Identification Of Near Wellbore Effects And Boundaries From Pressure Buildup Tests

Determination of Formation Characteristics From Two-Rate Flow Tests

The increased importance of underground gas storage has prompted the development of a new method for finding the average reservoir properties of a multiwell gas reservoir. This method provides the properties of a multiwell gas reservoir. This method provides the same information as a conventional pressure buildup analysis, but eliminates the need for monitoring the pressure buildup of each well. Introduction With the increased importance of underground gas storage, gas companies need accurate statements of gas in place as a function of pressure and as a measurement of reservoir performance. Since gas-storage reservoirs operate all year, the time available to obtain the data for a reservoir analysis is limited to a relatively short time period between the injection and the withdrawal cycles. In the past, an isobaric map of the short shut-in pressure of each well was used to arrive at an average reservoir pressure. This method did not give any indication of pressure. This method did not give any indication of reservoir performance, and, in tight reservoirs, it was seen that the short shut-in pressure would not give the stabilized reservoir pressure. Because of these reasons, a new method was sought to give the needed information. The principal method for estimating a formation's performance and pressure in a gas well is the analysis of performance and pressure in a gas well is the analysis of shut-in bottom-hole pressure-buildup data. Applying this method to a gas well requires that the well be produced to pseudosteady state and that it be shut in for produced to pseudosteady state and that it be shut in for a length of time sufficient to obtain a clearly defined straight line on the plot of bottom-hole pressure vs log (t + Delta t)/t. From the slope of this straight line and from other obtainable data, the effective permeability, flow efficiency, skin factor, and reservoir pressure at infinite shut-in time can be estimated. Using this process as a base, Matthews et al. developed a method for calculating the average reservoir pressure in a bounded reservoir - a reservoir with no water drive. Their procedure requires that each well's rate and pressure buildup be known before applying the method. This would require additional expenditures not normally necessary in a gas-storage field operation. From the foregoing discussion, it is apparent that it is desirable to have an alternative method for obtaining the same data as derived from the conventional buildup analysis. The Matthews et al. method is not practical for a gas-storage reservoir, but it does offer a solution to the problem. Using the same principle used by Matthews et al. for finding the average reservoir pressure, a new and practical method for estimating average reservoir properties is presented in this paper. This new method properties is presented in this paper. This new method does not require that the pressure buildup and rate of each well be known. The required pressure data are obtained by observing the transient behavior of the main header line with all producing wells open to the gathering lines. The new method yields the same information as the conventional pressure-buildup analysis, but avoids the need for shutting in each well and measuring the pressure buildup. Theory Using methods similar to those used by other authors, it is shown in the Appendix that the actual pressure drop at any point in a multiwell reservoir will be the sum of the pressure drops of the individual wells. pressure drops of the individual wells. JPT P. 835

This paper presents new procedures for analyzing pressure buildup data obtained from drillstem tests. The new methods apply for cases where the produced fluid does not reach the surface during the flowing period so that, the flow period represents a slug test. The combined effects of variable flow rate, short producing time and changing wellbore storage generally make it difficult to apply conventional analysis methods to DST buildup data. Two new straight-line methods for analyzing buildup data presented in this work account for both the variable rate during the flow period and producing time effects. If the buildup well-bore storage-skin group Csd exp(2s) is small, then shortly after shut-in, a well-defined straight line is obtained for both methods. Using the slope of the straight line obtained by either method, it is shown that the flow capacity (kh), the skin factor (s) and the initial reservoir pressure (pi) can be determined. If the group Csd exp(2s) is large, longer shut-in times are needed before the proper straight line can be obtained. However, for the latter case, it is shown that a multi-rate equivalent time can be constructed so that standard type-curve matching can be performed to obtain estimates of the flow capacity and the skin factor. A field example is presented to illustrate the applications of the proposed methods.

