Hydraulically-fractured vertical and horizontal wells completed in the tight formations typically exhibit long periods of transient linear flow that may last many years or decades.From this transient linear flow period,the linear flow parameter(xf k)may be extracted.However,changes in effective permeability to the oil phase during production,caused by wellbore pressure falling below the saturation pressure, affect the flow dynamics in tight oil reservoirs and complicate the analysis.The use of methods that assume single-phase flow properties,such as the square-root of time plot,can lead to significant errors in linear flow parameter estimates. In this study,an analytical method is introduced to mathematically correct the slope of the square- root-of-time plot for the effects of multi-phase flow through the use of modified pseudovariables. Although the correction was derived for wells producing at constant flowing pressure during transient linear flow,the method is extended for wells producing at variable rate/flowing pressures.In order to evaluate pseudovariables used in the correction,the saturation-pressure relationship must be known.In this work,an analytical method for evaluating the saturation-pressure relationship is also developed. The results of our new analytical method for linear flow analysis are validated against numerical simulation.The new method yields linear flow parameter estimates that are within 10%of those input into the numerical simulator.
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