Pressure Test Analysis Research Articles

Interpretation of temperature transient data from coupled reservoir and wellbore model for single phase fluids

This paper presents a non-isothermal, transient coupled reservoir/wellbore model that accounts for the Joule-Thomson (J-T), isentropic expansion, conduction and convection effects for predicting the transient temperature behavior and computing the wellbore temperature at different gauge depths. In this study, single phase fluid flow of oil or geothermal brine from a fully penetrating vertical or inclined well in an infinite-acting homogeneous single layer reservoir is modeled. The coupled simulator solves mass, momentum and energy conservation equations simultaneously for both reservoir and wellbore. We improve solutions by the functional iteration procedure that updates fluid properties based on available correlations as a function of pressure and temperature at a given time step. A comparison of the developed model with a commercial simulator is provided. To understand and identify diagnostic characteristics of temperature transients at gauge locations at the sandface and above the sandface that may arise during a well test, we examine the sensitivity of the model parameters appearing in the coupled non-isothermal reservoir/wellbore model through a synthetically generated test data sets and history matched field application. The drawdown and buildup sandface transient temperature data are obtained from the coupled model and used to interpret and analyze temperature transients. In addition to the J-T coefficient of fluid, history matching transient temperature data provides estimates for the skin zone radius and permeability when analyzed jointly with the conventional pressure test analysis (PTA). An investigation on the effect of gauge location on temperature data shows that the early-time response is influenced by the wellbore phenomena while the J-T effects are clearly identified at later times at typical gauge locations up to 100 m above the top of the producing horizon. Logarithmic derivative of temperature transients are found as a useful diagnostic tool to differentiate the wellbore phenomena from the reservoir response. It is also shown that the temperature transient is more reflective of the properties of the near wellbore region (e.g., skin zone) than the pressure transient. For this reason, analyzing temperature transients together with the pressure transients could add more value to the analysis to better examine near wellbore characteristics. • A fully implicit transient single phase coupled wellbore/reservoir non-isothermal simulator is presented. • New diagnostic plots for temperature transient analysis are provided. • For typical gauge locations (usually up to 100 m above the producing horizon), reservoir response is acquired through drawdown wellbore temperature data. • An effective well radius is introduced for history matching due to the placement of many tools in wellbore during temperature transient analysis. • Reservoir and skin zone parameters are estimated reliably by history matching pressure and temperature field data together.

Cross‐well pressure test analysis for CO2 plume characterization based on arrival time and peak pressure change observations

AbstractCO2 migration from the injection zone into an upper zone is possible through potential migration paths such as improperly abandoned wells or other weaknesses in the caprock overlying the injection zone. Various monitoring technologies may be used to obtain information on the resulting CO2 plume in an overlying zone. Cross‐well pressure testing—where water is to be injected/produced at a well and the pressure response to be observed at monitoring well(s)—has been previously investigated to characterize the CO2 plume. However, the methods proposed in the literature are not simple and may be computationally expensive either in forward modeling, inverse modeling, or both. For the cross‐well test analysis proposed herein, both the forward solution—a closed‐form analytical model—and the inverse model—a well‐posed overdetermined system of nonlinear equations—are simple. Consequently, a simple analysis methodology is presented to invert the cross‐well test data to obtain important information on the plume. To achieve this simplified approach, the migrated CO2 plume is assumed circular in shape with constant gaseous CO2 fraction over the plume area. The analysis methodology is first validated using a single‐phase model with a circular heterogeneity. Next, the methodology is applied to synthetic cross‐well pressure test data for a two‐phase system with CO2 plume. The arrival times and peak pressure change values from multiple monitoring wells are used to estimate the location and size of the plume. The estimated values are in good agreement with the actual plume size and locations used in generating the synthetic data. © 2021 Society of Chemical Industry and John Wiley & Sons, Ltd.

