A Novel Bounded Capillary Pressure Correlation with Application to Both Mixed and Strongly Wetted Porous Media
Authors: Andersen Pål Østebø , Skjæveland Svein Magne , Standnes Dag Chun 
Published: November 2017

Abstract
Capillary pressure curves are one of the main input parameters in reservoir simulation: They are used to characterize the initial fluid distribution in the reservoir and control the recovery potential by spontaneous imbibition in naturally fractured reservoirs. To effectively incorporate experimental capillary pressure data into mathematical models it is useful to implement correlations rather than lookup tables. This also allows variations in lithology, wettability etc. to be systematically varied by changing correlation parameters rather than interpolating between numerous tables. It is then essential that the correlation features the main experimentally observed characteristics such as monotonicity, plateaus and slopes and can be tuned to fit experimental values. Many correlations have been presented in the literature, mainly for strongly wetted media, but also for mixed-wet media, such as the Skjæveland correlation and the LET correlation. The majority of existing correlations consider an infinite capillary pressure at the residual saturation, but practically all capillary pressures are measured at finite values. Further, infinite capillary pressures are not readily incorporated by reservoir simulators which require either finite values in table form or must apply regularization techniques to treat the infinite values.
We present a novel correlation that can model both strongly and mixed wetted media. Unlike most correlations it is bounded, which is a benefit for implementation into tables, as normally applied by reservoir simulators, or directly fitting experimental data. The correlation applies normalized saturations and includes 3 terms with a total of 7 parameters which have high impact in the low, central and high saturation range, respectively. The involved parameters include: a) The end point capillary pressures located at the residual saturations. For a primary drainage curve this includes the threshold pressure. b) Two terms (with 2 parameters each) are related to the slopes near the residual saturations. For mixed-wet media this is highly useful to capture the inverted S-shape and the rate at which the curves approach high magnitudes. For strongly wetted media one term can be omitted. c) Finally, a parameter indicative of the capillary pressure at intermediate saturations is included.
The correlation (in reduced form) has been applied in previous works to produce synthetical simulation input. The goal of this work is to verify that the correlation can consistently model experimental data. We match measurements including drainage and imbibition tests from strongly and mixed wetted media. The proposed correlation with its intuitive form is easy to interpret and adjust to experimental data and is thus a good candidate when converting capillary pressure measurements into continuous data for modelling in a simulator. It performed equally well or better than the established LET and Skjæveland et al. correlations regarding data matching.