Transient fluid motions in a simplified model for oilfield plug cementing

Transient motions are considered in closed inclined slot filled with two miscible 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 satisfy the constraint of zero net-flow. Interface propagation is then studied via numerical solution of a hyperbolic conservation law, for which a third-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 parametric variation of shock propagation speed with the fluid yield stresses and plastic viscosities is studied. Finally, the fully transient problem is analysed qualitatively. It is shown that for sufficiently large yield stresses, for which the steady axial flow has only trivial solutions, the velocity of the fully transient problem decays to zero in a finite time. The decay timescale is controlled by the magnitudes of the yield stresses and plastic viscosities.