Development of a Finite Element Model for Pressure Test Simulation of Transformer Tanks With Skid Bases

Deciding the boundary conditions is the most difficult part of developing an effective finite element model. Incorrect boundary conditions can cause significant errors in analysis. The finite element analysis has become a popular method of design validation for the transformer tank but the boundary conditions to be used for simulating the pressure test by finite element analysis are not clear. The pressure test analysis is carried out by assuming the bottom surface of the transformer tank to be fixed. This common practice has not been validated and requires verification. In this work, a generalized model of the transformer tank under the pressure was solved to eliminate the assumption, and the results were compared with those of the usual practice. It was found that there was significant difference in the results of the two models indicating the incorrectness of the usual practice.

Transient pressure test analysis of horizontal wells in gas condensate reservoirs: Evaluation of conventional multi-phase pseudo-pressure solutions

Transient pressure test analysis, as a tool to well and reservoir characterization, is not well developed in two-phase horizontal wells. As our best knowledge, potential of conventional multiphase pseudo-pressure solutions in horizontal well test analysis of gas condensate reservoirs below dew-point pressure has not been demonstrated yet. The most challenge is that flow regime around horizontal wells is not constant. Also, high velocity effects near wellbore are the other main conflict which need more investigation.The objective of this paper is to express encountered challenges in transient pressure test analysis of horizontal wells in gas condensate reservoirs below saturation pressure. For this purpose, based on simulated models, potential of the conventional multiphase pseudo-pressure solutions to interpret pressure behavior of these wells is examined. Also, their potential to estimate well and reservoir properties is investigated. After that, the reason for inability of these solutions in well test analysis of horizontal wells is explored. Furthermore, the effects of near wellbore phenomena on two-phase horizontal gas wells are studied.The results show that, during early radial flow, once bottom-hole pressure falls below dew-point, pressure data shows a composite behavior; however, two phase pseudo-pressure responses calculated by both steady-state and 3-zone solutions, can accurately correct the effect of liquid saturation. In the result, reservoir permeability is estimated with a good accuracy. The study also expressed that, during other flow regimes, deviation from single phase flow due to condensate accumulation cannot be corrected using conventional solutions of two-phase pseudo-pressure function. The reason is that fluid composition is not constant during any of the flow regimes except radial flow. Though, constant fluid composition is the basic assumption for the conventional solutions. Moreover, the result shows that non-Darcy effect in two-phase flow is less than single-phase. Also, positive coupling effect around horizontal wells is not as much significant as vertical wells.

Analysis of pressure falloff tests of non-Newtonian power-law fluids in naturally-fractured bounded reservoirs

Abstract Application of non-Newtonian Power-law fluids (e.g. polymeric solutions) for production enhancement in petroleum reservoirs has increased over the last three decades. These fluids are often injected as viscous solutions to improve mobility ratio and enhance oil recovery during chemical flooding. As part of the flooding operation, surfactant (or micellar) solutions are first injected at the leading edge of the flood to reduce interfacial tension between water and oil. Subsequently, a slug of polymer solution is injected ahead of normal water to increase viscosity of the water, improve volumetric sweep efficiency and accelerate oil production. Analysis of pressure tests conducted pre and post injection, to evaluate mobility of these fluids, is more demanding than conventional techniques, which were developed strictly for Newtonian fluids. In naturally-fractured reservoirs, flow of non-Newtonian fluids is more complex due to fracture-matrix interaction which is usually resonated in the pressure footprints. Some models have been developed to aid interpretation of pressure tests, but boundary effects on down-hole measurements due to structural discontinuity and presence of an active aquifer, have not been thoroughly investigated. This article presents an analytic technique for interpreting pressure falloff tests of non-Newtonian Power-law fluids in wells that are located near boundaries in dual-porosity reservoirs. First, dimensionless pressure solutions are obtained and Stehfest inversion algorithm is used to develop new type curves. Subsequently, long-time analytic solutions are presented and interpretation procedure is proposed using direct synthesis. Two examples, including real field data from a heavy oil reservoir in Colombian eastern plains basin, are used to validate and demonstrate application of this technique. Results agree with conventional type-curve matching procedure. The approach proposed in this study avoids the use of type curves, which is prone to human errors. It provides a better alternative for direct estimation of formation and flow properties from falloff data.

