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Abstract Modern computing power has enabled very high accuracy and efficiency in complex calculations. Thus, it follows that reservoir engineering formulations need not be approximate solutions, as was sometimes historically the case. Being one of the most widely used techniques in reservoir engineering, the material balance equation (MBE) for gas is an excellent example of this. The MBE is used not only for estimating the original gas-in-place (OGIP), but also for calculating the decline in average reservoir pressure with depletion. In the majority of cases, the conventional p/Z formulation of the gas material balance is satisfactory. However, certain circumstances, which are sometimes unpredictable, demand formulations with greater accuracy. Although modifications to the standard approach have been presented, to the authors' knowledge, there is no published gas material balance formulation that is completely rigorous. This study presents a new, rigorous MBE for gas flow in the presence of a compressible formation and residual fluid saturation. Examples will be presented to highlight the capabilities of the new MBE. Introduction There has been a demand in the petroleum industry to plot the p/Z (or a similar plotting function) vs. cumulative gas production (Gp), as accurately as possible, so that the extrapolated line can point to the correct amount of OGIP. The primary value of this approach is to calculate the average reservoir pressures from the MBE. This has been one of the most powerful tools in reservoir engineering. Conventional MBE[1] for gas flow from a "volumetric" reservoir assumes the available pore volume to gas is constant by disregarding the effect of formation compressibility and the expansion of residual fluid during the productive life of the reservoir. Such assumptions may not be acceptable where the rock compressibility is of the same order of magnitude as residual fluid or gas. Ramagost and Farshad[2] modified the classical material balance equation and proposed a new plotting function as [(p/Z) (1- ce?p)] vs. Gp, based on an improved version of the conventional MBE. On a number of occasions with certain combinations of compressibility and saturation values, it has been observed that the Ramagost and Farshad MBE should have been more accurate in predicting the average reservoir pressure. We have examined how this MBE was derived. As will be shown later, the contributions of the shrinkage of the pore volume and of the expansion of residual fluid saturation were approximated in this approach. With the advent of computer power now-a-days, the accuracies of reservoir engineering calculations are warranted. The material balance equation (MBE) for gas flow has been used not only for estimating the OGIP, but also for estimating the average reservoir pressure. In addition, accuracies of MBE have to keep pace with the results from sophisticated reservoir simulations (both analytical and numerical). The following are the major applications of an MBE:To estimate average pressure for a given cumulative gas production. To estimate the cumulative gas production for a given average reservoir pressure. To estimate the OGIP from a given history of static pressure vs. cumulative production. To calculate pseudo-time[3] when using analytical solutions developed for liquids for modeling gas reservoirs. This study presents a new, rigorous MBE for gas flow in a compressible formation with residual fluid saturation. A new dimensionless parameter in the MBE will be identified and explained how this can predict the behavior the MBE. Examples will be presented to highlight the capabilities of the new MBE. The principal assumptions remain identical to those of Ramagost and Farshad[2] as compressibilities of rock and residual fluid are constant. Presentation of New MBE In the following sub-sections, we present the new, rigorous MBE, its implications and an explanation of the methodology of calculating the average reservoir pressure from it.
- North America > Canada (0.28)
- North America > United States (0.28)
Abstract This work presents the practical application of the recently developed B-spline based deconvolution methodology to analyze variable-rate/variable pressure drop well performance data from gas wells. As deconvolution provides the corresponding constant rate pressure drawdown response for a well/reservoir system which is affected by variable flowrates, we intend to use deconvolution of production data to identify the reservoir model and perform an analysis for estimating reservoir properties and reservoir volume. In this work we apply our B-spline based deconvolution methodology to production pressure and flowrate history data (which are typically available on a daily or monthly basis --- all field cases in this work (except Case 3) consider daily pro-duction data measurements). For this work, we apply our method using traditional gas well test data, as well as regularly measured gas well production data. We also demonstrate the appropriate handling of input data (particularly pressure test data and production data) to ensure stable/accurate deconvolution results. The application cases in this work should be considered typical for a reservoir or production engineer, and we would expect similar performance/robustness of our methodology as it becomes a common analysis practice. Objectives The following objectives are proposed for this work:To apply and extend the recent B-spline based deconvolution methodology to analyze variable-rate/variable pressure drop gas well performance data. To identify the critical issues which affect the success of deconvolution methodology when applied to production data. To state specific recommendations for practice and/or future work Introduction As orientation, we note that the conventional analysis of well test data involves the analysis of "high-frequency" pressure buildup data --- specifically, the derivative of the pressure drop function with respect to the logarithm of time --- using "superposition" or specialized time transforms. We can also perform a similar (albeit much simplified) approach for production data (i.e., boundary-dominated flow data). However, the purpose of using deconvolution is to "extract" the equivalent constant rate pressure drop (or pressure) function and to avoid the use of such "specialized" functions as described above. In short, the primary signature used to classify/establish the reservoir model is the constant-rate drawdown pressure behavior of a well/reservoir system --- and the goal of any deconvolution algorithm is to extract that signature with as little corruption as possible in the "extraction" process. All of which leads us to our present work for the analysis/interpretation of gas well production data using deconvolution. In many ways the gas well performance problem is prototypical --- we generally have production rates and pressures available on a per well basis (due to regulations, data collection practices, or both). These data are often measured daily, but, unfortunately we are often faced with surface pressure measurements of unknown quality (gas flowrates are typically accurate, although some "manifold averaging" often occurs as well). Put simply, although the data are not ideal, the gas well performance scenario is "data rich" compared to most other cases (oil, volatile oil, gas condensate, commingled production, etc.). Most deconvolution methods have been developed and applied to deconvolve "ideal" data (e.g., idealized pressure drawdown/buildup test sequences, monotonic or functional production rate decline sequences, etc.). Very few of these deconvolution methods perform well in practice due to the ill-conditioned nature of the deconvolution problem, which means that small changes in the input data (rate and pressure signals) cause large variations in the deconvolved, equivalent constant-rate pressures.