A one-dimensional, compositional, chemical-flood simulator was developed to calculate oil recovery as a function of several major process variables. The principal relationships included are phase behavior and interfacial tensions as a function of electrolyte and surfactant concentrations, and polymer viscosity as a function of electrolyte and polymer viscosity as a function of electrolyte and polymer concentration. Emphasis was on studying the polymer concentration. Emphasis was on studying the process itself, especially complex interactions that process itself, especially complex interactions that occur because of two- and three-phase behavior, interfacial tension, fractional flow, dispersion, adsorption, cation exchange, chemical slug size, and polymer transport.
Nelson and Pope reported laboratory flow results in which phase behavior plays a key role in oil recovery by chemical flooding. They show that many characteristics of chemical floods can be explained by considering the equilibrium mixing and transport of surfactant/brine/oil systems in light of phase behavior observed in external mixtures. phase behavior observed in external mixtures. Although based on highly idealized representations of the key properties involved, we believe that the simulator described here can yield significant insight into phase-related process mechanisms, such as "oil swelling," the interactions among process variables, and the relative merit of various process variables, and the relative merit of various chemical flooding strategies.
The framework for systematically improving the compositional aspects of numerical simulation of chemical flooding is evident with our approach. This is because a completely compositional model based on total concentrations, rather than saturations, is assumed from the start. Then, the calculation of phase concentrations, and from them phase saturations, for any desired number of phase saturations, for any desired number of components and phases with any type phase behavior is a relatively simple matter. Conceptually, mathematically, and numerically, this approach is simpler and easier to use than the traditional approach used in reservoir engineering simulation, although in principle they can be made equivalent.
The cases illustrated here are for up to six components and up to three phases, using highly simplified representations of the binodal and distribution curves for the surfactant/brine/oil systems and the properties of the various phases that form. Even so, as many as 64 parameters are required to specify the process.
The basic assumptions of the model are as follow.
The system is one-dimensional and homogeneous in permeability and porosity.
Local thermodynamic equilibrium exists everywhere.
The total mixture volume does not change when mixing individual components (delta VM = 0).
Gravity and capillary pressure are negligible.
Fluid properties are a function of composition only.
Darcy's law applies.
Physical dispersion can be approximated adequately with numerical dispersion by selecting the appropriate grid size and time step.
Additional assumptions are required to model various properties such as interfacial tension, viscosity, etc. However, for the most part, these are changed readily by the user and are not considered as basic as the above assumptions, which also can be relaxed, but only with considerably more effort. The auxiliary assumptions will be given, therefore, with the specific examples discussed below.
Given the above assumptions, the continuity equations for each component i and np phases are