Semilog Straight Line Research Articles

A Straight-Line Approach To Determine the Distance to Barriers

Summary The pressure response for a well located near a linear impermeable barrier is differentiated and rearranged so that a linear relation between the two variables of the pressure-derivative group and 1/t is obtained. A plot of log|2.303p′t/m − 1| vs. 1/í yields a straight line with a fixed intercept and a slope proportional to the square of the distance to the barrier (or boundary). The straight-line approach is also extended to apply to two perpendicular no-flow barriers and to buildup test data. The advantage of the approach presented here is that pressure data can be analyzed to determine the distance to barriers even if the late-time semilog straight line whose slope is twice or four times the slope of the first semilog straight line is not reached. A field example is included for illustration.

New Applications of the Pressure Derivative in Well-Test Analysis

Summary This work presents and illustrates a new general procedure for constructing type curves on the basis of a new pressure-derivative group that involves the dimensionless pressure change divided by its logarithmic derivative. When type curves based on this group are constructed, the vertical scale of the dimensionless derivative group is automatically aligned with the vertical scale of the field-data derivative group. This automatic alignment of the vertical scales simplifies type-curve matching and is advantageous for determining whether field data actually represent the solution assumed by a given type curve. It is also shown that the basic idea used in constructing the type curves can be used to ensure that proper semilog straight lines are chosen when well-test pressure data are analyzed by semilog methods.

A Simple Buildup Analysis Method To Determine Well Drainage Area and Drawdown Pressure for a Stabilized Well

Summary This paper presents a new method that applies to wells that are shut in after having reached pseudosteady-state flow conditions. Based on the complete Miller-Dyes-Hutchinson (MDH) equation, a corrected pressure is defined that allows extension of the semilog straight line by about two log cycles for symmetric systems and one-half log cycle for others. The drainage area is directly computed. If the final recorded shut-in pressures depart from the straight line, it is also possible to compute the shape factor and the average pressure independently of the initial pressure.

Pressure Analysis for Horizontal Wells

Summary This paper presents horizontal-well test design and interpretation methods. Analytical solutions are developed that can be handled easily by a desktop computer to carry out design as well as interpretation with semilog and log-log analysis. These analytical solutions point out the distinctive behavior of horizontal wells: (1) at early time, there is a circular radial flow in a vertical plane perpendicular to the Well, and (2) at late time, there is a horizontal pseudoradial flow. Each type of flow is associated with a semilog straight line to which semilog analysis has to be adapted. The horizontal pseudoradial flow takes into account a pseudoskin depending on system geometry, which is a priori defined and estimated. Practical time criteria are proposed to determine the beginning and the end of each type of flow and to provide a guide to semilog analysis and well test design. We study the behavior of uniform-flux or infinite-conductivity horizontal wells, with wellbore storage and skin. The homogeneous reservoir is infinite or limited by impermeable or constant-pressure boundaries. A method is also outlined to transform all our solutions for homogeneous reservoirs into corresponding solutions for double-porosity reservoirs.

A new derivative type-curve for pressure buildup analysis with boundary effects

This study investigates pressure buildup behavior of wells with wellbore storage and skin in bounded circular reservoirs, when inner and outer boundary effects interact to fully or partially dominate the well pressure response. Using dimensionless pressure derivative as the dependent variable, we show that early time response is governed by C D e 2 S and late time response by r eD 2/ C D. Equations are provided to estimate the limits of the intermediate time period, which corresponds to infinite acting radial flow and a semi-log straight line on a pressure-time graph. We present a new buildup derivative type-curve, incorporating inner boundary (early-time) and outer boundary (late-time) effects. Applications of this type-curve in buildup test design and interpretation are discussed.

Use of the Pressure Derivative for Diagnosing Pressure-Transient Behavior

The combined plot of log pressure change and log derivative of pressure with respect to superposition time as a function of log elapsed time was first introduced by Bourdet et al. as an aid to type-curving matching. Features that are hardly visible on the Horner plot or are hard to distinguish because of similarities between one reservoir system and another was easier to recognize on the pressure-derivative plot. Once the patterns have been diagnosed on the log-log plot, specialized plots can be used to compute reservoir parameters or the data can be matched to a type curve.

