Brent Lindquist

The bifurcation of tracked scalar waves

The dynamic evolution of tracked waves by a front-tracking algorithm may lead on either numerical or physical grounds to intersections of the waves. The correct resolution of these intersections is described locally by the solution of Riemann problems and requires a bifurcation of the topology defined by the tracked waves. An algorithm is described which is appropriate for the resolution of scalar tracked waves, such as material discontinuities, contact dicontinuities in gas dynamics, or constituent concetration waves including oil-water banks in oil reservoirs Even here the algorithm is not fully general, and the resolution of the intersections of an arbitrary set of curves in the plane for the above range of physical problems remains unsolved. However with the assumption that the set of intersections to be resolved is a small perturbation (resulting for example from a small time step in an evolution) of a valid, non-intersecting front, the algorithm seems to be general. In any case examples will be presented that show that complicated interfaces can be generated automatically from simple ones through successive bifurcations. 15 refs., 9 figs.

Polymer floods: a case study of nonlinear wave analysis and of instability control in tertiary oil recovery

Polymer flooding in oil reservoir simulation is considered in two space dimensions. The wave structures associated with such a process give rise to interesting phenomena in the nonlinear regime which have direct bearing on the efficiency of oil recovery. These waves influence and can prevent surface instabilities of the fingering mode. In this paper we resolve these waves by a front tracking method. We consider the fingering problem and the issue of oil recovery for the polymer flood. The details of these two phenomena depend on the separation between the waves and upon the viscosity contrast between the oil, water and polymer. We identify a nonlinear transfer of instability between adjacent waves and a nonlinear enhancement of recovery due to successive waves. The conclusions produced by this work are also pertinent to tracer flooding.One interesting conclusion applies to polymer injection followed by pure water injection. In this case the instability is transferred to the polymer-water interface, and th...

Front Tracking for Petroleum Reservoir Simulation

The front tracking method gives high quality solutions for problems with important discontinuities. The method has been applied to several model problems in reservoir simulation. Results are given for quarter 5-spot studies in an areal reservoir and the water coning problem in a vertical cylindrical section surrounding a production well. Both problems were treated as incompressible flow in the absence of capillary pressure. We have studied miscible and immiscible displacement for frontal mobility ratios of 1 and 5. Validation studies include mesh refinement, grid orientation and orthogonal coordinate changes.

Front Tracking and The Interaction of Nonlinear Hyperbolic Waves

Front tracking is a numerical method which offers high resolution for the computation of solutions containing important discontinuities, which we refer to as fronts. In this method, the discontinuities are treated as additional degrees of freedom, and points along them are propagated as Lagrangian or characteristic particles. The computational degrees of freedom thus consist of state variables specified at fixed locations on a regular grid, which represent the smooth variation of the solution away from fronts, a moving system of surfaces (curves in two dimensions) to represent the fronts, together with double-valued state variables specified along each urface to represent the discontinuous solution values.

Front Tracking, Oil Reservoirs, Engineering Scale Problems and Mass Conservation

A critical analysis is given of the mechanisms for mass conservation loss for the front tracking algorithm of the authors and co-workers in the context of two phase incompressible flow in porous media. We describe the resolution to some of the non-conservative aspects of the method, and suggest methods for dealing with the remainder.