Summary Methods for analyzing buildup data following a short flow period are presented, discussed, and illustrated. A new type curve for uniform-flux and infinite-conductivity vertically fractured wells is presented. By matching buildup data with this new type presented. By matching buildup data with this new type curve, we can determine the dimensionless flowing time before shut-in. A method for converting buildup data to equivalent drawdown data is discussed. This method can be used to combine buildup and drawdown data to obtain a longer band of data for type-curve matching. This method canbe used for constant-rate production, constant-pressure production, and for the case where both pressure and rate production, and for the case where both pressure and rate vary during production. Introduction Over the past decade, the use of type-curve matching toanalyze pressure data has gained increasing acceptance. The advantages and dis advantages of type-curve matchingare well recognized and the procedure has become astandard tool to analyze data qualitatively, to identify flow regimes, and, quantitatively, to determine iformation parameters. Virtually all type curves available in the literature examine the pressure response at a flowing well-i.e., only drawdown solutions have been examined. These type curves may be used to analyze shut-in pressure behavior provided that the flowing time before shut-in is provided that the flowing time before shut-in is significantly longer than the maximum shut-in time. This limitation has prevented type-curve analysis ofpressure buildup data following short flow periods. pressure buildup data following short flow periods. The effect of a short flow period on pressure buildup data influenced by either wellbore storage or vertical fractures was presented recently. It was shown that significant errors result if proper care is not taken in analyzing pressure buildup data when the producing timeis short. Procedures to account for the influence of producing time were outlined. producing time were outlined. The objectives of this paper areto present anew correlation that considerably simplifies the use of buildup type curves for vertically-fractured wells givenin Ref. 1, andto suggest a procedure to analyze pressure buildup data by means of drawdown type pressure buildup data by means of drawdown type curves. The procedures discussed here can be applied to single- or multiwell tests, to data obtained after shortor long flow periods, to constant or variable flow rates, and to virtually all wellbore conditions including data influenced by wellbore storage and skin and fracturesof finite or infinite conductivity. Theory The basic pressure buildup equation based on the principle of super position is given by principle of super position is given by (1) Here, t is flowing time and Delta t is shut-in time. Thesymbols p and t denote dimension less wellbore pressure drop and dimension less time, respectively, and are defined as follows. JPT P. 904

Two simple and equivalent procedures are suggested for improving the calculated average reservoir pressure from pressure buildup tests of liquid or gas wells in developed reservoirs. These procedures are particularly useful in gas well test procedures are particularly useful in gas well test analysis, irrespective of gas composition, in reservoirs with pressure-dependent permeability and porosity, and in oil reservoirs where substantial gas porosity, and in oil reservoirs where substantial gas saturation has been developed. A knowledge of the long-term production history is definitely helpful in providing proper insight in the reservoir engineering providing proper insight in the reservoir engineering aspects of a reservoir, but such long-term production histories need not be known in applying the suggested procedures to pressure buildup analysis. Introduction For analyzing pressure buildup data with constant flow rate before shut-in, there are two plotting procedures that are used the most: the procedures that are used the most: the Miller-Dyes-Hutchinson (MDH) plot and the Horner plot. The MDH plot is a plot of p vs log Deltat, whereas the Horner plot is a plot of p vs log [(t + Deltat)/Deltat]. Deltat is the shut-in time and t is a pseudoproduction time equal to the ratio of total produced fluid to last stabilized flow rate before shut-in. This method was first used by Theis in the water industry. Miller-Dyes-Hutchinson presented a method for calculating the average reservoir pressure, T, in in 1950. This method requires pseudosteady state before shut-in and was at first restricted to a circular reservoir with a centrally located well. Pitzer extended the method to include other Pitzer extended the method to include other geometries. Much later, Dietz developed a simpler interpretation scheme using the same MDH plot: p is read on the extrapolated straight-line section of the pressure buildup curve at shut-in time, Deltat,(1) where C is the shape factor for the particular drainage area geometry and the well location; values for C are tabulated in Refs. 5 and 13. For a circular drainage area with a centrally located well, C = 31.6, and for a square, C = 30.9.Horner presented another approach, which depended on the knowledge of the initial reservoir pressure, pi. This method also was first developed pressure, pi. This method also was first developed for a centrally located well in a circular reservoir.Matthews-Brons-Hazebroek (MBH) introduced another average reservoir pressure determination technique, which has been used more often than other methods: first a Horner plot is made; then the proper straight-line section of the buildup curve is proper straight-line section of the buildup curve is extrapolated to [(t + Deltat)/Deltat] = 1 (this intercept is denoted p*); finally, p is calculated from(2) m is the absolute value of the slope of the straightline section of the Horner plot:(3) pDMBH (tDA) is the MBH dimensionless pressure pDMBH (tDA) is the MBH dimensionless pressure at tDA, and tDA is the dimensionless time:(4) tp k a pseudoproduction time in hours:(5) PDMBH tDA) for different geometries and different PDMBH tDA) for different geometries and different well locations are given in Refs. 6 and 13.The second term on the right-hand side of Eq. 2 is a correction term for finite reservoirs that is based on material balance. Thus, for an infinite reservoir, p = pi = p*, where pi is the initial reservoir pressure. SPEJ P. 55

