Pore Network Modeling of Laboratory Experiments on Heterogeneous Carbonates
Authors: Kamath J. , Xu B. , Lee S.H. , Yortsos Y.C. 
Published: December 2007

Abstract
Many carbonate rocks have pore features that are large at the core plug scale. Laboratory assessment of recovery behavior in such carbonates can be unreliable. We review 3-d Computed Tomography (CT) images of the porosity distribution and of multi-rate waterfloods on a dolomite sample. These clearly show conventional analysis is inadequate, and we investigate use of large pore network models to improve our evaluation. Through parametric studies, we determine whether our large pore network models contain characteristics observed in the core floods. We then calibrate our models to laboratory inputs to improve quantitative interpretation. The model inputs are distributions of pore body and throat radii, throat length, coordination number, wettability and degree of local and spatial correlation. The laboratory inputs are porosity, permeability, thin section analyses, scanning electron microscopy images, mercury injection, and centrifuge capillary pressure. Finally we compare model predictions of miscible and water flood behavior to experimental data.

Introduction
Carbonate rocks often display heterogeneities significant at the core plug scale. Conventional analysis is likely to be inadequate, and it is not surprising that the literature contains few references to multiphase flow studies on such rocks. A review of studies on carbonate systems by Espie et al. shows a wide range of process efficiency. They find that the residual oil saturation to water flood varies from 28 to 80% oip and that to tertiary miscible flood varies from 0 to 50% oip.
Since the pioneering work of Fatt to simulate flow in porous media by a mesh of tubes, many such pore network models have been published. These models typically simulate 2-dimensional flow and have usually been of limited size. However, Lee et al. have recently implemented a 3-d half-million node model on massively parallel computers. This development, coupled with the increased application of 3-d flow visualization to laboratory corefloods, provided the impetus for the present work.

Laboratory Studies on Heterogeneous Carbonates
Archer and Wong found that conventional relative permeability calculation methods were inadequate for their experiments on a vugular, full diameter carbonate sample. Early water breakthrough had a strong effect on the relative permeability calculations, and the water relative permeability, krw, showed anomalous humps and plateaus.
Ehrlich measured drainage relative permeability for vugular, low-permeability samples from the Westerose reservoir. He used the steady state method and full diameter cores. These relative permeability curves also showed significant plateau regions.
MacAllister et al. performed steady-state, water-displacing-oil tests on a mixed-wet Baker dolomite sample (k =110 md, =22%) using pressure drops of 4 psi and 100 psi. Both krw and kro were significantly lower at 100 psi. In the 4 psi case, CT images showed that oil and water flow occurred through separate macroscopic regions. This resulted in high relative permeability to both phases. In the 100 psi case, the saturation was more uniformly distributed and the relative permeability values were lower.
Narayanan and Deans studied miscible xenon-helium displacement in a full diameter, vugular carbonate sample from Gulf-Connor Fenn-Big Valley, Canada. They concluded that centimeter-scale heterogeneities control flow distribution and that laboratory miscible flood behavior was dominated by convection.
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