Fundamentals of Fluid Flow in Porous Media
The Equation of Continuity in Porous Media: Solutions to the One-Dimensional Convection-Dispersion Model
Scaling Capacitance Model Parameters to the Field
In improved oil recovery by miscible displacement, a large dispersion coefficient and the presence of capacitance increase the length of the mixing zone, thereby contributing to slug degradation and low oil recovery efficiency. While the capacitance model has been used to gain a better understanding of mass transport processes in miscible displacements, it is not altogether clear how parameters determined in the laboratory should be scaled to the field. It has been suggested that the capacitance model simply provides a convenient mathematical tool which allows improved estimates of dispersion coefficients from laboratory experiments by correcting for laboratory restrictions. Scaling of the model parameters to field conditions is not straightforward (Coats and Smith, 1964; Stalkup, 1970; Brigham, 1974; Baker, 1977; Shuler, 1978; Bretz et al., 1986; Bretz and Orr, 1987).
Mixing due to capacitance depends on the Stanton number, St = KL / v. On the field scale, L is very much larger and v is frequently smaller than in the laboratory. Mass transfer is thus instantaneous on the field scale, and the effects of capacitance observed in the laboratory are reduced or absent in the field. However, it is still necessary to take into account capacitance when modeling a laboratory displacement in order to determine the proper dispersion coefficient to use in field calculations. The length of a mixing zone in a laboratory core with capacitance depends both on dispersion and on mass transfer into the stagnant volume. If both mixing effects are lumped into the dispersion coefficient, the magnitude of the dispersion coefficient, and therefore the length of the mixing zone and the slug size required in the field, can be grossly overestimated. Capacitance may thus not be important in the field, but is important in obtaining meaningful parameters from laboratory experiments. The choice of boundary conditions for the capacitance model is also important if parameters are to be scaled to the field (Brigham, 1974).