American Institute of Mining, Metallurgical and Petroleum Engineers, Inc. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract Methods of analyzing pressure buildup data from stabilized wells have been presented by several authors. All of the methods attempt to use some type of straight-line Horner plot. This paper must be considered controversial in that it shows that there is no theoretical basis for expecting a straight-line Horner plot from a stabilized well's pressure buildup data regardless of the "producing time" used. A simplified method is presented which analyzes buildup data by working with only the pressure change caused by the negative rate induced when the well is shut in. The pressure change that would have occurred had the well not been shut in is taken into account before the pressure plot is constructed. This approach permits the calculation of the undamaged transmissibility of the reservoir, the skin factor or damage ratio, and the average pressure in the well's drainage radius. These calculations can be completed with less data than required for the analysis of a pressure buildup from an infinite acting reservoir, provided the pressure change with time during stabilized production is known from past surface pressure observations, past BHP surveys, or a pressure survey just before shut-in. Introduction Except for pressure surveys run in connection with drillstem tests, most pressure buildup data are obtained from wells that are stabilized at the time of shut-in. The well known Horner type of pressure buildup analysis is based on infinite acting reservoir equations and thus is not directly applicable to most of the available pressure buildup data. Several methods have been proposed for analyzing pressure buildup data from stabilized wells, but all of the methods present some difficulties in application. The published methods attempt to adapt the Horner plot to stabilized wells. They also require trial-and-error solutions and/or reservoir data which are not normally available. The method developed in this paper does not require a trial-and-error solution nor does it require any more reservoir data than does the Horner type of analysis of an infinite acting reservoir. The Horner pressure buildup equation can be written in two terms in practical units as, The first term represents the pressure change that would occur in (tp + delta t) days, if the well had not been shut in. The second term represents the pressure increase which occurs due to introducing a -q rate at the well when the well is shut in for delta t days. van Everdingen and Hurst showed that these pressure changes are a function of the log of the time only as long as the reservoir is infinite acting. This paper presents a method of analysis that concerns itself with the second term of this equation and for a delta t small enough for the effect to be infinite acting.

