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Behmanesh, H.. (Anderson Thompson Reservoir Strategies) | Anderson, D. M. (Anderson Thompson Reservoir Strategies) | Thompson, J. M. (Anderson Thompson Reservoir Strategies) | Nakaska, D. W. (Anderson Thompson Reservoir Strategies)
Abstract Analytical modeling of multi-fractured horizontal well performance can be overly complex and cumbersome due to the use of Laplace space and pseudo-time. State-of-the-art analytical solutions are typically developed using Laplace space, which is not easily understood and often requires numerical inversion. Pseudo-time (for gas reservoirs) is iterative and has demonstrated issues with accuracy, particularly in stress-sensitive reservoirs. In this work, we present a new, practical semi-analytical model which provides a direct time domain solution using the succession of steady-states method without the need for pseudo-time. The well-reservoir description used in our approach is based on the enhanced fracture region model introduced by Stalgarova and Mattar (2012). It is a composite system consisting of a stimulated (inner) region connected to a fracture and adjacent to an unstimulated (outer) region. Wattenbarger's bounded linear flow solution (1998) is utilized to account for linear flow contributions from both regions, in succession. The proportion of flow through time from the inner and outer regions is determined using a transient productivity index during transient flow and using material balance during boundary-dominated flow. The accuracy of the model is evaluated by comparing its results to an equivalent numerical model, encompassing a wide variety of tight oil and gas descriptions with varying reservoir properties and operating conditions. For all cases studied, this model achieves either the same consistency with numerical simulation results, in comparison to its Laplace space counterpart. This new model is also more accurate for gas reservoirs with pressure-dependent rock and fluid properties. The associated nonlinearities are handled using a modified productivity index during transient flow, which is a function of the average reservoir pressure within the region of influence. This average pressure is traditionally calculated using a material balance performed over the area of investigation through an iterative procedure. In order to avoid such a procedure, an explicit relationship has been developed which correlates the average reservoir pressure to the initial reservoir pressure and the bottomhole flowing pressure. This new technique provides a simple engineering workflow and an alternative to numerical simulation for modeling complex fracture networks. To the authors knowledge, this is the first analytical model which does not require an iterative approach to obtain its solution during transient flow. Since it is solved in the time domain (unlike models in Laplace space), it can be more easily implemented in a spreadsheet application. It is also more accurate, requires less calculation effort and can be extended to accommodate additional complexities, such as multiphase flow.
Abstract This paper presents the results of an investigation concerning the development of a reliable and accurate technique for establishing the stabilized deliverability performance of multi-layer commingled systems using multi-rate production log measurements. Both linear and non-linear systems are addressed in this paper, providing a basis for the analysis of reservoirs exhibiting Darcy and non-Darcy flow, respectively. Extension of the conventional Selective Inflow Performance analysis is also presented in this paper to obtain estimates of the formation and well completion properties such as effective permeability, radial flow steady state damage /stimulation skin effect, and non-Darcy flow coefficient. In the specific case where the deliverability performance of a vertically fractured well is considered, estimates of the effective fracture half-length and average fracture conductivity may be derived from the analysis. In cases where the multi-rate deliverability tests are performed under boundary dominated flow conditions, conventional deliverability analysis techniques may also be employed to derive estimates of the reservoir drainage area in addition to the well and reservoir parameters that can be obtained in a transient flow analysis. Applications of the analyses reported in this paper demonstrate the use of the analyses to evaluate the inflow performance measurements of commingled multi-layer reservoirs obtained using multi-rate production logs. Introduction The analysis of the effect of a variable flow rate production history on the pressure transient performance of a well under Darcy flow conditions has conventionally been accomplished using the convolution of the varying flow rate and pressure history of the well to evaluate the transient performance. This relationship is presented in integral form in Eq. 1 and has been utilized for quite a long time in the analysis of the transient pressure behavior of oil and gas wells.
This paper introduces a direct method to use the results of Houpeurt deliverability analysis to derive the constants "C" and "n" in the Rawlins and Schellhardt gas well deliverability equation. The motivation for this effort is the need to report the results of Rawlins and Schellhardt analysis to regulatory agencies, and the widespread use of their deliverability equation by engineers. We present a detailed procedure which shows how these results can be applied to deliverability forecasting. This paper includes an illustrative example in which the new method is paper includes an illustrative example in which the new method is applied to field data from the literature. This example presents comparisons between Houpeurt and Rawlins and Schellhardt analyses and shows the correlation between the two methods.
