... permeability and capillary pressure, together with the continuity equation and Darcy's law, the displacement can be described mathematically. For the simple case of a stable, vertical, downward diplacement of oil by gas ( Fig. 1 ), we end up with a single equation: enhanced recovery breakthrough...

... for the individual components present in the compressible miscible flow system present in the compressible miscible flow system are assumed. These flow equations together with the individual component continuity equations are used to arrive at the pressure equation. Crank-Nicolson and backward-in-time approximation...

... extensive, uniform, flat-lying units. It may readily be adapted treat the compaction of sands. The principal elements of the model are: (1) continuity equations for the water and solid matrix; (2) Darcy's law; (3) an expression for the fluid potential; (4) an equation for the total vertical stress; (5...

... width decreases along the fracture according to a simple formula that contains the fracture length. In the derivation of this formula, fluid loss and fracture volume change are neglected in the continuity equation and the fracture length is not determined. In a subsequent application, a "reasonable...

... by giving fixed values to NN + NNCE of these variables and solving for the necessary values of the remaining NN variables such that the node continuity equations residuals (F) equal zero. The list of NN unknown variables is given the name S. NEWTON-RAPHSON SOLUTION WITH SPARSE MATRIX CONSIDERATIONS The n...

... of the physical dispersion in the solution. In a one-dimensional system, the technique involves an addition of a negative dispersion term to the continuity equation. The negative dispersion term, which is called the numerical dispersion coefficient, depends upon the flow velocity, the time-step size and the block...

... reservoirs, these computations still can be carried out satisfactorily, provided small irregularities in the physical properties of the rock are distributed in a random fashion. The flow equations are derived as solutions of the continuity equation, and their solutions are dependent upon the assumption...