Development of the beta-pressure derivative

Abstract

The proposed work provides a new definition of the pressure derivative function [that is the β-derivative function, Δp βd(t)], which is defined as the derivative of the logarithm of pressure drop data with respect to the logarithm of time This formulation is based on the "power-law" concept. This is not a trivial definition, but rather a definition that provides a unique characterization of "power-law" flow regimes which are uniquely defined by the Δp βd(t) function [that is a constant Δp βd(t) behavior]. The Δp βd(t) function represents a new application of the traditional pressure derivative function, the "power-law" differentiation method (that is computing the dln(Δp)/dln(t) derivative) provides an accurate and consistent mechanism for computing the primary pressure derivative (that is the Cartesian derivative, dΔp/dt) as well as the "Bourdet" well testing derivative [that is the "semilog" derivative, Δpd(t)=dΔp/dln(t)]. The Cartesian and semilog derivatives can be extracted directly from the power-law derivative (and vice-versa) using the definition given above.