The purpose of deliverability testing is to determine a gas well's production capabilities under specific reservoir conditions. A production capabilities under specific reservoir conditions. A common productivity indicator obtained from these tests is the absolute open flow (AOF) potential, which is defined as the maximum rate at which a well could flow against a theoretical atmospheric backpressure at the sandface. Although in practice the well cannot produce at this rate, the AOF is often used by regulatory agencies for establishing field proration schedules and setting maximum allowable production rates for individual wells.
A number of testing techniques have been developed to assess a gas well's deliverability characteristics. Flow-after-flow tests are conducted-by producing the well at a series of different flow rates and measuring the stabilized bottomhole flowing pressures. Each flow rate is established in succession without an intermediate shutin period. The primary limitation of these tests is the long time required to reach stabilization in low permeability reservoirs Consequently, the isochronal and modified isochronal tests were developed to shorten test times.
An isochronal test is conducted by alternatively producing the well, then shutting it in and allowing it to build up to-the average reservoir pressure prior to the beginning of the next flow period. The modified isochronal test is conducted similarly, except the duration of the shut-in times often is not long enough to reach the true average reservoir pressure in the well's drainage area. Although isochronal and modified isochronal tests were developed to circumvent the long flow times required in low permeability reservoirs, these tests may still require a single, stabilized flow period at the end of the test in order to estimate the stabilized period at the end of the test in order to estimate the stabilized producing capacity of the well. producing capacity of the well. The conventional deliverability test analysis technique was proposed by Rawlins and Schellhardt. They observed that a proposed by Rawlins and Schellhardt. They observed that a log-log plot of the difference between the squares of the average reservoir pressure and the bottomhole flowing pressure against gas flow rate can be represented by a straight line defined by
where C is defined as the stabilized performance coefficient, and n is the reciprocal of the slope of the straight line. Extrapolation of this line to the difference between the squares of the average reservoir pressure and the bottomhole flowing pressure equal to atmospheric pressure defines the AOF.
Eq. 1 was developed empirically from the observation of a number of gas well tests. Extrapolation of Eq. 1 over large variations in pressure can result in incorrect estimates of the AOF. Subsequent theroretical developments by Houpeurt have shown that a more accurate analysis for gas flow is possible with where the flow coefficients, a and b, are defined by
where the flow coefficients, a and b, are defined by
Eq. 2 is a solution to the diffusivity equation for radial flow. Although the Houpeurt equation has a theoretical basis and is rigorously correct, the more familiar but empirically based Rawlins and Schellhardt equation continues to be used, indeed favored, by the natural gas industry.
This paper presents a new method for correlating real gas pseudopressure values of gas reservoirs containing large amounts of CO2- Special attention is devoted to gas reservoirs in Colorado, New Mexico, and Utah. These reservoirs have 95 to 100% CO2 concentrations. The effects of CO2 on the skin factor also are analyzed.
The main results of this study are that (1) the effects of CO2 on the conventional pressure analysis techniques are severe at higher mole fractions and at pseudoreduced pressures greater than one, (2) if real gas pseudopressure data are not properly corrected, the reservoir permeability calculated from pressure buildup and drawdown tests will be considerably less than the actual value, and (3) the proposed technique is simple, quick. and accurate enough to calculate pseudopressure values. This method is also useful in gas reservoirs with 0 to 100% CO2 concentrations.
CO2 affects the skin zone both physically and chemically, in most cases favorably. The total skin factor is slightly dependent on time for very short transient flows. However, it ultimately will become constant as the CO2 gas sweeps the entire skin zone.
The bulk of industry research and field testing of CO2 has been directed toward miscible displacement. This method of using CO2 appears to have greatest potential for oil recovery not possible by conventional producing methods. However, the potential for this process will he significant only if CO2 Can be found in enough quantity to treat many fields. The most plausible source of adequate volumes Of CO2 at a cost low enough for CO2 flooding appears to be either from existing known and undeveloped sources of naturally occurring CO2 or from future such discoveries.