Multiple-Well Interference Testing in the Ohaaki Geothermal Field

SummaryMultiple interference tests were carried out in the Ohaaki geothermal field between 1979 and 1983. Data were collected for periods of up to 200 days per test with both wellhead-mounted water-level recorders and quartz crystal pressure gauges, each with a resolution of about 0.0145 psi [100 Pa], Data are analyzed by conventional log-log type-curve matching techniques, followed by application of recently developed semilog type-curve matching techniques that allow linear boundary detection without developing two semilog straight lines. One type curve exists for each of the drawdown and buildup data, which are produced by mathematically collapsing the family of curves produced in the solution for a system containing a line source and linear boundary. The type curve for die buildup data has not been previously published. The method allows the inference ellipse for a linear boundary to be determined without any knowledge of reservoir parameters.The data in some tests show the presence of a no-flow boundary for which inference ellipses have been located. Four interference tests performed on the same doublet show that vastly different reservoir parameters can be found unless careful interpretation is made.

Pumping tests in nonuniform aquifers — The radially symmetric case

Traditionally, pumping-test-analysis methodology has been limited to applications involving aquifers whose properties are assumed uniform in space. This work attempts to assess the applicability of analytical methodology to a broader class of units with spatially varying properties. An examination of flow behavior in a simple configuration consisting of pumping from the center of a circular disk embedded in a matrix of differing properties is the basis for this investigation. A solution describing flow in this configuration is obtained through Laplace-transform techniques using analytical and numerical inversion schemes. Approaches for the calculation of flow properties in conditions that can be roughly represented by this simple configuration are proposed. Possible applications include a wide variety of geologic structures, as well as the case of a well skin resulting from drilling or development. Of more importance than the specifics of these techniques for analysis of water-level responses is the insight into flow behavior during a pumping test that is provided by the large-time form of the derived solution. The solution reveals that drawdown during a pumping test can be considered to consist of two components that are dependent and independent of near-well properties, respectively. Such an interpretation of pumping-test drawdown allows some general conclusions to be drawn concerning the relationship between parameters calculated using analytical approaches based on curve-matching and those calculated using approaches based on the slope of a semilog straight line plot. The infinite-series truncation that underlies the semilog analytical approaches is shown to remove further contributions of near-well material to total drawdown. In addition, the semilog distance-drawdown approach is shown to yield an expression that is equivalent to the Thiem equation. These results allow some general recommendations to be made concerning observation-well placement for pumping tests in nonuniform aquifers. The relative diffusivity of material on either side of a discontinuity is shown to be the major factor in controlling flow behavior during the period in which the front of the cone of depression is moving across the discontinuity. Though resulting from an analysis of flow in an idealized configuration, the insights of this work into flow behavior during a pumping test are applicable to a wide class of nonuniform units.

Pressure Buildup Analysis For Wells Influenced By Fractures And Other Heterogeneities

Abstract A new approach has been devised to analyze pressure buildups in heterogeneous reservoirs. The proposed procedure is a modification of the semi-log straight line plotting of Horner analysis. It is also an improvement over the conventional type curve matching technique in that the effect of flow time, and the rate variations during drawdown, are incorporated. Applications of this procedure to analyze heterogeneities characterized by a linear boundary, natural fractures, and a vertical fracture demonstrate the strength of the approach. Introduction The Horner plot(1,2) has been used successfully in the analysis of buildups taken after constant rate drawdowns from infinite acting, homogeneous reservoirs. If all the underlying assumptions are valid, then a plot of shut-in pressure versus the logarithm of the Horner time group results in a straight line. Parametric estimations can be made from the slope and intercept of this line. Any type of heterogeneity in the reservoir introduces deviations from linearity in such a plot. For mild near wellbore heterogeneities such as wellbore storage or skin, only the early time data is affected. If, however, the duration of the shut-in time is short, then the initial deviation from linearity may cause some uncertainty in determining the start of the semi-log straight line. Ramey(3) introduced the type curve matching technique to resolve this problem. It has been used mainly to detennine the start of the semi-log straight line. Homer analysis is still required for parametric estimation purposes. In situations with more complex heterogeneities, the deviation from linearity in Homer plots is more serious. In some cases, such as pressure buildups taken from wells intersecting vertical fractures, the data points in a Horner plot curve continuously upward, making the choice of an appropriate semi-log straight line difficult, if not impossible. Clearly, Horner analysis is inadequate in these situations and, instead of being a supporting tool, type curves themselves are being used increasingly for parametric estimation. Because most of the type curves are a dimensionless pressure solution to the constant rate drawdown boundary condition, their use for buildup analysis requires an extra assumption of the total flow time being much longer than the shut-in time. When this assumption is not valid, McKinley(4), and Raghaven(5) suggested using buildup type curves. Thus, from one single drawdown curve it is necessary to generate a number of buildup type curves for different flow times. As the number of drawdown type curves multiplies, the choice of a best match among the multitude of buildup curves is not an easy one. Another problem associated with the constant rate assumption is that it can be impractical to maintain the rate constant during the field test. Bostic et. al.(6) attempted to modify the drawdown type curves to take into account rate variations. Their derivation, however, depends on an erroneous substitution of the measured pressure into the dimensionless pressure. Hence the subsequent derivation cannot be used. Recently, Rosa and Horne(7), Kucuk et al.(8), and Lee and Brockenbrough(9) devised least squares optimization schemes to resolve the above-mentioned problems with type curve matching.

