A New Method To Account for Producing Time Effects When Drawdown Type Curves are Used To Analyze Pressure Buildup and Other Test Data

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 other hand, 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. References and illustrations at end of paper. INTRODUCTION Type curves have appeared in the petroleum literature since 1970 to analyze pressure transient (pressure drawdown and pressure buildup) tests taken on both un fractured and fractured wells. The majori.ty of type curves l g 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 toP the shut-in time, ~t [that is (t +~t)/t 1], for liquid systems, it is reasonablg to anRlyze 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 +~t)/t » 1], the drawdown type curves may not bePused tg 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 time are to be analyzed, the Horner method lo is recommended over the MDH (Miller-Dyes-Hutchinson) method. 9 '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 pre-fracturing 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 this regard. McKinleyll has published type curves for analyzing buildup data for a radial flow system. However, his buildup type curves were generated on the assumption of long producing times; and these type curves are therefore very similar to drawdown 2 A NEW METHOD TO ACCOUNT FOR PRODUCING TIME EFFECTS WHEN DRAWDOWN TYPE CURVES ARE USED TO ANALYZE PRESSURE BUILDUP AND OTHER TEST DATA SPE 9289 type curves and are obviously unsuitable for cases where producing times prior to shut-in are relatively short. Crawford, et ar.,12 pointed out the above limitations for McKinley type curves in analyzing pressure buildup data from the DST tests. They also presented buildup curves for short producing times. Since their curves deal with specific values of real producing times prior to shut-in, they are limited in scope and utility. Recently, the effect of producing time on analysis of pressure buildup data using drawdown type curves has been discussed by Raghavan. 13 His study clearly points out the limitations of drawdown type curves for analyzing buildup data collected after small producing times. A family of buildup type curves is presented both for unfractured and fractured wells with producing time as a parameter. Although these type curves offer a definite advantage over the existing drawdown type curves, they are difficult to use because of the multiplicity of type curves. In a recent paper, Agarwal 14 also discussed the limitations of using drawdown type curves for analyzing buildup data obtained after small producing times but no details were given. These limitations are discussed here in this paper. Recently Gringarten, et al. 15 , presented drawdown type curves, plotted in a slightly different form, and suggested some gUidelines regarding the portions of buildup data which may be analyzed by drawdown type curves. Although these guidelines may be useful in certain cases, the basic problem still remains. To overcome the above-mentioned difficulties and to eliminate dependence on producing time, a new method has been developed. This method should provide a significant improvement over the current methods because (1) this permits us to account for the effects of producing time, and (2) data are normalized in such a fashion that instead of utilizing a family of type curves with producing time as a parameter, the existing drawdown type curves may be used. This concept appears to work for both unfractured and fractured wells. Wellbore storage effects with or without damage may also be taken into account provided that producing time prior to shut-in is long enough to be out of such wellbore effects. This method has been extended to include analysis of data from two-rate tests 8 'l6'l7 and multiple rate tests 8 ,17'18 by type curve methods. Although not shown, it appears to have a potential for applying type curve methods to other kinds of testing. This new method, although originally conceived for type curve analysis of buildup data, is quite suitable for the conventional semi-log analysis. It is similar to the Horner method because it includes the effects of producing time, and may be used to determine formation flow capacity, skin factor and the initial reservoir pressure. However, it has an added advantage. It allows the plotting of pressure buildup data, with and without producing time effects, on the same time scale as the graph paper. This enables a better comparison of data using the MDH and Horner type graphs. Although the new method will be developed using the solutions for liquid systems, its applicability to gas wells will also be indicated. BASIS OF DRAWDOWN AND BUILDUP TYPE CURVES A type curve is a graphical representation of a mathematical solution (obtained analytically or numerically) for a specific flow type. The solution is normally plotted, in terms of dimensionless variables, on log-log graph paper. The graph thus prepared becomes the type curve for the specific flow problem with given inner and outer boundary conditions. Depending on the type of solution (drawdown or buildup), drawdown and buildup type curves are generated. Drawdown Type Curves As the name implies, these type curves are based on the drawdown solutions. The pressure drawdown solution for a well producing at a constant rate as a function of flowing time, t may be written as kh[Pi-Pwf(t)] 141.2 qB~