The Pressure Derivative RevisitedImproved Formulations and Applications
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AbstractThe proposed work provides a new definition of the pressure-derivative function [i.e., the -derivative function, pd(t)], which is defined as: pd(t)=dln(p)dln(t)=1ptdpdt=pd(t)p(pd(t) is the "Bourdet" well testing derivative)This formulation is based on the "power-law" concept (i.e., the derivative of the logarithm of pressure drop with respect to the logarithm of time) this is not a trivial definition, but rather a definition that provides a unique characterization of "power-law" flow regimes.The "power-law" flow regimes uniquely defined by the pd(t) function are: [i.e., a constant pd(t) behavior] Casepd(t) Wellbore storage domination:1 Reservoir boundaries: Closed reservoir (circle, rectangle, etc.).1 2-Parallel faults (large time).1/2 3-Perpendicular faults (large time).1/2 Fractured wells: Infinite conductivity vertical fracture.1/2 Finite conductivity vertical fracture.1/4 Horizontal wells: Formation linear flow.1/2In addition, the pd(t) function provides unique characteristic responses for cases of dual porosity (naturally-fractured) reservoirs.The pd(t) function represents a new application of the traditional pressure derivative function, the "power-law" differentia-tion method (i.e., computing the d ln(p)/d ln(t) derivative) pro-vides an accurate and consistent mechanism for computing the primary pressure derivative (i.e., the Cartesian derivative, dp/dt) as well as the "Bourdet" well testing derivative [i.e., the "semilog" derivative, pd(t)=dp/d ln(t)]. The Cartesian and semilog derivatives can be extracted directly from the power-law derivative (and vice-versa) using the definition given above.ObjectivesThe following objectives are proposed for this work:
