Petroleum Reservoir Simulation

A technique is presented to improve the treatment of wells in reservoir simulators by the use of an orthogonal curvilinear grid (cylindrical or elliptical) in well regions and a rectangular grid elsewhere in the reservoir. Special methods are developed to handle irregular blocks connecting the two types of regions. The nonlinear equations for the two regions are solved with different levels of implicitness; the simultaneous solution (implicit) method is applied to the well regions, while an implicit pressure, explicit saturation (IMPES) technique is used for the reservoir region. An efficient approach, requiring no outer iterations, between well and reservoir regions is used to couple different regions. The scheme is validated by the simulation of the flow of a slightly compressible fluid in a square domain with one boundary open to flow. For this case, the numerical solution with the hybrid grid approach matches the analytical solution exactly. A computer model based on the approach was developed for simulating two-phase flow in multiwell horizontal reservoirs. We show that the proposed technique provides much better prediction of the phase split in the producers than the conventional approach.

Use of a Hybrid Grid in Reservoir Simulation

\n We present a study of the low–salinity effect during oil recovery using microfluidics experiments in an attempt to narrow the gap between pore–scale observations and porous–media–flow mechanisms, and to explain one type of low–salinity effect with delayed oil recovery and without the presence of clay. A microfluidic toolbox is used, including single–pore–scale microchannels, a pore–network–scale (approximately 102 pores) micromodel, and a reservoir–on–a–chip model (approximately 104 pores with heterogeneity), all with 2D connectivity. Experiments at the single–pore scale reveal a time–dependent oil dewetting and swelling behavior when a crude–oil droplet is in contact with low–salinity water. An interplay between water chemical potential and oil–phase polar compounds explains this pore–scale observation well. Experiments at the pore–network scale illustrate that the dewetting and swelling of residual oil in the swept region increase the water–flow resistance, modifying the flow field and thus redirecting the flooding liquid into unswept regions. This pore–network–scale effect is re–expressed into a macroscale model as a sweep–efficiency improvement derived from the change of relative permeabilities, which requires time to develop. Finally, experiments on our “reservoir–on–a–chip” model show significant incremental oil recovery during tertiary low–salinity waterflooding and confirm that late–time sweep–efficiency improvement contributes to most of the incremental oil recovery. On the basis of this microfluidic framework, we emphasize the following three findings: Low–salinity tertiary waterflooding can improve oil recovery by an improvement of sweep efficiency, which is a consequence of residual–oil dewetting and swelling.The low–salinity effect can occur without the existence of clay.The wettability alteration and oil swelling are time–dependent processes and should be expressed as a function of oil/water contact time rather than dimensionless time [pore volume (PV)], which explains some observations from previous coreflood experiments.

Microfluidic Investigation of Low-Salinity Effects During Oil Recovery: A No-Clay and Time-Dependent Mechanism

Treatment of nonlinear terms in the numerical solution of partial differential equations for multiphase flow in porous media

Representing Wells in Numerical Reservoir Simulation: Part 1 - Theory

A reservoir simulation technique that employs semi- implicit approximations to relative permeabilities exhibits excellent stability and convergence characteristics when applied to water- or gas-coning problems. Recent workers in this area have made a simplifying assumption in order to linearize the flow terms of the semi-implicit finite- difference equations. A method is described of solving efficiently the nonlinear form of the equations and demonstrates that time-step sensitivity is reduced by iterating on the nonlinear terms. In addition, it addresses the problem of allocating a well's production among multiple grid blocks. Example problems include both water-coning and gas-percolation applications.

Tests of the Stability and Time-Step Sensitivity of Semi-Implicit Reservoir Stimulation Techniques

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Tests of the Stability and Time-Step Sensitivity of Semi-Implicit Reservoir Stimulation Techniques