A Note on the Duration of the Transitional Period of Responses Influenced by Wellbore Storage and Skin

SummarySeveral correlations are available for computing times at which storage effects can be considered to be negligible. The times given by these correlations are not in agreement principally because the criteria used to determine times for storage effects to become negligible are different. This paper clarifies the reasons for the differences and provides a unified treatment of the rules proposed in the literature. We show that correlations that specify the duration of the various flow periods depend on the manner in which the estimates are computed and on the tolerance used to obtain the estimate.A new correlation to determine the time for the start of the semilog straight line is presented. This correlation is based on the slope of the pressure trace and ensures that the slope of the semilog straight line will be correct within a specified tolerance.

Analysis of Fractured Wells Producing at High Flow Rates Using Late-Time Data

Summary This paper presents a method for analyzing late-time data for high-flow-rate wells that cause turbulent flow within the fracture. Fracture conductivity has been determined on the basis of early-time pressure data. The pseudoradial flow period, however, can be used to check the fracture conductivity by identifying the semilog straight line and by determining the total skin factor. Late-time analysis will increase the confidence in the fracture conductivity. In small fractures, early-time data may not be long enough to calculate fracture conductivities. In these cases, late-time data are the only option available for calculating these fracture parameters. In high-flow-rate wells, the calculated fracture conductivity is significantly lower than the true fracture conductivity. Methods have been presented for correcting these apparent values to obtain the true fracture conductivity. We have found that early-time correlations cannot be used to correct apparent fracture conductivities obtained in the late-time analysis. This is because the flow regime has changed significantly between the early and late periods. Examples are presented that use either both early- and late-time data or only late-time data for determining the true fracture conductivity.

Pressure-Transient Test Design in Tight Gas Formation

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. Summary. This paper outlines a procedure for pre- and postfracturepressure-transient test design in low-permeability (tight) gas formations. Theprocedures proposed are based on many years' experience in evaluatinglow-permeability formations, and particularly on recent experience with GasResearch Inst, (GRI) programs in eastern Devonian gas shales and in westerntight-gas formations. Introduction Postfracture tests are frequently needed to evaluate stimulation treatmentsfor one of two major reasons:to diagnose the cause of disappointingproductivity following a fracture treatment, with possible causes includingshort propped-fracture length, low fracture conductivity, low formationpermeability, or low formation pressure, orto optimize fracture treatmentdesign in a new or important area by examining the detailed results oftreatments pumped. Several authors have observed that the ambiguity of postfracture testanalysis is diminished considerably if a prefracture test has been run so thatan estimate of effective permeability to gas is available for use in thepostfracture test analysis. Although the possibility of communication with morenet pay following a fracture treatment is real, the reduction in error possiblewith a prefracture test permeability estimate is still essential. The importantpoint is that proper postfracture test analysis requires the results of aprefracture test; thus, a logical design for the prefracture test is animportant part of the testing program. Knowledge of discovery pressure in the drainage area of a tested well isimportant for a number of reasons, not the least of which is to help ensurevalid prefracture test analysis. In low-permeability formations, a well willrarely build up completely to discovery pressure following a production periodof any significant length in a buildup test of practical length. However, knowledge that the test data are on the proper semilog straight line (on aHomer graph) headed toward a known discovery pressure can help ensure thecorrectness of an otherwise uncertain test analysis. Thus, good test designwill attempt to obtain a reliable value of discovery pressure, pi, before aflow period that is followed by a shut-in test. To achieve the objectives of estimating permeability to gas, kg, anddiscovery pressure, pi, in a prefracture test, and fracture half-length, Lf, and fracture conductivity, KtD, in a postfracture test, the tests must bedesigned thoughtfully. For example, a common problem in transient tests inlow-permeability formations is that the test is too short- not only too short ashut-in period, but a flow period preceding a buildup test so short thatwellbore unloading is incomplete (mass rate out at the surface exceeds massrate in through the perforations). This results in uninterpretable andessentially useless buildup data even when a bottomhole shut-in is used tominimize the duration of wellbore storage (afterflow). This paper presents some field-tested thoughts on test design that willusually provide test data that allow the engineer to achieve the testobjective. More specifically, after a brief review of the modest theoryrequired for proper test design, this paper presents procedures (1) to estimatea value of kg sufficiently accurate for test design purposes, (2) to design aprefracture pressure-buildup test, and (3) to design a postfracturepressure-buildup test. The paper concludes with an application of theseprocedures to an example well. JPT P. 1185^

