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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 article discusses the implementation and analysis of the modified isochroncal testing for gas well deliverability tests. Both the Rawlins and Schellhardt and Houpeurt analysis techniques are presented in terms of pseudopressures. The time to build up to the average reservoir pressure before flowing for a certain period of time still may be impractical, even after short flow periods. Consequently, a modification of the isochronal test was developed to shorten test times further. The objective of the modified isochronal test is to obtain the same data as in an isochronal test without using the sometimes lengthy shut-in periods required to reach the average reservoir pressure in the drainage area of the well.
This paper presents a review of the practical backpressure test analyses available for estimation of the stabilized absolute open flow (AOF) potential of natural gas wells. Linear regression analysis techniques have been used to correlate the field-recorded deliverability data and statistical influence tests have been used to identify possible out-liers in the test data.
The types of backpressure tests considered in this study are the conventional flow-after-flow (four point), single point, regular and modified isochronal backpressure tests, and the multiple modified isochronal test. The deliverability analyses considered in this paper are the Rawlins-Schellhardt pressure-squared, and the Houpeurt (quadratic) real gas pseudopressure and pressure-squared analyses. Modified versions of these analyses are used in the analysis of multiple modified isochronal tests.
The analysis techniques developed for multiple modified isochronal tests were reviewed and found to permit a rapid and adequate means of estimating the stabilized AOF potentials of slow-in-stabilizing wells in homogeneous reservoirs, using only the semilog transient isochronal deliverability data. Theoretical considerations are also introduced which may provide a means of estimating stabilized AOF potentials of gas wells completed in naturally fractured reservoirs. A discussion is also included on the estimation of stabilized AOF potentials of wells completed in homogeneous reservoirs, which have been vertically fractured to increase their productivity.
Deliverability testing of natural gas wells for the estimation of stabilized absolute open flow (AOF) potentials is generally performed using backpressure tests. A backpressure test is a drawdown flow test in which a well is produced at a series of flow rates and associated sandface pressures in order to establish the deliverability behavior of the well.
Varying definitions of stabilized AOF potential of a gas well can be found in the literature. While the lack of consistency in the definition of AOF potential generally does not significantly affect the values of stabilized AOF potential obtained, it does add confusion to a discussion about stabilized AOF potential determination. Since a natural gas well will not exhibit a flowing sandface pressure of less than atmospheric pressure for normal production operations, we shall use the definition of stabilized AOF potential as the theoretical stabilized rate at which the well would produce at a stabilized flowing sandface backpressure of atmospheric pressure. While this definition of stabilized AOF potential has the limitation of variable atmospheric pressure values, the limitation is negligible since in most areas, the standard atmospheric pressure is regarded to be about 14.7 psia.
Estimates of stabilized AOF potentials of gas wells have been used by the natural gas industry and regulatory agencies for several purposes, such as setting allowable production rates, pipeline and gathering system design, planning field development, and for the negotiation of sales contracts. The various types of backpressure tests and analyses available were reviewed to determine their applicability to the various types of reservoirs commonly found today.
Basic concepts, which include flow equations for unsteady-state, pseudosteady-state, and steady-state flow of fluids, are discussed first. Various flow geometries are treated, including radial, linear, and spherical flow. The pseudosteady-state equations provide the basis for a brief discussion of oil well productivity, and the unsteady-state equations provide the basis for a lengthy discussion of pressure-transient test analysis. For pressure-transient test analysis, semilog techniques, type curves, damage and stimulation, modifications for gases and multiphase flow, the diagnostic plot, bounded reservoirs, average pressure in the drainage area, hydraulically fractured wells, and naturally fractured reservoirs are included. The chapter also discusses transient and stabilized flow in horizontal wells and gas-well deliverability tests. It concludes with considerations of coning in vertical and horizontal wells. Many important applications of fluid flow in permeable media involve 1D, ...
The isochronal test is a series of single-point tests developed to estimate stabilized deliverability characteristics without actually flowing the well for the time required to achieve stabilized conditions at each different rate. Both the Rawlins and Schellhardt and Houpeurt analysis techniques are presented in terms of pseudopressures. The isochronal test is conducted by alternately producing the well then shutting it in and allowing it to build to the average reservoir pressure before the beginning of the next production period. Pressures are measured at several time increments during each flow period. The times at which the pressures are measured should be the same relative to the beginning of each flow period.