Pressure Buildup Analysis With Wellbore Phase Redistribution

Abstract

Abstract This paper presents an analysis of the effects ofwellbore phase redistribution on pressure builduptests. Wellbore phase redistribution is shown to be awellbore storage effect and is incorporatedmathematically into a new solution of the diffusivityequation. Dimensionless pressure solutions based onan infinite radial reservoir are presented fortype-curve matching to analyze pressure buildup testsinfluenced by wellbore phase redistribution, andexample analyses of actual field data are included.The parameters that affect phase redistribution andgas humping are documented also. This informationpermits analysis of many anomalous pressure permits analysis of many anomalous pressure buildup tests which previously could not be analyzedquantitatively. Introduction Pressure buildup tests and other types of transient Pressure buildup tests and other types of transient pressure tests have been used for many years to pressure tests have been used for many years to evaluate reservoir fluid flow characteristics and wellcompletion efficiency. The basic theory andequations for the analysis of these tests are welldocumented. Many factors that influence thepressure response in transient flow conditions have pressure response in transient flow conditions have been investigatedi.e., the effects of reservoirboundaries, heterogeneities, and fractures, wellborestorage of fluids, and various types of wellimpairments, skin effects, and completion practices.However, little information concerning the effects ofthe redistribution of gas and liquid phases in thewellbore has been presented.The phenomenon of wellbore phase redistributionoccurs in a well which is shut in with gas and liquidflowing simultaneously in the tubing. As shown byStegemier and Matthews, when such a well is shut inat the surface, gravity effects cause the liquid to falland the gas to rise to the surface. Because of therelative incompressibility of the liquid and theinability of the gas to expand in a closed system, thisredistribution of phases causes a net increase in thewellbore pressure. When this phenomenon occurs ina pressure buildup test, the increased pressure in thewellbore is relieved through the formation, andequilibrium between the wellbore and the adjacentformation will be attained eventually. However, atearly times the pressure may increase above theformation pressure, causing an anomalous hump inthe buildup pressure which cannot be analyzed withconventional techniques. In less severe cases, thewellbore pressure may not rise sufficiently to attain amaximum buildup pressure.General analyses of wellbore phase redistributionhave been presented by Stegemeier and Matthewsand by Pitzer et al. Both of these investigationsdocumented the association of the pressure builduphump with phase redistribution and indicated thatthe size of the hump was correlated with the amountof gas flowing in the tubing. Stegemeier andMatthews also noted an apparent correlation betweenestimated gas rise velocity and the time at which thehump occurred.Earlougher also noted (on the basis of the shapeof the log Deltap vs. log Deltat plot of buildup testdata) that phase redistribution seems to be related tothe problem of wellbore storage. Other authors haverecognized the significance of wellbore phaseredistribution; however, no complete analysis of thephenomenon has been presented and general phenomenon has been presented and general methods for analyzing buildup data influenced byphase redistribution in the wellbore have not been phase redistribution in the wellbore have not been available. SPEJ P. 259