Classical Riemann problem solutions for two-phase, multi-component flows in porous media are based on the assumption of constant flow rates. When the pressures at the inlet and outlet boundaries are constant, the flow rate will vary as a function of time, and hence, existing analytical solutions are no longer valid.
In this presentation, existing Riemann problem solutions for constant flow rates are generalized to constant pressure boundaries. This generalization is achieved through the determination of an analytical closed form solution for the flow rate and pressure distribution within the porous medium as a function of time.
The new analytical solution is valid for arbitrary flow geometries in the sense that the cross sectional area of the flow medium between injection boundary and producer boundary is arbitrary. In particular, it is shown that the flow velocity varies not only because of widening/narrowing of the flow channel, but also because the geometry has a nontrivial effect on the structure of the Riemann solution itself.
As examples on arbitrary flow geometries, the constant pressure boundary Riemann solutions for radial flow, spherical flow in addition to standard linear flow will be presented.
The new solutions have numerous applications to flow calculations between injectors and producers in oil reservoirs, for example as combined with streamline modeling with arbitrarily shaped stream tubes. Such applications will be discussed for water flooding and gas flooding of oil reservoirs.
Finally, the new analytical solutions will be compared to standard numerical approximations for the purpose of grid sensitivity analysis.