Pressure build-up analysis of Devonian shale gas reservoirs is very critical and essential for determining the reservoir formation properties such as the flow capacity (Kh), skin factor (S), and the average reservoir pressure (P̄). Due to the complexity of the shale reservoir (its typically very low permeability and the presence of a dual porosity system), valid and accurate results of pressure build-up analysis are important to the optimization of individual well completions or depletion plans for gas reservoirs in the shale. Horizontal wells may allow operators to take better advantage of the shale fracture systems and anisotropic flow regime, but they present a new challenge for well testing and analysis. This paper documents a technical procedure with field examples, using pressure build-up data from horizontal and vertical wells, to assist the reservoir engineer in evaluating the reservoir prior to any decision-making process. This procedure implements two conventional build-up analysis techniques: (1) type curve matching, and (b) Horner's technique. Pressure and pressure-derivative values are used to estimate values of skin, flow capacity, and average reservoir pressure. A newly-developed technique known as the rectangular hyperbolic method (RHM) is implemented in the pressure build-up analysis for comparison to results determined by the previous techniques. The RHM technique is accurate/valid for estimating the various reservoir properties and, in particular, the average reservoir pressure. In addition, reservoir engineering simulation is used to verify the results of the various techniques by using either the pressure build-up data or the production history for the history matching process.

Shunnan Block in North-West China is one of the toughest HPHT gas reservoirs with vertical depth over 7500 m, formation temperature over 200 and pressure gradient varying from 1.3 to nearly 2. The condition is close to temperature and pressure limit of well testing tools, therefore, the tools are hard to be sent to downhole and chances are that well testing operations usually failed. The pressure buildup data are with bad quality and needed to be converted into downhole data. Meanwhile, it's hard to diagnose accurate flow regimes and interprete because the block is typically carbonate reservoirs with porous medium including pores, natural fractures and caves. In this paper, we reviewed the exploration wells in this block and find that interpretation by pressure buildup or transient production data can only reflect part of the formation information; therefore the two kinds of data are combined to get more accurate interpretation results. For pressure buildup interpretation, three models including dual porosity model, composite model, and dual porosity with composite model are chosen and compared. For the production data, dual porosity model with boundary is selected because the wells usually show characteristics of multiple porous medium and boundary dominated flow. Parameters interpreted from pressure buildup data are simultaneously transferred into the model for production data. Results show that the combined interpretation by pressure buildup and production data can reduce the un-uniqueness of models as well as enhancing the accuracy of formation and wellbore parameters evaluation. The model and parameters can satisfy both pressure buildup and production data history. Although Shunnan block is considered as one greatly promising reservoir from the short period open flowing, the combined interpretations suggest very limited drainage volume. Reasons for this paradox phenomenon may be that the wells are severe contaminated by drilling fluid, or the wells were only producing gas in caves and natural fractures nearby the wells while other caves are not connected.

