Pore-Scale Characterization and PNM Simulations of Multiphase Flow in Carbonate Rocks

This paper deals with pore-scale two-phase flow simulations in carbonate rock using the pore network method (PNM). This method was used to determine the rock and flow properties of three different rock samples, such as porosity, capillary pressure, absolute permeabilities, and oil–water relative permeabilities. The pore network method was further used to determine the properties of rock matrices, such as pore size distribution, topological structure, aspect ratio, pore throat shape factor, connected porosity, total porosity, and absolute permeability. The predicted simulation for the network-connected porosity, total porosity, and absolute permeability agree well with those measured experimentally when the image resolution is appropriate to resolve the relevant pore and throat sizes. This paper also explores the effect of the wettability and fraction of oil-wet pores on relative permeabilities, both in uniform and mixed wet systems.

Study of Reservoir Properties of Turonian Formation Using Digital Core Analysis

The work demonstrates results of reservoir properties evaluation using a complex of laboratory and multiscale digital core or digital rock analysis. Rock properties (including relative phase permeabilities) were studied at different scales: from nanometers to meter (whole core). For the first time, cores from Turonian formation were characterized with digital rock analysis, which provided stationary relative permeabilities for gas-water under reservoir conditions. Lab determination of relative permeabilities was rather challenging for some low-permeability samples (<0.02 md), while digital analysis was successful even for them. Gas recovery in a depletion mode from different rock types was studied on a whole core model for different capillary pressures. Such studies are not conducted in the lab.

Experimental Study and History-Match of Near-Miscible WAG Coreflood Experiments on Mixed-Wet Carbonate Rocks

Water-alternating-gas (WAG) injection, both miscible and immiscible, is a widely used enhanced oil recovery method with over 80 field cases. Despite its prevalence, the numerical modeling of the physical processes involved remains poorly understood, and existing models often lack predictability. Part of the complexity stems from the component exchange between gas and oil and the hysteretic relative permeability effects. Thus, improving the reliability of numerical models requires the calibration of the equation of state (EOS) against phase behavior data from swelling/extraction and slim-tube tests, and the calibration of the three-phase relative permeability model against WAG coreflood experiments. This paper presents the results and interpretation of a complete set of two-phase and thee-phase displacement experiments on mixed-wet carbonate rocks. The three-phase WAG experiments were conducted on the same composite core at near-miscible reservoir condition; experiments differ in the injection order and length of their injection cycles. First, the two-phase water/oil and gas/oil displacement experiments and first cycles of WAG were used to estimate the two-phase relative permeabilities. Then, a synchronized history-matching procedure over the full set of WAG experiments and cycles was carried out to tune Larsen ans Skauge WAG hysteresis model—namely the Land gas traping parameter, the gas reduction exponent, the residual oil reduction factor and three-phase water relative permeability. The second part of this paper deals with the multiphase upscaling of microscopic displacement properties from plug to coarse grid reservoir scale. The two-phase relative permeability curves and three-phase WAG parameters were upscaled using a sector model to preserve the displacement process and reservoir performance. The result of the coreflood calibration indicate that the two-phase displacement and first cycles of WAG yield a consistent set of two-phase relative permeabilities. Including the full set of WAG experiments allowed a robust calibration of the hysteresis model.

Issue with Stone-II Three Phase Permeability Model, and A Novel Robust Fundamentals-Based Alternative to It

The objective of this paper is to present a fundamentals-based, consistent with observation, three-phase flow model that avoids the pitfalls of conventional models such as Stone-II or Baker's three-phase permeability models. While investigating the myth of residual oil saturation in SAGD with comparing model generated results against field data, Gupta et al. (2020) highlighted the difficulty in matching observed residual oil saturation in steamed reservoir with Stone-II and Baker's linear models. Though the use of Stone-II model is very popular for three-phase flow across the industry, one issue in the context of gravity drainage is how it appears to counter-intuitively limit the flow of oil when water is present near its irreducible saturation. The current work begins with describing the problem with existing combinatorial methods such as Stone-II, which in turn combine the water-oil, and gas-oil relative permeability curves to yield the oil relative permeability curve in presence of water and gas. Then starting with the fundamentals of laminar flow in capillaries and with successive analogical formulations, it develops expressions that directly yield the relative permeabilities for all three phases. In this it assumes a pore size distribution approximated by functions used earlier in the literature for deriving two-phase relative permeability curves. The outlined approach by-passes the need for having combinatorial functions such as prescribed by Stone or Baker. The model so developed is simple to use, and it avoids the unnatural phenomenon or discrepancy due to a mathematical artefact described in the context of Stone-II above. The model also explains why in the past some researchers have found relative permeability to be a function of temperature. The new model is also amenable to be determined experimentally, instead of being based on an assumed pore-size distribution. In that context it serves as a set of skeletal functions of known dependencies on various saturations, leaving constants to be determined experimentally. The novelty of the work is in development of a three-phase relative permeability model that is based on fundamentals of flow in fine channels and which explains the observed results in the context of flow in porous media better. The significance of the work includes, aside from predicting results more in line with expectations and an explanation of temperature dependent relative permeabilities of oil, a more reliable time dependent residual oleic-phase saturation in the context of gravity-based oil recovery methods.

PERMEABILITY MODELS FOR TWO-PHASE FLOW IN FRACTAL POROUS-FRACTURE MEDIA WITH THE TRANSFER OF FLUIDS FROM POROUS MATRIX TO FRACTURE

Study of transport mechanism of two-phase flow through porous-fracture media is of considerable importance to deeply understand geologic behaviors. In this work, to consider the transfer of fluids, the analytical models of dimensionless relative permeabilities for the wetting and non-wetting phases flow are proposed based on the fractal geometry theory for porous media. The proposed models are expressed as functions of micro-structural parameters of the porous matrix and fracture, such as the fractal dimension ([Formula: see text] for pore area, the fractal dimensions [Formula: see text] for wetting phase and for non-wetting phase, porosity ([Formula: see text], the total saturations ([Formula: see text], the porous matrix saturation ([Formula: see text] of the wetting and non-wetting phases, fractal dimension ([Formula: see text] for tortuosity of tortuous capillaries, as well as the ratio ([Formula: see text] of the maximum pore size in porous matrix to fracture aperture. The ratio ([Formula: see text] has a significant impact on the relative permeabilities and total saturations of wetting phases. The results reveal that the flow contribution of wetting phase from the porous matrix to both the seepage behavior of the fracture and total wetting phase saturation can be neglected as [Formula: see text]. The models may shed light on the fundamental mechanisms of the wetting and non-wetting phase flow in porous-fracture media with fluid transfer.

Porous Flow with Diffuse Interfaces

This chapter presents a model developed by the author, in publications dated from 2002 to 2016, on flow in porous media assuming diffuse interfaces. It contains five sections. Section 1 is an Introduction, tracing the origin of the diffuse interface formalism. Section 1 also presents the traditional compositional model, pointing out its emphasis on phases and questioning the concept of relative permeabilities. Section 2 presents the mass, momentum, and energy balance equations, for a multicomponent continuous fluid, in their most general form, at the pore level. The existence of constitutive equations with phase-inducing terms is mentioned, but the equations are not introduced at this level, and phases are not an explicit concern. Section 3 is about the averaging of the pore level equations inside a region containing many pores. There is no explicit mention of phases and therefore not of relative permeabilities. Section 4 is the technical basis from which the constitutive equations of the model arise, and it is shown that many models can exist. Section 5 introduces constitutive equations and presents a minimal model for multicomponent, multiphase, and thermal flow in neutrally wetting porous media, i.e., a model with a minimal amount of phenomenological parameters.