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Keywords: time effect

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Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Annual Technical Conference and Exhibition, October 3–6, 1993

Paper Number: SPE-26457-MS

... for estimating the reservoir permeability distribution directly from pressure drawdown data. When applied to buildup data, these methods often suffer from producing

**time****effects**. The two methods presented in Ref. 1 for computing the permeability distribution from pressure data are referred to as the...
Abstract

SPE Members Abstract This work focuses on the analysis of pressure buildup data obtained at a well at the center of a cylindrical reservoir in which the absolute permeability is a function of distance from the well, i.e., is a function of the radial coordinate. It is shown that the permeability distribution can be estimated directly from pressure buildup data by application of an inverse solution algorithm. For cases where permeability is a function of both r and, it is shown that our inverse solution procedure yields an "equivalent" radial permeability distribution. It is also shown that the reservoir pressure profile at the instant of shut-in can be approximated from the buildup pressure data. Finally, we discuss briefly, the stabilized inflow performance relations for a well producing from the center of a cylindrical heterogeneous reservoir. Introduction The emergence of reservoir characterization has stimulated efforts to obtain improved information on reservoir heterogeneities. Like Ref. 1, this work focuses on single-phase radial flow to a well in the center of a cylindrical reservoir where permeability varies with distance from the well. Ref. 1 presented two procedures for estimating the reservoir permeability distribution directly from pressure drawdown data. When applied to buildup data, these methods often suffer from producing time effects. The two methods presented in Ref. 1 for computing the permeability distribution from pressure data are referred to as the inverse solution algorithm (ISA) and the modified Yeh-Agarwal procedure. The ISA procedure was motivated by the approximate analytical solution which Oliver constructed using perturbation analysis. As shown in Ref. 1, the modified Yeh-Agarwal method sometimes yields permeability distributions which are slightly less accurate than those obtained from ISA. Thus, this paper considers only the ISA. Oliver's analytical solution, which was constructed with a regular perturbation method, gives the dimensionless wellbore pressure drawdown solution (and its derivative) at a single well in an infinite-acting reservoir where absolute permeability varies with position. His solution assumes that permeability varies slightly about a reference, base or "average value," k and that porosity is constant. In Ref. 1, starting with Oliver's perturbation theory solution, we constructed a new recursive inverse solution algorithm (ISA) which can be applied to construct the radial permeability profile, k(r). It was shown that ISA gave good estimates of the true permeability distribution even for multicomposite reservoirs with large discontinuous changes in permeability between zones. (Although not discussed here, we sometimes encountered stability problems when attempting to apply the Baccus-Gilbert method which Oliver used for one synthetic example in Ref. 5.) Rosa and Horne examined the same basic problem as Oliver. While they concluded that the pressure response for a multirate test was more sensitive to reservoir heterogeneities, like Oliver, they concluded that the inverse problem, i.e., the determination of a permeability distribution pressure data, does not have a unique solution. While we recognize that the inverse problem may not have a unique solution (see Refs. 1 and 7), we have shown that in most cases, including the multicomposite reservoir case, we can construct a good approximation to the permeability distribution directly from well-test pressure data. In this work, we consider the application of ISA to buildup data obtained after constant rate production. It is shown that if the pressure drawdown data is recorded during a short period immediately prior to shut in, then buildup data can be modified to radically reduce producing time effects. ISA can then be applied to this modified buildup data to generate an approximation to the reservoir permeability distribution that is essentially as accurate as can be obtained from a constant rate drawdown test. P. 417^

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Annual Technical Conference and Exhibition, September 21–24, 1980

Paper Number: SPE-9289-MS

... tests. While analyzing buildup data by the conventional semi-log method, the Horner method takes into account the effect of producing time. On the otherhand, 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...
Abstract

Abstract 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 otherhand, 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. Introduction Type curves have appeared in the petroleum literature since 1970 to analyze pressure transient(pressure drawdown and pressure buildup) tests taken on both unfractured and fractured wells. The majority of type curves which have been developed and published to date were generated using data obtained from pressure drawdown solutions and obviously are most suited to analyze pressure drawdown tests. These drawdown type curves are also commonly used to analyze pressure buildup data. The application of drawdown type curves in analyzing pressure buildup data is not as bad as it may first appear. As long as the producing time, t, prior to shut-in is sufficiently long compared to the shut-in time, Delta t [that is (t +Delta t)/t 1], for liquid systems, it is reasonable to analyze pressure buildup data using drawdown type curves. However, for cases where producing times prior to pressure buildup tests are of the same magnitude or only slightly larger than the shut-in times [that is, (t + Delta t)/t »1], the drawdown type curves may not be used to analyze data from pressure buildup tests. The above requirement on the duration of producing times is the same for the conventional semi-log analysis. If pressure buildup data obtained after short producing pressure buildup data obtained after short producing time are to be analyzed, the Horner methodic is recommended over the MDH (Miller-Dyes-Hutchinson)method. The MDH method is generally used to analyze buildup data collected after long producing times, whereas the Horner method is used for those obtained after relatively short producing times. Although pressure buildup tests with short producing times may occur often under any situation, they are rather more common in the case of drill stem tests and prefracturing tests on low permeability gas wells. Thus, there is a need for generating buildup type curves, which account for the effects of producing time. Some limited work has been done in producing time. Some limited work has been done in this regard. McKinley has published type curves for analyzing buildup data for a radial flow system.