RUSSELL, D.G.,* MEMBER AIME, SHELL DEVELOPMENT CO., HOUSTON, TEX. Abstract Two techniques have been developed with which the applicability of pressure build-up analyses can be extended to include pressure data which previously have been considered virtually unusable. One of the interpretation methods makes possible the analysis of pressure build-up performance during the wellbore fill-up or after production period which occurs soon after a well is closed in. The other technique is an extension of a method for analyzing pressure build-up performance during the late-time portion of the pressure build-up which occurs after boundary effects first begin to alter the shape of a conventional pressure build-up curve. With both of these methods it is possible to obtain estimates of the kh product, the skin factor and the reservoir pressure. In addition, with the late-time analysis technique it is possible to obtain an estimate of the contributory drainage volume of the well being tested. This means that in some cases a check on reservoir limit test and (or) material-balance calculations can now be obtained from pressure build-ups. Both methods are slightly more time-consuming than conventional pressure build-up analysis methods because trial-and-error plots of pressure data must be made. The late-time method for analysis of pressure build-ups is in principle applicable to the late-time portion of a two-rate flow test or a pressure drawdown test. The interpretation formulas and procedures for these types of tests are also outlined. In these cases, as with pressure build-ups, it is significant that an estimate of the contributory pore volume is also obtained. Oil the basis of limited experience with the new techniques, it appears that satisfactory estimates of the kh product, skin factor, reservoir pressure and, for late-time analysis, contributory drainage volume can be obtained. Introduction The analysis of bottom-hole pressure build-up behavior in closed-in wells has been a subject of interest in petroleum engineering circles for many years. In fact, few other subjects have received as much attention as pressure buildup analysis methods have. The cause for this interest is essentially twofold in nature. First, the pressure behavior of a well can normally be measured with a reasonably high degree of accuracy so that good data for analysis can be obtained. Secondly, over a fairly wide range of operating conditions, valuable information as to the quality of the reservoir rock and completion efficiency of the well can be obtained at a nominal cost. In recent years, numerous papers have been prepared on the effects of various operating conditions and reservoir heterogeneities on pressure buildup behavior. Very little work has been done, however, on extension of pressure build-up analysis methods to those pressure data which are not amenable to analysis by the present methods. The theory upon which the analysis of shut-in bottomhole pressure build-up data is based is derived from the solution of the radial flow equation for a slightly compressible fluid for constant-rate conditions. It requires that the well be closed in for a sufficient period of time to obtain a clearly defined linear portion on the plot of observed bottom-hole pressure vs log (t + t)/ t (where t is shutin time, and t is producing time to the instant of shut-in). From the slope of the plot and other normally obtainable data, the formation permeability, the well damage or skin factor, and the reservoir pressure at infinite shut-in time (if the reservoir were infinite) can be estimated. The successful application of this procedure depends on being able to recognize the straight-line section on the basic pressure build-up plot. The presently used pressure build-up interpretation theory also assumes that a well is closed in at the sand face and that no production into the well occurs after shut-in. In practice, of course, the well is closed in at the surface, and inflow into the well continues until the well fills sufficiently to transmit the effect of closing-in to the formation. This adjustment period is commonly referred to as the "after production" or "fill-tip" portion of the pressure build-up. During the period that the well fillup effect is most pronounced, the basic pressure build-up plot is nonlinear. At later shut-in times after the effects of a drainage boundary have been felt at the well, deviation from the straight-line behavior of the pressure build-up plot also results. In many cases either of these effects or a combination of both can make the straight-line portion on the pressure build-up plot difficult to recognize. Obviously, an extension of pressure build-up analysis methods to include the after production period and the period in which boundary effects are being felt would be desirable and might render valuable pressure data which for years have been considered virtually unusable. The principal reference of note concerning pressure buildup analysis during the after production period is a paper by Gladfelter, Tracy and Wilsey. In the approach of these authors it is necessary to measure the rate of influx into the well during the after production period. JPT P. 1624ˆ

Currently, type curve analysis methods are being commonly used in conjunction with the conventional methods to obtain better interpretation of well test data. Although the majority of published type curves are based on pressure drawdown solutions, they are often applied indiscriminately to analyze both pressure drawdown and buildup data. Moreover, the limitations of drawdown type curves, to analyze pressure buildup data collected after short producing times, are not well understood by the practicing engineers. This may often result in an erroneous interpretation of such buildup tests. While analyzing buildup data by the conventional semi-log method, the Horner method takes into account the effect of producing time. On the other hand, for type curve analysis of the same set of buildup data, it is customary to ignore producing time effects and utilize the existing drawdown type curves. This causes discrepancies in results obtained by the Horner method and type curve methods. Although a few buildup type curves which account for the effect of producing times have appeared in the petroleum literature, they are either limited in scope or somewhat difficult to use. In view of the preceding, a novel but simple method has been developed which eliminates the dependence on producing time effects and allows the user to utilize the existing drawdown type curves for analyzing pressure buildup data. This method may also be used to analyze two-rate, multiple-rate and other kinds of tests by type curve methods as well as the conventional methods. The method appears to work for both unfractured and fractured wells. Wellbore effects such as storage and/or damage may be taken into account except in certain cases. The purpose of this paper is to present the new method and demonstrate its utility and application by means of example problems.