Investigation on flow regimes and non-Darcy effect in pressure test analysis of horizontal gas wells

Abstract Transient pressure test of horizontal wells compared to vertical wells is more complicated due to the occurrence potential of different transient flow periods. Although various mathematical models were developed for horizontal well test analysis their evaluation in different well and reservoir conditions needs more investigation. In specific, in vertical wells non-Darcy flow which causes an extra pressure drop, has a significant impact on well test data but its impact on horizontal well test data needs more investigation. The objective of this paper is to examine transient pressure behavior of horizontal gas wells under various conditions including high velocity flow. For this purpose, a horizontal gas well in a finite rectangular reservoir with typical geometry is simulated using a commercial reservoir simulator. Synthetic well data are used to plot pseudo-pressure derivative curves which identify appeared flow regimes. Sensitivity study is done considering relative well lengths and well location with respect to horizontal boundaries as well as non-Darcy flow parameter. The results show that the appearance of elliptical and pseudo-radial flow regimes depends on relative well length and formation thickness. In addition, the effect of off-centered wells with respect to upper and lower boundaries in transient pressure data is expressed. The results also show that non-Darcy flow can cause a significant skin in transient data of a horizontal gas well. Magnitude of the skin is mainly affected by reservoir permeability and production rate of the horizontal well. Contrary to the general belief regarding negligible effect of non-Darcy flow in analysis of horizontal gas well test, this study showed that it can cause a significant error in analysis of the well test data.

Investigation on flow regimes and non-Darcy effect in pressure test analysis of horizontal gas wells

Investigation on flow regimes and non-Darcy effect in pressure test analysis of horizontal gas wells

Type Curves for a Reservoir Subject to Active Bottom Water Drive

The use of dimensionless pressure and dimensionless pressure derivative type curves has fully overcome the challenges experienced in the use of straight line methods and has brought about major successes in well tests analyses. Flow periods and reservoir boundary types are easily delineated and identified with the use of these curves. Furthermore, near wellbore characterization results are now more reliable. In this study, type curves for a reservoir subject to bottom water energy and a vertical well completion are developed to reveal specific signatures that can be used to achieve efficient pressure test analysis. Both early and late flow periods were considered for a wellbore of negligible skin and wellbore storage influences. Results obtained show that dimensionless pressures depart from infinite-acting behavior and attain steady state at dimensionless time of order proportional to the square of dimensionless reservoir thickness. Wellbore dimensionless radius affects dimensionless time of attainment of steady state inversely, which is rather accelerated by large fluid withdrawal rates (large pressure drawdown). On the other hand, dimensionless pressure derivatives show gradual collapse to zero after expiration of infinite flow. The rate of collapse is strongly affected by wellbore properties and pressure drawdown. Radial flow is generally characterized by a constant slope of 1.151 during which period the dimensionless pressure derivative gave a value of 0.5. Following assumption of negligible wellbore skin and storage, no early time hump is observed on dimensionless derivative curves.

Four Layers Weaved once Structure Design and Conduction Pressure Testing Analysis for Fabric Switch

In order to overcome these shortcomings, the project is aim to design a structure similar to the traditional keyboard. The experiment using polyester staple fiber, sizing process after the polyester staple, polyester filament, sizing of polyester filament, stiffing agent treatment of polyester filament to weave. To compared the performance by the measurement of conduction pressure. It is concluded that with stiffing agent treatment of polyester filament is the best material for weaving fabric switches.

Bonding Integrity Study between Steel Pipeline andComposite Wraps Using Structural Health Monitoring Technique

This paper presents results and analysis of pressure tests performed on carbon steel pipes with external defects repaired using composite materials. These results are part of a broader study on the structural health monitoring of the use of composite repairs to rehabilitate damaged carbon steel pipework. The surface of pipe that contains the arc-shaped defects was appropriately prepared prior to installation of the composite repair, and monitoring of the performance was achieved through strain gauges. Rectangular strain gauge rosettes were installed beneath and on the outer surface of the composite repair, and the output strain data were acquired using the real-time Labview software and a Compact Rio system. The hoop and axial strains measured by each of these gauges showed a consistency in the strain distribution through the composite repair and demonstrated that the load was transferred from the steel pipe into the composite material.

