing wellbore storage, this work introduces a new method of analysis for these tests with insufficient duration to reach radial flow conditions. The use of the methodology proposed in this work is illustrated with synthetic examples and a field case. For some synthetic cases the type curve matching procedure may yield completely erroneous values of the parameters, while with the suggested method reasonable estimates are obtained. Introduction Wellbore storage is recognized as a phenomenom that affects the recorded pressure behavior at early times during a well test. Sometimes, the phenomena related to mass balance and fluid momentum that occur inside the wellbore, constrain the application of some analysis procedures, especially if the test does not show transient radial flow conditions, and can even disguise completely the pressure response. Phase redistribution occurs when a producing well (that contains more than one phase) is closed at the surface, and due to gravitational forces these phases segregate from each other, this causes a distorsion on early time data of the test. In 1981, Fair introduced a model which takes into account the phase redistribution phenomenom in the diffusivity equation solution as applied to buildup analysis. He assumed an exponential increase in wellbore storage. More recently, Hegeman et. al., proposed an extension to Fair's model, obtaining a general solution in Laplace space, which allows to add the changing wellbore storage effect for a variety of analytical well-reservoir models. These authors considered two models of changing wellbore storage, the exponential function and the error function. For the error function, the transition period is more abrupt than with the exponential function. In 1992, Fair presented another study on the influence of a wide range of wellbore phenomena including mass-balance and momentum phenomena. Also, in that work wellbore phenomena such as fluid temperature changes (represented by an exponential function as in the case of wellbore storage), phase changes inside the production tubing and inertial effects were considered. Currently, the only available method to estimate the reservoir permeability and skin factor from insufficient transient data (tests affected by changing wellbore storage and that have not reached radial flow period) is the type-curve matching technique. To apply this procedure it is necessary to identify the function (exponential or error function) that fits best the storage effect. Nevertheless, the absence of data in the infinite acting period difficults the matching procedure, resulting in a match with high uncertainty. With the purpose of modeling in a more rigorous way the reservoir-wellbore system, it is necessary an algorithm that couples the mechanistic behavior of the well with that of the reservoir, such as that of Hasan and Kabir, Winterfeld propose the use of a completely numerical scheme that simulates the transient conditions of the system.

Annulus Unloading Rates as Influenced by Wellbore Storage and Skin Effect

1972 ◽  
Vol 12 (05) ◽  
pp. 453-462 ◽  
Author(s):  
Henry J. Ramey ◽  
Ram G. Agarwal
Keyword(s):  
Test Data ◽  
Skin Effect ◽  
Transient Flow ◽  
Test Problems ◽  
Well Test ◽  
Pressure Drops ◽  
Wellbore Storage ◽  
Unloading Rate ◽  
Short Time ◽  
Storage Type

Abstract The modern trend in well testing (buildup or drawdown) bas been toward acquisition and analysis of short-time data. Pressure data early in a test are usually distorted by several factors that mask the conventional straight line. Some of the factors are wellbore storage and various skin effects such as those due to perforations, partial penetration, non-Darcy flow, or well stimulation effects. Recently, Agarwal et al. presented a fundamental study of the importance of wellbore storage with a skin effect to short-time transient flow. This paper further extends the concept of analyzing short-time well test data to include solutions of certain drillstem test problems and of cases wherein the storage constant, CD, undergoes an abrupt change from one constant value to another. An example of the latter case is change in storage type from compression to liquid level variations when tubinghead pressure drops to atmospheric Arks production. The purpose of the present paper is to: production. The purpose of the present paper is to:present tabular and graphical results for the sandface flow rate, qsf, and the annulus unloading rate, qa, as a fraction of the constant surface rate, q, andillustrate several practical well test situations that require such a solution. Results include a range of values of the storage constant, CD, and the skin effect, s, useful for well test problems. problems. Annulus unloading or storage bas been shown to be an important physical effect that often controls early well test behavior. As a result of this study, it appears that interpretations of short-time well test data can be made with a greater reliability, and solutions to other storage-dominated problems can be obtained easily. Techniques presented in this paper should enable the users to analyze certain short-time well test data that could otherwise be regarded as useless. Introduction In a recent paper, Agarwal et al. presented a study of the importance of wellbore storage with a skin effect to short-time transient flow. They also presented an analytical expression for the fraction presented an analytical expression for the fraction of the constant surface rate, q, produced from the annulus Although the rigorous solution (inversion integral) and long- and short-time approximate forms were discussed, neither tabular nor graphical results ofdpwD the annulus unloading rate, CD, were given.dtD It now appears that such solutions are useful in certain drillstem test problems and in cases wherein the storage constant, CD, changes during a well test. An example is change in storage type from compression to liquid level change when tubinghead pressure drops to atmospheric during production. pressure drops to atmospheric during production. The purpose of this study is to (1) present tabular and graphical results for the sandface flow rate and the annulus unloading rate and (2) illustrate several practical well test situations that require the practical well test situations that require the solutions. THE CLASSIC WELLBORE STORAGE PROBLEM The problem to be considered is one of flow of a slightly compressible fluid in an ideal radial flow system. SPEJ P. 453

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