A simulation model of a reservoir with a symmetrical-horizontal fracture extending from the wellbore to the midpoint of the drainage radius was constructed. The mathematical equation was developed for the case of single-phase unsteady state fluid flow. A solution for an infinite reservoir was obtained numerically and used for pressure drawdown and buildup analysis. The pressure drawdown and buildup analysis. The numerical results shows that: 1. On pressure drawdown and buildup curves, two straight lines are obtained; the first straight line with lower slope yields the effective permeability of the matrix and fracture, and the second straight line with greater slope yields the permeability of matrix. 2. The time of bend between the straight lines increases with increase in fracture radius. As the fracture radius approaches infinity, only one straight line of the Odeh type is obtained. 3. Extrapolation of the first straight line portion of the buildup curve may lead to an incorrect value of the static reservoir pressure. Introduction Analysis of pressure buildup and drawdown data is recognized as a powerful tool by the production and reservoir engineer seeking to production and reservoir engineer seeking to characterize the reservoir. Most pressure analysis techniques have assumed homogeneous reservoirs, i.e. the porosity and permeability are constant. However, some prolific wells produce from fractured reservoirs. These produce from fractured reservoirs. These reservoirs contain two distinct types of porosity and permeability, namely fracture porosity and permeability, namely fracture and matrix. Since the fractured region has higher permeability, reservoir-engineering analysis based on a homogeneous reservoir may lead to erroneous results. The purpose of this study is to develop a mathematical model which will simulate the pressure drawdown and buildup curves that would be obtained from a reservoir with a symmetrical-horizontal fracture around the wellbore. The mathematical model is developed by assuming a cylindrical reservoir of drainage area of uniform thickness is penetrated by a single production well at its center. The two -dimensional diffusivity equation for single phase flow was used to obtain pressure buildup phase flow was used to obtain pressure buildup and drawdown curves. It was necessary to obtain a constant rate solution to the equation because of the mathematical complexities introduced by the fractured reservoir geometry.

Analysis of the pressure response obtained from a drill stem test (DST) provides important additional information for deciding whether it is economical to complete a well. Interpretation of DST pressure buildup data has been based on the Horner method. The basic assumption of the Horner method is that the well is produced at a constant rate before the shut-in. When rate changes with time, a cumbersome application of the superposition principle is required to analyze the pressure buildup data. Furthermore, the solution of the diffusivity equation for a constant production rate gives a declining flowing pressure with time, but most DST's show an increasing flowing pressure during production. Therefore, the application of the Horner method may lead to inconsistent results in the interpretation of DST pressure buildup data. An original approach was used to model the DST problem. A DST can be characterized as a changing wellbore storage problem following an instantaneous pressure drop at the well. During production the wellbore storage coefficient is given by the rate of fluid accumulation inside the wellbore. After the shut-in of the well the wellbore storage mechanics change due to the compressibility of the fluid below the bottom hole valve. Therefore, using this concept, the flowing and the pressure buildup phases are modeled with a single inner boundary condition. In this paper an analytical solution correct for both the flowing and shut-in periods was obtained by solving the diffusivity equation with a single inner boundary condition which included the mixed conditions for flow and buildup. Both a skin effect and wellbore storage were considered. Solution was obtained by Laplace transformation. The solution was used to develop methods of interpretation for the pressure buildup period of drill stem tests. Application of these new methods of interpretation to DST field data may provide the initial reservoir pressure, the formation permeability and the skin effect. The interpretation methods are based on graphical analysis of the data and are easily applied in the field. The interpretation methods are generalized to include multiple production-shut-in cycles, including step changes in the wellbore storage coefficient due to changes in the drill pipe diameter and/or due to variations in fluid properties. Unlike the results obtained from the application of the Horner method, interpretation of field data using these new methods show excellent agreement between the parameters obtained from the analysis of the first and second shut-in periods of short term double-cycled DST's. Field examples are presented.