How To Recognize "Double-Porosity" Systems From Well Tests

Introduction Well tests are performed to acquire qualitative and quantitative knowledge of the well and the reservoir being, tested. Typically, a well test involves modification of the rate or the pressure at one or more wells in the reservoir and observation of the resultant reservoir response (a change in pressure or rate, respectively) at the perturbed well and/or adjacent wells. The reservoir response is then used to construct a well test interpretation model from which well and reservoir parameters, such as permeability and skin, can be calculated. The well test interpretation model describes the pressure or rate behavior of the actual well/reservoir system during the test and must be identified from the shape of the reservoir response. This information is different from, but complementary to, the information provided by other interpretation models that can be derived, for example, from log measurements or geologic observations. A well test interpretation model indicates primarily how many media with significantly different permeabilities and porosities are involved in the flow process and how these media interact. One possible well test interpretation model is the double-porosity model, which describes double-porosity behavior. Double-porosity behavior is obtained when two different media are involved in the flow process: a higher-permeability medium that produces fluid into the well and a lower-permeability medium that recharges the higher-permeability medium. Double-porosity behavior is typical of fissured reservoirs and multilayered reservoirs with high permeability contrast between layers. Different double-porosity behaviors are possible, depending on the degree of interaction, or interporosity flow, between the two constitutive media. The two extremes are (1) restricted. or "pseudosteady-state," interporosity flow, obtained when there is a significant impediment to flow, or interporosity skin, between the most-permeable and the least-permeable media, and (2) unrestricted, or "transient," interporosity flow, obtained when there is no interporosity skin. The following describes the various techniques available for identifying double-porosity behavior from well test pressure data. Conventional Analysis Conventional analysis involves plotting test pressure data vs. some function of time on a semilog plot (Figs. 1a and 1b). In theory, double-porosity behavior yields two parallel straight lines on a semilog plot, provided there are no near-wellbore or outer-boundary effects. Such a semilog plot is schematically represented in Fig. la. The first semilog straight line represents the homogeneous behavior of the most-permeable medium before the least-permeable medium starts recharging. As Fig. 1a indicates, this first straight line lasts longer for restricted interporosity flow than for unrestricted interporosity flow. The second semilog straight line represents the homogeneous behavior of both media when recharge from the least-permeable medium is fully established. The two parallel straight lines are separated by a transition zone that corresponds to the onset of interporosity flow. The transition can be a straight line in the case of unrestricted interporosity flow. The slope of such a transition straight line is equal to half that of the two parallel straight lines. In practice, however, the two parallel straight lines may or may not be present. This depends on the condition of the well, the composition of the reservoir fluid, and the duration of the test. As a result, the same well may yield different responses in different tests. Fig. 1b illustrates a case of double-porosity behavior where only the last semilog straight line exists. This straight line represents the homogeneous behavior of the total system and is not characteristic of double-porosity behavior. Thus a semilog plot is not an efficient tool for identifying double-porosity behavior. More generally, straight-line analysis techniques are not valid as diagnostic tools, because an apparent straight line through a range of data does not necessarily prove the existence of a specific flow regime. Log-Log Analysis Log-log analysis involves a log-log plot of pressure change vs. elapsed time (Fig. 2). Double-porosity behavior yields an S-shaped log-log pressure curve on a log-log plot, as illustrated in Fig. 2. The initial portion of the curve represents a homogeneous behavior resulting from depletion in only the most-permeable medium. This corresponds to the region labeled "homogeneous behavior (most-permeable system)" in Figs. la and lb. A transition follows, corresponding to interporosity flow, during which pressure in the two media tends to equilibrate. Finally, homogeneous behavior resumes again, as a result of depletion in both constitutive media at the same time. JPT P. 631^