There are several areas in the U.S. where CO2 is known to occur naturally. Fig. 1 illustrates locations of wells that have produced significant concentrations of CO2. The pressure tests and correlation charts presented in this paper are from wells located in southern Colorado as shown in this figure. Actual CO2 reserves that might be contained in these various geographical areas ar-e unknown. Future large reserves of naturally occurring CO2 most likely would be located in the Four Corners area, the northeast New Mexico/southeast Colorado area, and central Mississippi, and would occur in reservoirs of high-purity CO2. This study analyzes pressure behavior of such reservoirs.
Gas flow through porous media has been the object of considerable research. Up to the mid-1960's most published articles dealt with ideal gas. But most of these studies were- inadequate for gas reservoirs having high reservoir pressures, low permeabilities, and/or containing large amounts of contaminants such as CO2, nitrogen (N2), and hydrogen sulfide (H2S)- Several theories dealing with these problems were published. The most pertinent ones to this study are the papers by Al Hussainy et al., Al Hussainy and Ramey, and Zana and Thomas. Al Hussainy et al. introduced the concept of real gas potential, which eliminates the need to neglect the pressure dependence of gas viscosity and the gas deviation factor. The assumption of small pressure gradients was also eliminated. Al Hussainy and Ramey showed how the concept of real gas potential or the real gas pseudopressure could be used to analyze pressure transient tests. A few years later, Zana and Thomas investigated some of the effects of gas contaminants on real gas flow. They generated tables of the real gas pseudopressure function for various concentrations of N2, CO2, and H2S. Their study, however, did not consider the case of the high-purity CO2 reservoirs- Some of the other papers found useful to this study are by Carter, Dranchuk and Chwyl, Coats et al., Aziz et al., Robinson et al., Buxton, and Dewitt and Thodos. For instance, the study by Robinson et al. showed that there is a definite departure by the gas compressibility curve for CO2 from that of hydrocarbons, and that the value of this departure increases for higher amounts Of CO2. This departure is most significant at approximately 2,000 psia [13.8 MPa] and at low temperatures. Buxton determined the values of the gas compressibility factor at different concentrations Of CO2 in a mixture with hydrocarbon gases. Finally, Dewitt and Thodos experimentally demonstrated that the viscosities of various mixtures of gases increase with pressure as the CO2 content increases.
This study investigates the pressure behavior of high- purity CO2 reservoirs-i.e., reservoirs with 60 to 100% CO2 concentrations. In particular, pseudopressure values of such reservoirs are generated and semiempirical relations are developed. Furthermore, a study by Keio Toi on diffusion of CO2 through glassy polymers and Ref. 12 provide the basis to investigate qualitatively the effects Of CO2 on the skin factor.
Real Gas Pseudopressure Function
As shown in Ref. 1, transient flow of real gas through porous media can be described by
Summary. This paper presents a simplified method for predicting the performance of a gas well. A method for determining the deliverability of performance of a gas well. A method for determining the deliverability of an unfractured gas well by use of a single-point flow test and a dimensionless Vogel-type inflow performance curve was proposed by Mishra and Caudle. Their procedure necessitates the calculation of real-gas pseudopressures for shut-in and flowing bottomhole pressures (BHP) obtained pseudopressures for shut-in and flowing bottomhole pressures (BHP) obtained from pressure-buildup and stabilized-flow tests, respectively. This paper offers a simplification of this technique in which a range of pressure values is defined over which pressure-squared terms can be substituted for pseudopressures. A comparison is made between results obtained from analysis of well-test data on several gas wells made with conventional multipoint test methods, with the Mishra-Caudle technique, and with the simplified method presented in this paper. The simplified method offers the engineer who might not have access to a pseudopressure computer program or pseudopressure tables a method for pseudopressure computer program or pseudopressure tables a method for estimating gas-well deliverabilities. The method of Mishra and Caudle and the simplified method were both observed to yield slightly conservative estimates of gas-well deliverabilities compared with the deliverabilities calculated from multipoint flow-test analyses. The simplified technique was found to be useful for predicting the performance of fractured gas wells as well as unfractured wells.
