Hosseinpour-Zoonozi, Nima (2006-12). Development of the beta-pressure derivative. Master's Thesis.
The proposed work provides a new definition of the pressure derivative function [that is the ????-derivative
function, ????p ????d(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 ????p ????d(t) function [that is a constant ????p ????d(t) behavior].
The ????p ????d(t) function represents a new application of the traditional pressure derivative function, the
"power-law" differentiation method (that is computing the dln(????p)/dln(t) derivative) provides an accurate
and consistent mechanism for computing the primary pressure derivative (that is the Cartesian derivative,
d????p/dt) as well as the "Bourdet" well testing derivative [that is the "semilog" derivative,
????pd(t)=d????p/dln(t)]. The Cartesian and semilog derivatives can be extracted directly from the power-law
derivative (and vice-versa) using the definition given above.