RATE TRANSIENT ANALYSIS FOR HOMOGENEOUS AND HETEROGENEOUS GAS RESERVOIRS USING THE TDS TECHNIQUE

In this study pressure test analysis in wells flowing under constant wellbore flowing pressure for homogeneous and naturally fractured gas reservoir using the TDS technique is introduced. Although, constant rate production is assumed in the development of the conventional well test analysis methods, constant pressure production conditions are sometimes used in the oil and gas industry. The constant pressure technique or rate transient analysis is more popular reckoned as "decline curve analysis" under which rate is allows to decline instead of wellbore pressure. The TDS technique, everyday more used even in the most recognized software packages although without using its trade brand name, uses the log-log plot to analyze pressure and pressure derivative test data to identify unique features from which exact analytical expression are derived to easily estimate reservoir and well parameters. For this case, the "fingerprint" characteristics from the log-log plot of the reciprocal rate and reciprocal rate derivative were employed to obtain the analytical expressions used for the interpretation analysis. Many simulation experiments demonstrate the accuracy of the new method. Synthetic examples are shown to verify the effectiveness of the proposed methodology.

Well Test Analysis in the New Economy

Abstract This paper provides a chronological history of the evolution of advancement in well testing techniques in order to examine how the technology has progressed to its present state. The first factors examined are those that strongly influenced technological development in well-test analysis. The next discussion concerns the problems that still require resolution, and finally, the authors will present what they envision for the future of well-test analysis. Introduction The origin of fluid flow through porous media may be traced back to the experiments run by Darcy during the 19th century to investigate the flow of water, a Newtonian fluid, through a bed of unconsolidated sand filter. This sand filter probably had a fairly high permeability. Darcy's equation was developed and became the basis for significant further development. It was not a great surprise to find that the equations governing flow of a Newtonian fluid in high permeability formations under laminar conditions are identical to those that govern heat flow in solids. The original idea of analyzing pressure vs. time data from a producing or shut-in well to obtain information on the producing stratum first appeared in the field of hydrology. Hydrologists were mainly interested in the behaviour of underground water flow in large aquifers. Shortly thereafter, The is(1) published his work on fluid flow in porous media, which included his point-source solution. Muscat(2) was probably the first to study a problem relating to oil reservoirs-the eventual static pressure behaviour of a shut-in well in a closed oil reservoir. When compared to the initial reservoir pressure, this new static pressure can be used to measure the quantity of hydrocarbons produced up to the time of the test. The need for reliable quantitative analysis has primarily been driven by economics since accurate formation permeability determination is needed for forecasting reservoir production. Initial reservoir pressure and drainage boundaries provide the information needed to determine the amount of hydrocarbon in place. However, determination of well condition (i.e., skin factor) is also necessary to predict how much expenditure will be needed to improve productivity. Since Muscat, literally thousands of papers have been published on the analysis of pressure tests. Numerous new tests have been devised to determine specific reservoir parameters. This explosion in literature was basically due to the ease by which pressure behaviour could be measured and the enormous value of the parameters calculated from these tests. In addition to the information mentioned, pressure tests can be used to estimate:How efficiently a well is completed;The need for and anticipated success of a stimulation treatment;The general type of well treatment desired; and,The degree of connectivity of one well to another. Modern well-test analysis started when Horner(3) and Miller et al.(4) presented their famous papers where semi-log straight lineswere introduced as the first technique for analyzing pressure tests. Within a few years, Van Everdingen and Hurst(5) and Moore et al.(6) introduced other fundamental developments with the concept of wellbore storage.