Predicting the performance of gas wells is a process that has relied Predicting the performance of gas wells is a process that has relied almost exclusively on some form of multipoint well-testing procedure. The conventional backpressure or flow-afterflow, the procedure. The conventional backpressure or flow-afterflow, the isochronal, and the modified isochronal tests have been used to predict the short- and long-term stabilized deliverability of gas wells. predict the short- and long-term stabilized deliverability of gas wells. In a typical multipoint deliverability test, a well is produced at a minimum of four different flow rates with shut-in periods of various lengths separating flow periods. Pressure is monitored during both the flow and shut-in periods throughout the test. Analysis of the BHP vs. flow rate yields results that, when plotted on log-log paper as shown in Fig. 1, produce a straight line that reflects the paper as shown in Fig. 1, produce a straight line that reflects the stabilized deliverability behavior of a gas well.
The empirically derived relationship given by Eq. 1 represents the equation of a stabilized deliverability curve such as the one shown in Fig. 1. (1)
The constant C reflects the position of the stabilized deliverability curve on the log-log plot. The value of the exponent, n, is equal to the reciprocal of the slope of the stabilized deliverability curve and normally has a value between 0.5 and 1.0.
The stabilized deliverability curve or its equation may be used to predict the ability of a well to produce against a given sandface backpressure. The absolute open flow (AOF) of the well is also frequently calculated. The AOF is the theoretical maximum flow rate a well can maintain against a zero surface backpressure. The AOF is used mainly in comparing wells and by regulatory billies in establishing production allowables.
Multipoint backpressure tests yield very reliable deliverability projections when correctly conducted in the field. Frequently, projections when correctly conducted in the field. Frequently, however, these tests require a commitment of manpower, equipment, and time that may render the tests cost-prohibitive. This is particularly true in the case of low-permeability reservoirs, where testing particularly true in the case of low-permeability reservoirs, where testing times may be very long. The problem is further compounded in terms of lost revenues if gas must be flared throughout the test.
Alternative methods for forecasting as-well deliverability have been proposed by several authors. A replot of the stabilized deliverability curve shown in Fig. 1 on Cartesian coordinate graph paper (Fig. 2) produces an inflow performance, or IPR, curve paper (Fig. 2) produces an inflow performance, or IPR, curve similar to those observed in the testing of oil and gas producing wells. Russell et al. showed that IPR curves constructed with Eq. 1 gave predicted gas-production rates lower than those observed in the field. predicted gas-production rates lower than those observed in the field. Russell et al. proposed an equation that depicted gas-inflow performance more accurately performance more accurately (2)
Greene documented that Neely rewrote Eq. 2 by collecting the parameters that were constant for a given well in a constant, C,, parameters that were constant for a given well in a constant, C,, yielding the gas-well inflow performance equation:
The constant C, in Eq. 3 may be determined from a single flow test if the shut-in BHP is known. The constant C, will not vary with flow rate; however, it may change over the life of the well because of changes in the producing condition of the wellbore or formation.
Greene noted that a valid IPR curve could be constructed for a well from a single C1-factor determination and a known shut-in BHP. This could be done by assuming values of pwf, calculating corresponding ug and z values, and substituting in Eq. 3 to find corresponding values of q. BHP could then be plotted vs. flow rate to obtain the IPR curve.
Vogel extensively studied the inflow performance of solution-gas-drive reservoirs. He suggested that the dimensionless IPR curve shown in Fig. 3 could be used to generate actual IPR curves for wells in which oil and gas were flowing. With Vogel's method, only a value for shut-in BHP and a single flow-test point are necessary to generate an IPR curve for a well completed in a solution-gas-drive reservoir. Browns reported that field experience has shown that Vogel's dimensionless IPR curve also yields good approximations of flow behavior when the method is applied to wells producing oil, gas, and water. Vogel suggested that dimensionless producing oil, gas, and water. Vogel suggested that dimensionless IPR curves could be constructed for wells producing only liquids or only gas, as shown in Fig. 3. However, he did not propose an actual dimensionless IPR curve that could be used to predict gaswell performance.
Mishra and Caudle presented a method for predicting the deliverability of a gas well in an unfractured reservoir.