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

SUMMARY This paper examines applicability and limitations on the use of rectangular hyperbolas to analyze pressure buildup data, with emphasis on the determination of average pressure and flow capacity. It is shown that the method can be used with confidence only if it is applied to data that can also be analyzed by conventional semilog methods, and that it for such data is essentially equivalent to the conventional methods in terms of information needed and information obtained. If we use semilog data, then we can determine the flow capacity from the slope of the hyperbola, and we can determine the average pressure indirectly from the asymptote, provided we know the drainage area and the MBH function of the reservoir. Following stabilized flow we only need the shape factor in addition to the area. If we use the direct approach, and assume that the asymptote is equal to the average pressure, then we need the same type of information to make a proper choice of interval where the hyperbola should match the buildup curve. For this direct approach we will normally get. an estimate of average pressure that is less than m/1.151 psi (kPa) above the last wellbore pressure being used in the analysis, where m is the conventional semilog slope. Moreover, if we use only semilog buildup data following pseudosteady-state flow, then we can only get an accurate estimate of average pressure by this approach if the shape factor is close to 21, or higher. If nothing is known about the reservoir, then the hyperbola method can be used to get. a rough estimate of the average pressure, but with a high degree of uncertainty if we only have data from a short buildup period. This claim follows from the many examples included in this paper of asymptotes determined from hyperbolas matched to dimensionless synthetic buildup data plotted vs. interval midpoints.

The fundamental aim of well stimulation treatments is to enhance the revenues from oil and gas wells by improving their productivity or, in the case of injection wells, their injectivity, This can be accomplished by removing or bypassing any damage or impairment from around the wellbore, or by creating conductive fractures, emanating from the wellbore, which enhance the formation's ability to flow. Although perhaps a simplification, stimulation treatments can be divided into those using acids and those employing proppants such as sand, sintered bauxite, or ceramics. This article will concentrate on stimulation of well performance using acids. Acid treatments can generally be divided into acid washes, matrix treatments and acid fracs. However before reviewing these techniques, the relevant factors affecting the productivity (or injectivity) of an oil gas (or injection) well need to be understood. The productivity index or PI for oil and gas wells can be expressed by: Equation (1) (Available in full paper) Equation (2) (Available in full paper) Where: Q = production rate re = drainage radius p = average reservoir pressure rw = wellbore radius pwf = flowing bottomhole pressure S = skin factor k = permeability Z = compressibility factor for gas u = viscosity h = formation height Bo = oil formation volume factor CI, C2 = constants for units T = temperature In damage removal/bypass treatments, in which acids are generally used, we increase well productivity by decreasing the parameter (S) - the skin factor. In fracturing treatments, we can increase productivity by increasing the wellbore radius (rw) to some fictitious radius called the effective wellbore radius (rw). FIGURE 1: Effect of skin. (Available in full paper) The skin factor (S) is a term which reflects a zone of altered permeability around a wellbore. Invasion by drilling fluids, cement filtrate and completion fluids together with perforation damage can effectively decrease the permeability of the formation rock near the wellbore. This decrease in permeability results in a pressure drop in excess of that predicted by the radial flow (diffusivity) equation. Thus in the damaged case, the additional pressure drop is accounted for by a 50-called positive skin factor. On the other hand, stimulation techniques such as acidizing will normally increase permeability in the near well bore region, Thus in the stimulated case, we should see less pressure drop than predicted by the radial flow equation. In the stimulated case, a negative skin is sought. These concepts are illustrated in Figure 1. The degree of damage, or lack of it, can be determined by analyzing pressure build-up (PBU) data and deriving a skin factor. If the skin factor is positive and attributable to damage mechanisms, as against turbulence or other limited entry effects stimulation treatments such as acidizing may be required. Increase in Effective Wellbore Radius Fracturing is often used to increase the productivity of low permeability formations. The effect of fracturing can be interpreted as an enlargement of the wellbore radius (rw) to some imaginary radius called the effective wellbore radius (rw).