Steady-State and Unsteady-State Flow of Non~Newtonian Fluids Through Porous Media

Non-Newtonian fluids may be injected into a reservoir during secondary recovery operations. The non-Newtonian fluid used in this work is a power-law type of fluid; that is, the viscosity of the fluid decreases as the flow rate or rate of shear increases. Equations are presented for steady-state linear and radial flow of such fluids, transient behavior results from a finite difference model of a radial system, and transient behavior results from a field test. The equations that describe the flow of a non-Newtonian fluid are non-linear and are solved numerically. Finite difference solutions are presented as curves of dimensionless pressure drop at the well bore vs. dimensionless time for a constant injection rate. Solutions were obtained for 5%, 10%, and 100% PV of a non-Newtonian fluid for injection rates of 1, 10, 100, and 1,000 cc/sec and for a 5% PV of non-Newtonian fluid located at r = rDwU, 3, 10, 20, 50, and 100 ft for a flow rate of 1 cc/sec. The buildup curves do not exhibit a straight-line portion as is the case for Newtonian flow through porous media. Correlations also are shown for the productivity index vs. rate for the computer model study and the fieldmore » tests.« less