Integration of Geology, Geophysics, and Numerical Simulation in the Interpretation of a Well Test in a Fluvial Reservoir

SummaryThe focus of this paper is the incorporation of geologic and geophysical data in the analysis of pressure tests in a fluvial reservoir. Using a 3,105,851-cell "porosity cube" derived by seismic and well-log data, this work outlines the steps involved in developing a 3D model with 7,128 cells that was used to estimate reservoir properties (such as permeability, skin, permeability/porosity relationship, reservoir connectivity, and fault factor). The principal steps involved in developing the reservoir model include:identifying all points in the porosity cube that were connected to the wellbore, with porosities above a specified cutoff to identify high-porosity channels and low-porosity overbanks, upscaling the porosity cube to a reasonable size for well-test simulation while preserving pay thickness, pore volume, and connectivity between high- and low-porosity materials; and matching the observed pressure and pressure-derivative responses with a numerical simulator and a regression program to automatically adjust the reservoir permeability description.A well test in a gas-condensate reservoir is used to demonstrate the ideas outlined in this work. This approach allowed us to identify not only horizontal permeability but also vertical permeability. The issues that need to be considered and the conclusions that are derived on the basis of this work differ significantly from conventional interpretations.

Influence of residual stress on the relationship between pipe pressure and C-ring tests

The effects of residual stress in modified poly(vinyl chloride) pipes upon the relationship between pressure tests and C-ring tests have been studied. A series of pressure tests were carried out at different hoop stresses using both fixed-end and free-end enclosures. The C-ring test was used to determine the yield strength of the material as a function of time. The difference in behavior between the fixed end and free end configurations was less than predicted by the von Mises analysis assuming the only stresses in the pipe wall were generated by the applied internal pressure. Both configurations produced lower results than predicted on the basis of the C-ring tests. The residual stresses in the hoop and longitudinal directions were measured. Taking into account the residual and applied stresses, the von Mises criterion for yield was used to calculate the uniaxial yield stress of the material for both end enclosure configurations. The results were similar to the yield stress measured in uniaxial tension. The von Mises criterion for yield has been shown to provide an acceptable method of analysis of pressure tests with fixed and free end enclosures and the C-ring, when residual stress is taken into account.

A new method for pressure test analysis of a vertically fractured well producing commingled zones in bounded square reservoirs

Although hydraulically or naturally fractured wells located in stratified bounded reservoirs are common, reliable techniques available to analyze the pressure test data for such reservoirs are lacking. This paper presents a mathematical model that describes the pressure behavior of a vertically fractured well located in a stratified, bounded, square reservoir. The fracture can be either a uniform flux or an infinite conductivity fracture. It was found that the dimensionless pressure function and its derivative and the fractional production rate from the different layers are mainly controlled by the fracture penetration into the formation, and that transmissibility and storativity affect the fractional production rate and the pressure derivative but have little effect on the dimensionless pressure function. Type curves of dimensionless pressure and dimensionless pressure derivative can be used to evaluate the reservoir characteristics. The selection of the appropriate type curve is guided by the behavior of the layer fractional production rate obtained from flow rate survey carried out during well testing. Type curves for uniform flux and infinite conductivity fractures exhibit similar features. Two examples are presented to demonstrate the application of the new method of analysis presented in this paper.

