## LSU Historical Dissertations and Theses

1993

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

Robert Desbrandes

#### Abstract

A pressure profile obtained from the formation tester defines the wettability, free water level, and hydrocarbon and water densities as well as the capillary pressure above the free water level. Correlating the pressure values to the water saturation values determined from the resistivity logs results in a capillary pressure/water saturation, $\rm P\sb{c}(S\sb{w}),$ curve characteristic of the reservoir. A relative permeability curve then can then be derived from this $\rm P\sb{c}(S\sb{w})$ curve using empirical relationships. This approach was tested in the laboratory using an eight-foot vertical sandstone core to simulate the formation. The core was fitted with electrode arrays, and resistivity measurements were used to construct the water saturation profile. The capillary pressure values were calculated from both the densities and the height above the free water level values. The free water level was indicated by a tube connected to the core setup. Chapter III documents the laboratory details of this experimental work together with its results and conclusions. A technique that can be used to extrapolate existing core data to cases where such data is absent or not representative of in-situ conditions is of interest. Chapter IV of this dissertation documents a new approach that has been developed and is based on using log data to derive a water saturation versus depth profile in the transition zone of the formation of interest. The log derived water saturation distribution is then correlated to generalized capillary pressure curves typical of the formation studied. This curve matching yields, by comparison, a capillary pressure curve specific to the formation of interest. The capillary pressure type curves are generated from already available core data and other petrophysical information. Relative permeability curves are subsequently generated using correlations based on Purcell's model. The technique is successfully applied to several field examples. Special attention is given to cases of tight sands where relative permeability measurements on core samples are very complex, time consuming, and inaccurate due to the very small pore space available to the fluid to move through the tight sand cores. In Chapter V, the above mentioned technique is extended to tight sand cases where a special relationships characteristic of tight sands are developed and mathematically manipulated to adapt already existing relative permeability equations.

153

COinS