The behavior of naturally fractured reservoirs including fluid flow in matrix blocks

An alternative analytical solution to the system of equations for fluid flow through a double-porosity medium with a boundary condition of an equipotential surface is given in this paper. The problem is reduced to solving an integral equation. The solution is straight-forward, and involves only ordinary Bessel functions. Numerical results show that D, the ratio of matrix system permeability to fracture system permeability, has a strong effect on the two semilog straight lines characteristic of the pressure response in a double-porosity medium. As D increases from zero (the Warren-Root model) to one, the first semilog straight line moves closer to the second. This is similar to the effect of increasing ω, the ratio of storage capacity of the fracture system to total storage capacity, in the Warren-Root model which neglects the flow within matrix blocks.

Pressure Transient Analysis in Poorly Consolidated Reservoirs

Summary This study uses a numerical solution technique to investigate the effect on well test data of sand accumulation in the wellbore from poorly consolidated reservoirs. The results show that in anisotropic reservoirs, this sand column creates a pressure drop in the wellbore similar to that caused by infinitesimally thin skin around the wellbore. In this case, however, the slope of the semilog straight line for a buildup test is increased, indicating that the conventional analysis method would not yield accurate results. Log-log type curves and semilog plots of dimensionless pressure vs. dimensionless time are presented in this paper for different cases. These graphs can be used to detect the presence of sand in the wellbore and to analyze the transient pressure data instead of the Horner and Miller-Dyes-Hutchinson (MDH) methods. Graphs for various cases are provided for use in determining the pseudoskin factors caused by the presence of a sand column in the wellbore.

Analysis of Pressure Buildup Data Influenced by Wellbore Phase Redistribution

Summary This work considers the influence of wellbore phase redistribution effects on the analysis of pressure buildup data. First, we show that the pressure responses observed when phase redistribution effects exist consist of three distinct types and delineate the conditions under which each type exists. Second, we investigate the reliability of Fair's type curves for analyzing pressure data. Third, for each type of pressure response, we provide rules for determining when the conventional semilog straight line will begin on a semilog plot of pressure data vs. time. We also consider general procedures that are based on Duhamel's principle for analyzing pressure data when sandface flow rates are also available. We discuss the application of these methods to analyze pressure data influenced by wellbore storage effects and investigate the effect that errors in the measured sandface rate have on the analysis.

Analysis of Buildup Tests With Short Producing Time

Summary Pressure buildup data with short producing time are often difficult to analyze. Although the semilog method, known as the Horner1 method, can be used, the drawdown type curve should not. Thus it is difficult to determine whether the semilog plot actually includes the correct straight line. In this paper, a new log-log graph specially designed for a pressure buildup test with short producing time is suggested. This graph allows the user to determine easily the type of flow regime (linear, bilinear, or radial). Consequently, it can be used to detect the presence of the correct semilog straight line. The new graph can also be used to calculate the formation permeability or fracture conductivity in a fashion similar to the semilog method. The analytical models used to develop the new technique are presented. The models consider both well-bore storage and skin effect. A field example is presented and discussed. Use of the new technique to analyze a buildup test with short producing time is presented and briefly compared with the existing techniques.

Wellbore Pressure Response in Naturally Fractured Reservoirs

Wellbore Pressure Response in Naturally Fractured Reservoirs

Detection of Linear Boundaries by Drawdown Tests: A Semilog Type Curve Matching Approach

A new method for pressure drawdown analysis in reservoirs affected by linear boundaries is developed. This method is based on a semilog curve matching approach and may be applied to both constant pressure and impermeable linear boundary cases. A semilog type curve is presented by which the distance between a well and the linear boundary may be estimated. The new analysis method is an improvement over the current double straight line analysis method. The pressure response of the well is matched without the need to find two straight lines, and several advantages result. First, the analysis may be performed for interference tests for which the first semilog straight line never develops. Second, the duration of the test required for the new method is shorter by an order of magnitude than that required for existing semilog methods, since it is not necessary to wait for the second straight line to develop.