Injectivity Testing in Underpressured Reservoirs

SPE Members Abstract A simple technique is presented to determine injectivity in underpressured reservoirs. This technique, called the Falling Head Test (FHT), allows calculations of kh and skin by utilizing type-curves developed for drillstem tests. Results from the FHT compare favorably with values obtained from conventional buildup tests. The tests cited in this paper were conducted in heavy oil reservoirs. Introduction In conducting engineering studies on heavy oil reservoir performance, it is necessary to identify the location, thickness and transmissibility of water zones. If the water leg is located high within the oil sand, it may cause excessive override of injected steam, in which case, the dominant reservoir mechanism would be a steam drag process. However, if steam can be injected and kept low in the reservoir, gravity drainage may become the dominant recovery mechanism. Location and thickness of water legs within oil sands can be obtained from logs. To determine the injectivity of these zones, injection tests have to be conducted and the subsequent pressure response analyzed. This paper discusses the application of pressure testing analysis as applied to underpressured heavy oil reservoirs and presents a modified DST technique to obtain formation transmissivities and wellbore skin. WATER ZONES IN HEAVY OIL RESERVOIRS Heavy oil reservoirs generally exhibit pore pressures lower than hydrostatic. This can be seen in many of the Canadian and California heavy oil and tar sands deposits. Further, the initial reservoir oil viscosity can be two to six orders of magnitude greater than that of any mobile water present in the reservoir. Consequently, if the water saturation of any zone is high enough, it can provide a large water flowrate compared to oil rates from richer oil zones. The high water saturation zone may also act as a conduit for injected fluids commonly used in thermal recovery. During steam injection, the presence of high mobility water zones may not be a detriment if the zones are placed low in the pay. In this case, the injected steam can enter low in the formation and create a heating pad which would allow for gravity drainage of the oil above. However, if the zone mobility is excessively high, the injected steam could break through into neighboring producers quickly, resulting in an inefficient process. The mobility contrast between rich oil zones and any higher water saturation zones that may exist is greater in most of the Canadian heavy oil reservoirs. These reservoirs are, on the average, about 11C (20F) cooler than the California deposits, resulting in oil viscosities about an order of magnitude greater. Reservoir oil viscosities greater than 1000 cp are common, which does not allow economic cold production of the oil. These reservoirs have to be steamed from the onset to produce any oil. However, due to the low initial withdrawals from the wells, injection pressures rise quickly to formation breakdown pressures. If this does not present a problem, steam injection can be continued. However, if water sands exist nearby, the induced fracture could connect with them resulting in wasted heat during injection and/or rapid watering out of the well upon production. If higher water saturation zones exist within the deposits, they could be used to perform controlled injection into the reservoir. To assess the transmissibility of zones present in the pay, it is necessary to conduct injectivity or productivity tests. However, as mentioned previously, many of the heavy oil reservoirs are underpressured and present wellbore storage problems during these tests. The next section discusses the types of pressure transient analysis used for underpressured reservoirs. P. 179^

Well-Test Analysis for Wells Producing From Two Commingled Zones of Unequal Thickness

Established methods of analyzing pressure buildup for two-layer no-crossflow systems are extended here to include the effect of the thickness of each zone for a wide range of permeability ratios. In addition, methods are presented for estimating the permeability of the individual layers. Introduction In 1961, Lefkovitz et al. presented solutions describing the pressure behavior of a well producing at a constant rate from a bounded, producing at a constant rate from a bounded, noncommunicating multilayer reservoir. Their study provided a basis for pressure test analysis of wells producing from commingled zones. They recommended a Homer graph for determining average formation flow capacity but found it unsatisfactory for the evaluation of mean or average reservoir pressure. As a result, they suggested that the pressure. As a result, they suggested that the Muskat graph be used to calculate the static reservoir pressure. More recently Cobb et al., using the results of Lefkovitz et al., examined the pressure behavior of a two-layer reservoir for a wide range of producing and shut-in conditions. They assumed that each zone was of equal thickness and they presented results along lines suggested by the general pressure buildup theory for a wide range of permeability ratios. An important conclusion of Ref. 4 was that the permeability and thickness of each individual layer permeability and thickness of each individual layer cannot be evaluated by the conventional semilog techniques. Accordingly, they recommended that an independent effort be made to determine the individual layer characteristics. The primary objective of this paper is to extend the pressure buildup analysis of wells producing from two commingled zones by including the effect of the thickness of each zone for a wide range of permeability ratios. The results presented in this paper correspond to thickness ratios of 2 and 5. It will be shown that the results may also be used to analyze reservoirs with thickness ratios of 1/2 and 1/5, provided the permeability ratio is less than or equal to 10. The permeability ratio is less than or equal to 10. The second objective of this paper is to present methods for estimating the permeability of the individual layers. These methods may also be applied to earlier work related to two-layer commingled fluid production. We consider here a two-layer reservoir that is horizontal and cylindrical; it is enclosed at the top, bottom, and at the external drainage radius by an impermeable boundary. Each layer is homogeneous and is filled with a fluid of small and constant compressibility. The pressure gradients are small, and gravity effects are negligible in the reservoir. The porosity of the layers is assumed to be equal; the porosity of the layers is assumed to be equal; the permeability and thickness of the two zones are the permeability and thickness of the two zones are the parameters under investigation. The initial reservoir parameters under investigation. The initial reservoir pressure is the same in both layers and the surface pressure is the same in both layers and the surface production rate is constant. Finally, it is also assumed production rate is constant. Finally, it is also assumed that the instantaneous sand-face pressure is identical in both layers. Analysis of Dimensionless Pressure And Time Data For convenience of discussion we shall use the dimensionless variables listed below, defined in English engineering units. JPT P. 1035

