Numerical Simulation of Hysteretic Flow in Porous Media

Abstract

Thesis Approved:De~of the Graduate College ii PREFACE This dissertation is c<;>ncer:qed with the development of a nup,erical simulator for the three-dimensional flow of two immiscible, compressible :fluid phases in porous media, including the effects of gravity, capillarity, heterogeneity, and hysteresis in relative permeability and capillarity.The primary objective of the research project was the development of an evaluation-prediction tool for gas recovery from gas fields under active water drive, cyclic gas movement in aquifer gas storage and, in particular, to determine the quantity of residual gas remaining in an aquiferreservoir complex at abandonment.The secondary objective was the investigation of the qualitative and quantitative effects of rigorol.ls representation of hysteretic relative permeability and capillarity, on the numerically computed saturation and pressure distributions.A set of two, second-order, non-linear, parabolic partial differential equations governing two-phase, hysteretic flow were derived. An analogous system of difference equations were developed for numerical solution by an alternating direction implicit iterative method. Semiempirical r.elationships spanning the domain of relative permeability and capillarity data were derived from laboratory data and statistical-capillaric models of the porous media.iii Parametric ~ensitivity studies of the effects of relative permeability and capillarity on the numerical calculation of fluid saturation-pressure distributions were made by simulation of hypothetical systems representing typical prototype reservoirs.

Three-Dimensional, Randomized, Network Model For Two-Phase Flow Through Porous Media

“…After the imbibition is completed, the relative permeability curves are reversible; the second drainage curves retrace the imbibition curves. This agrees with some experimental results (Geffen et al, 1951;Sandberg et al, 1958;Land, 1971), but disagrees with others (Colonna et al, 1972;Evrenos and Comer, 1969). Evrenos and Comer (1969) suggest that the hysteresis behavior observed depends upon the design of the experiment.…”

Relative Permeability Correlation for Mixed-Wet Reservoirs

“…Many measurements have been made of these processes. 7,26,28,34 Hysteresis between secondary drainage and imbibition curves has also been recognized by several authors, 4,10,25,29,30,32 but there are few published data on relative permeability scanning curves. The most extensive set of such data is that of Braun and Holland, 4 who used a pseudosteady-state method.…”

“…4,10,25,29,30 Illustrations by Honarpour 31 and measurements by Eikje et al, 32 however, indicate the opposite behavior. To allow for both possibilities and the inverted S-shape curve, we introduce the tortuosity exponent m as a generalization of the Burdine 3 empirical tortuosity exponent of 2.0.…”

“…With all tortuosity exponents m equal to 2, as offered by Burdine, the Corey-type relative permeability expressions are strictly monotonic functions of saturation; they have no inflection points. Several researchers 4,7,10,25,[28][29][30] have ob- served, however, inverted S-shape oil relative permeability curves with an inflection point, especially for the bounding oil imbibition curve if oil is the nonwetting phase. There is almost no hysteresis in the wetting-phase properties.…”

Relative Permeability Correlation for Mixed-Wet Reservoirs

“…Most of the measurements indicate that the bounding oil drainage curve lies below the bounding oil imbibition curve 4,10,25,[29][30] . Illustrations by Honarpour 31 and measurements by Eikje, 32 however, indicate the opposite behavior.…”