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Summary

This is one of three companion papers describing a micellar/polymer or chemical flood simulator and comparing it to experimental data. A three-dimensional version of this simulator has been developed, but in this paper we describe only the one-dimensional (1D) flow equations because we focus on comparisons with linear coreflood data and related physical properties. All physical property models are the same in both versions, however. The property models described in this paper are (1) inaccessible PV, (2) permeability reduction, (3) polymer-phase viscosity, (4) adsorption, (5) residual phase saturations as a function of capillary number, and (6) relative permeabilities.

Flow Equation and Solution Technique

The general equations for describing isothermal. multiphase, multicomponent fluid flow in permeable media were presented by Laket al. For a 1D geometry , the continuity equation reduces to Eq. 1.

(1)

Eq. 1 is solved numerically by forward differencing in time, t. The convective term is solved by backward differencing and the dispersive term by three-point central differencing with upstream weighting (see the Appendix).

Boundary Conditions

Fractional flows and phase concentrations are specified at an imaginary injector block located upstream of x =0. These are held constant over fixed time periods and can be changed in a stepwise manner to simulate slug injections. The most common situation is the injection of a single-phase chemical slug followed by a singlephase polymer drive.

The concentrations at an imaginary producer block located downstream of x = 1 are calculated from Eq. 2.

(2)

In solving Eq. 1, the dispersive term at the last block (x = 1) is zero.

Physical Property Relationships Physical Property Relationships Mathematical modeling of the physical properties and phenomena that occur in micellar/polymer processes is a requirement for compositional simulators. The process properties discussed in this paper include: polymer inaccessible PV, permeability reduction, polymer-phase viscosity, adsorption, residual saturations, and relative polymer-phase viscosity, adsorption, residual saturations, and relative permeabilities. Other important process properties, which include a permeabilities. Other important process properties, which include a new phase behavior concept, saturation-dependent dispersivities, interfacial tensions (IFT's), cation exchange, and microemulsion-phase viscosities are discussed in two companion papers.

Inaccessible PV. It has been observed experimentally that for flow in porous media, polymer molecules usually flow faster than the solvent or smaller noninteracting components, such as chloride, in the solution. This effect can be explained by assuming that the area of flow for the polymer is smaller than that for the solvent, hence the name "inaccessible PV."

In general, the inaccessible PV phenomenon strongly depends on the characteristics of the porous medium, especially its permeability. It also depends on the polymer and electrolyte type, permeability. It also depends on the polymer and electrolyte type, concentrations, saturations, temperature, and velocity. Lower permeabilities cause larger inaccessible PV. Other factors such as polymer permeabilities cause larger inaccessible PV. Other factors such as polymer gels, trapped phases, surfactant/polymer interactions, and emulsions may be significant and sometimes may completely dominate. Dawson and Lantz observed that as much as 30% of the PV may be inaccessible to polymer. This effect can be accounted for by reducing the porosity for the polymer in the component mass-balance equation. Such observations, though modeled as if the polymer is inaccessible to a fraction of the pore, do not imply that the polymer actually by-passes certain pore spaces, but rather that the polymer velocity is larger than for a reference tracer. Although several studies have been done, the detailed mechanisms involved are not completely understood. It should be pointed out, however, that whatever the microscopic cause is, any practical model must involve a finite averaging that would be equivalent to the inaccessible PV concept. It seems likely that the effect is caused mostly by pore-wall exclusion of the polymer molecule relative to the very small molecules, such as water, that make up the polymer solvent. It could also be caused by rheological properties. The shear rate is considerably different in different parts of a given pore and also from pore to pore. Another cause can be the amount and type of retention. An adsorbed polymer coil effectively excludes a certain volume of the pore to further penetration by a mobile polymer coil. Whatever the cause, a porosity correction factor is used to model the lumped effect.