Transient Pressure Behavior in Vertically Fractured Reservoirs

Abstract The transient pressure behavior of a well which produces a single compressible fluid through a single-plane vertical fracture has been investigated mathematically. The fracture is assumed to possess infinite flow capacity, to be of limited radial extent, and to penetrate the producing formation completely in the vertical direction. Previous studies of vertically fractured wells have been concerned primarily with production rate performance or semisteady-state pressure behavior. This study was undertaken to ascertain the influence of vertical fractures on transient pressure tests such as pressure build-ups and flow tests. In a vertically fractured system, flow in the region nearest the fracture is practically linear, whereas farther away from the fracture essentially radial flow prevails. Thus, transient pressure analyses based on radial flow theory are sometime inaccurate. As fracture penetration increases radially, kh values calculated from pressure build-up and flow test curves become increasingly larger than true values. Failure to consider the effect of fracture penetration also introduces inaccuracies into the calculation of fracture length from the apparent skin factor and into the determination of average reservoir pressure. If the total length of the fracture is 20 per cent, or greater, of the drainage radius of the well, corrections must be made to pressure build-up and flow test results. Methods for correcting such results are discussed in this paper. For wells with prefracturing pressure build-up or flow test data, it is possible to estimate fracture length by comparison with postfracturing build-up or flow test results. In new wells or wells without prefracturing build-up or flow test data, fracture length must be estimated to correct the values obtained from analysis of pressure tests after fracturing. Fracturing efficiency calculations should be made whenever possible to provide an estimate of fracture length. Tables of the dimension less pressure drop as a function of time and fracture penetration are included in this paper. Using these values should permit analysis of other types of transient pressure behavior in vertically fractured wells. Introduction Hydraulic fracturing has been used quite successfully for over a decade as a completion and stimulation technique in oil and gas wells completed in low-permeability reservoirs. During this period a considerable amount of theory has evolved on the performance of hydraulically fractured reservoirs and on more efficient means of artificial fracturing. Although theory has been developed, no rigorous investigation has been made of pressure build-up and flow test behavior in such wells. Prats et al. first discussed the performance of vertically fractured reservoirs for the case of a compressible fluid. Their work was primarily concerned with production performance at constant flowing pressure. These authors also considered large-time (semisteady-state) constant production rate behavior for vertically fractured wells: however, transient pressure behavior at constant rate was not investigated. McGuire and Sikora and Dyes, Kemp, and Caudle employed an electrical analog to investigate the influence of artificial vertical fractures on well productivity and pressure build-up. They found that fractures which extend beyond 15 per cent of the drainage radius away from the well alter the position and slope of the straight-line portion of the build-up curve. They concluded that these effects must be considered both in the determination of the effective permeability of the formation and in any calculations of final build-up pressure. Although these authors did not undertake an exhaustive study of the influence of vertical fractures on pressure build-up performance, their limited results were quite interesting from the standpoint of the effects they demonstrated. In a more recent paper, Scott reported the results of an investigation of the effect of vertical fractures on pressure behavior, which was conducted with a heat flow model. Scott's results appear to be consistent with those reported in Refs. 1 and 2. However, the effects of different fracture lengths on performance were not investigated. Pressure build-ups and transient flow tests are among the most diagnostic tools available to the reservoir engineer or production engineer. Since a very high percentage of present-day well completions incorporate the hydraulic fracturing technique, a definite need exists for information on the effect of fractures on transient pressure performance. For these reasons we have undertaken a rigorous study of pressure build-up and flow test behavior in vertically fractured reservoirs. The objectives of this study were to obtain synthetic pressure build-up and flow test curves to assess the effects of a vertical fracture, and to determine the modifications which need to be made to conventional pressure build-up and flow test analysis theory for the case of a vertically fractured well. JPT P. 1159ˆ