Transient fluid motions in a simplified model for oilfield plug cementing

Transient motions are considered in closed inclined slot filled with two mi scible Bingham fluids of differing densities. This situation forms a simple model for buoyant flows found in the oilfield process of plug cementing. A minimisation method is used to compute the volume flux in each phase, to s atisfy the constraint of zero net-flow. Interface propagation is then studi ed via numerical solution of a hyperbolic conservation law, for which a thi rd-order compact finite difference method is used. Shocks are found to form for all nontrivial solutions. There are typically two shocks, moving both up and down the inclined slot, stretching the interface between them. The p arametric variation of shock propagation speed with the fluid yield stresse s and plastic viscosities is studied. Finally, the fully transient problem is analysed qualitatively. It is shown that for sufficiently large yield st resses, for which the steady axial flow has only trivial solutions, the vel ocity of the fully transient problem decays to aero in a finite time. The d ecay timescale is controlled by the magnitudes of the yield stresses and pl astic viscosities. (C) 1999 Elsevier Science Ltd. All rights reserved.