A Mathematical Model for the Solvent Leaching of Tar Sand
- M. Oguztoreli (U. of Alberta) | S.M. Farouq Ali (U. of Alberta)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- November 1986
- Document Type
- Journal Paper
- 545 - 555
- 1986. Society of Petroleum Engineers
- 4.1.2 Separation and Treating, 2.4.3 Sand/Solids Control, 5.1 Reservoir Characterisation, 5.4.6 Thermal Methods, 5.8.5 Oil Sand, Oil Shale, Bitumen, 4.3.4 Scale, 1.2.3 Rock properties, 5.2.1 Phase Behavior and PVT Measurements, 5.4.7 Chemical Flooding Methods (e.g., Polymer, Solvent, Nitrogen, Immiscible CO2, Surfactant, Vapex)
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Solvent flooding is the basis for a wide range of EOR methods and has been shown to be a possible method of creating initial steam injectivity in tar sands. This paper presents a unique model of the dissolution of a semisolid bitumen, resulting from the injection of a solvent. The solution of the mathematical equations describing this phenomenon is discussed. Results, including phenomenon is discussed. Results, including a series of two-dimensional (2D) problems, are presented. Numerical aspects are addressed. presented. Numerical aspects are addressed. The mathematical treatment is based on a pore model that contains bitumen particles dissolving pore model that contains bitumen particles dissolving in an interstitial solution. Macroscopic transport mechanisms, based on the microscopic phenomenon, trace the course of diffusing species in a dynamically interactive solid/liquid network. The bitumen particles are given a spherical symmetry such particles are given a spherical symmetry such that a radial dissolution integro-differential equation accounts for the volume changes from solvent transfer into an initially immobile bitumen. An overall numerical approach to the nonlinear system of equations determines the state vector of pressure, saturation, and concentration of the leaching solution. We show that three dimensionless groups control the bitumen-leaching process. The Damkohler and solvent capacity numbers govern the dissolution process, while the Peclet number governs miscible displacement.
The solution process of polymer/solvent systems has been investigated thoroughly. Current literature for transport problems with adsorption phenomena in porous media assumes a small porosity change in the reaction zone, limited to solution mining of minerals. Diffusion in spheres with constant radii and linear moving-boundary problems have also been studied in great detail. We relate porosity change to the dissolution of bitumen porosity change to the dissolution of bitumen spheres subject to solvent adsorption. Mathematically, a radial, spherical moving-boundary problem determines the instantaneous radii on the basis of an average local size distribution for a given-number density in the porous medium. The average radius of the spherical dissolution front provides the necessary information to determine the liquid pore space over the duration of the entire dissolution pore space over the duration of the entire dissolution history. The convective-diffusion transport phenomenon describes the miscible displacement of constituent species in the fluid phase. Numerical solutions to the 2D problem pose difficulties at high Peclet numbers caused by large convective truncation errors. These errors arise from large concentration gradients at the initial solvent/oil discontinuity. In the combined miscible displacement and dissolution problem, these numerical difficulties are reduced problem, these numerical difficulties are reduced by assuming that solvent instantaneously invades the medium to give a uniform initial solvent distribution. The oil/solvent discontinuity is implicit in the dissolution equation, and dissolution kinetics are governed by the Damkohler number. In this manner, concentration gradients remain small at the expense of a time-dependent saturation.
The mathematical treatment for the solvent leaching of tar sands on the macroscopic scale is based on the following assumptions that pertain mainly to the microscopic phenomenon at the pore-size scale.
1. The initial viscosity of the bitumen is large enough that it can be treated as virtually immobile or semisolid. Semisolid implies that upon sufficient dilution, the tar can gain the necessary mobility to flow under the imposed injection pressures. In contrast, the solid sand grains constitute a firm rock matrix. Mobility is gained by the differential phase change to be described in the dissolution model. 2. An initial liquid continuity is established throughout the porous medium by the rapid displacement of the connate water by the injected solvent. The inert rock matrix provides the pore space for both liquid and semisolid phaseseach with distinct solvent/bitumen compositionsto coexist over the entire porous region. The initial conditions investigate the semisolid phase as bitumen and void of any solvent, while the liquid phase is purely a solvent with an initial nonzero invasion purely a solvent with an initial nonzero invasion saturation, So. 3. The liquid phase consists of an incompressible flowing fluid in which constituent species propagate by both convective and diffusive transport mechanisms. The immobile semisolid is composed of a discrete set of smooth particles confined to the pores of the matrix rock. Constituent semisolid species propagate by diffusion only. The liquid phase propagate by diffusion only. The liquid phase completely wets all semisolid particles to provide the maximum surface area for interphase mass transfer.
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