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Figure 1.1--Production System and associated pressure losses. Mathematical models describing the flow of fluids through porous and permeable media can be developed by combining physical relationships for the conservation of mass with an equation of motion and an equation of state. This leads to the diffusivity equations, which are used in the petroleum industry to describe the flow of fluids through porous media. The diffusivity equation can be written for any geometry, but radial flow geometry is the one of most interest to the petroleum engineer dealing with single well issues. The radial diffusivity equation for a slightly compressible liquid with a constant viscosity (an undersaturated oil or water) is ....................(1.1) The solution for a real gas is often presented in two forms: traditional pressure-squared form and general pseudopressure form. The pressure-squared form is ....................(1.2) and the pseudopressure form is ....................(1.3) The pseudopressure relationship is suitable for all pressure ranges, but the pressure-squared relationship has a limited range of applicability because of the compressible nature of the fluid.
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.
This article summarizes the fundamental gas-flow equations, both theoretical and empirical, used to analyze deliverability tests in terms of pseudopressure. The four most common types of gas-well deliverability tests are discussed in separate articles: flow-after-flow, single-point, isochronal, and modified isochronal tests. Deliverability testing refers to the testing of a gas well to measure its production capabilities under specific conditions of reservoir and bottomhole flowing pressures (BHFPs). A common productivity indicator obtained from these tests is the absolute open flow (AOF) potential. The AOF is the maximum rate at which a well could flow against a theoretical atmospheric backpressure at the sandface.
Abstract As an increasing number of horizontal gas wells are drilled, the need for a quick and reliable method to estimate the pressure-rate behavior of these wells is important to optimize well performance and make operational decisions. A reliable empirical relationship will provide engineers a technique to assess the performance of horizontal gas wells prior to undertaking extensive and often time-consuming simulation studies to model the well behavior. This work presents an analysis of the pressure-rate performance of horizontal gas wells using a three-dimensional finite difference reservoir simulator for different reservoir and wellbore conditions. The primary objective of this work is to study the pressure-rate behavior of horizontal gas wells and develop an empirical inflow performance relationship to predict their behavior. The study investigates a range of reservoir conditions to assess their effect on horizontal gas well behavior. Parameters studied include reservoir permeability, permeability anisotropy, gas gravity, drainage area, pay thickness and horizontal wellbore length. The obtained data is used to develop empirical inflow performance relationships (IPRs) to predict the pressure-rate behavior of gas wells. The IPRs are presented in terms of pressure, pressure-squared, and pseudopressure. The resulting IPRs provide a tool by which the petroleum engineer can quickly estimate the performance of a horizontal gas well without undertaking a time-consuming simulation study. Introduction As an engineer, we are often called upon to predict the pressure-production behavior of oil and gas wells to determine their productive capacity. Having an idea of the pressure-rate behavior enables the engineer to evaluate various operating scenarios to ascertain the optimum production scheme and to design and install surface and subsurface production equipment when necessary. Knowledge of the pressure-rate behavior can be quite helpful in designing and evaluating stimulation treatments or any operation that improves flow efficiency.1 Horizontal wells have become popular for producing oil and gas reservoirs in many regions around the world. The objectives of horizontal wells include increasing oil and gas production, turning a non-commercial oil or gas reservoir into a commercial reservoir and controlling severe coning problems. Due to the fact that horizontal wells can enhance reservoir recovery, they should be taken into consideration when planning a field development. While horizontal wells are generally more expensive to drill than vertical wells, they often reduce the total number of wells required in a reservoir development. To determine if horizontal wells are appropriate in a particular reservoir an incremental economic analysis must be performed based upon the investment for the horizontal wells and the anticipated increased productive capacity of the horizontal wells. Inflow performance relationships (IPRs) are pressure-rate relationships used to predict performance of oil and gas wells. Vogel2 was one of the first to propose an IPR for predicting the performance of vertical oil wells. This IPR was immediately accepted in the industry because it was easy to apply and yielded reasonable results. Bendakhlia and Aziz3 showed that using IPRs of a vertical well to forecast the performance of a horizontal well led to unsatisfactory results. As the use of horizontal and multilateral wells is increasing in modern exploitation strategies, inflow performance relationships for horizontal wells are needed. The objective of this research is to study the performance of horizontal gas wells and develop empirical IPRs for horizontal gas wells that are easy to apply. Relationships will be developed in terms of pressure, pressure-squared and pseudopressure. Al-Hussainy, Ramey and Crawford4 proposed the use of the real gas pseudopressure. It has been shown that gas flow behavior can be most accurately described using the pseudopressure function, pp, which takes into account the variability of gas viscosity and gas deviation factor as a function of pressure.
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.