Analysis of Simultaneously Measured Pressure and Sandface Flow Rate in Transient Well Testing (includes associated papers 13937 and 14693 )

Analysis of Simultaneously MeasuredPressure and Sandface Flow Rate in Pressure and Sandface Flow Rate in Transient Well Testing Summary New well test interpretation methods are presented thateliminate wellbore storage (afterflow) effects. These new methods use simultaneously measured sandface flow rateand wellbore pressure data. It is shown that formationbehavior without storage effects (unit response orinfluence function) can be obtained from deconvolution of sandface flow rate and wellbore pressure data. The storage-free formation behavior can be analyzed to identify the system (reservoir flow pattern) that isunder testing and to estimate parameters. Convolution(radial multirate) methods for reservoir parameter estimation and a few synthetic examples for deconvolution and convolution also are presented. Introduction Well testing with measured sandface flow rate can betraced to the beginning of reservoir engineering. The rate must be measured over time to calculate and/or approximate constant rate to obtain even a single reservoir parameter from pressure measurements. This approximate parameter from pressure measurements. This approximate constant rate has been sufficient for estimating permeability, skin, and initial formation pressure during permeability, skin, and initial formation pressure during the radial infinite-acting period. During this period, the well should produce at a constant rate at the sandfaceor at a zero rate if a build up test is conducted. Becauseof compressible fluid in the production string (wellbore storage effects), it takes a long time to reach the radial infinite-acting period. The effect of outer boundaries alsomay start before the end of the wellbore storage effects. In general, the storage capacity of the wellbore, wellbore geometry, near-wellbore complexities, and external boundaries affect transient behavior of a well. During the analysis of pressure-time data, each of these phenomena and its duration must be recognized for the phenomena and its duration must be recognized for the application of semilog and type curve techniques to determine formation flow capacity (kh), damage skin, and average formation pressure. The influence of these phenomena on transient behavior of a well progresses over phenomena on transient behavior of a well progresses over time. For the sake of convenience, the test time can be divided into three periods according to which phenomenonis affecting the pressure. These periods are defined as follows. Early-Time Period The combined effects of wellborestorage, damage skin, and pseudoskin (which includepartial penetration, perforation, acidizing, fractures, partial penetration, perforation, acidizing, fractures, non-Darcy flow, and permeability reduction caused by gassaturation around the wellbore)dominate pressurebehavior. The stratification and dual porosity also mayaffect wellbore pressure during this period. Middle-Time Period During this period, radial flow isestablished. Conventionally, semilog techniques are usedto determine formation, kh and initial pressure and skin. Late-Time Period During this period, outer boundaryeffects start to distort the semilog straight line. For example, the gas cap shows a curve-flattening effect on log-log and Horner plots. Sometimes the separation of these periods from eachother is impossible; particularly, the effects of bottom-water influx and/or gas cap may start during themiddle-time period. Thus, the semilog approach sometimescannot be applied at all. Furthermore, the drawdown or buildup tests as conductedtoday tend to homogenize the reservoir behavior. In other words, most of the reservoirs behave homogeneously duringthe storage-free radial infinite-acting period because mostof the heterogeneous behavior takes place during theearly-time period. The type-curve approaches have been introduced toovercome some of these problems. The theories, applications, and elaborations of the type curve methods, as wellas many references, can be found in Ref. 1. In 1979, Gringarten et al. introduced new type curves that usedifferent parametrization than the earlier ones, namelyRamey, Agarwal et al., McKinley, and Earlougher and Kerschtypes. All the type curves presented by these authors, andmany others, were developed under the assumption that thefluid compressibility (density) in the tubing and annulusremains constant during the test period. During the earlytime, particularly for buildup tests, shut-in pressureincreases very rapidly; thus, the compressibility is usuallyhigher than the compressibility of the fluid in the reservoirfor producing wells. Since the pressure in the wellbore is afunction of the depth, the compressibility of the fluid atthe wellhead can be 10 or even 100 times greater than thecompressibility of the fluid at the bottom. Thus, theassumption that the wellbore storage coefficient is constantduring the drawdown, and particularly during buildup, maynot be correct. JPT p. 323