Helical Boundary Conditions To Capture Interpattern Flow in In-Situ-Upgrading-Process Pattern Simulations
Authors: Vink Jeroen C. , Gao Guohua , Ginestra Jean-Charles C. 
Published: October 2015

Summary
The in-situ upgrading process (IUP) involves very complicated multiphase thermal transport and chemical reactions. Numerical simulation of IUP is computationally expensive, and direct simulation of field-scale IUP models becomes prohibitive. A practical way is to simulate a sector model under proper boundary and initial conditions and then upscale the simulation results to the full field scale with superposition techniques. Because of nonsymmetric pattern configuration and time delay of developing patterns sequentially, interpattern flow may become significant, and its impact on the simulation results cannot be neglected. Therefore, no-flow boundary conditions become inappropriate for such IUP sector models.
In this paper, we proposed a new type of “helical” boundary conditions (HBCs) in which pressures and temperatures are periodic in space, except for a shift in time. The HBCs are specifically designed for a field-scale IUP development in which patterns are developed sequentially in time, along a long strip. In such a development, each pattern has exactly the same well configuration and operational schedule, except for a time delay. Because of high viscosity of heavy oil and low heat conductivity of formation rock, the impact of field boundary conditions on interpattern flow will be dampened quickly within only a few patterns, and a repetitive “pseudosteady state” of interpattern flow develops, in which the energy and mass fluxes from the previous pattern to the current pattern are the same as those from the current pattern to the next pattern, except for the delay time. By use of a 1D heat-transfer model, we analytically demonstrate that the pseudosteady state and therefore the HBCs hold for a long strip of patterns. A practical procedure to implement these HBCs in numerical simulation is developed, in which the state variables (pressure, temperature, and fluid composition) are iteratively updated in gridblocks on both edges of a sector model that is composed of two patterns. This iterative approach to impose HBCs was implemented in our in-house simulator.
This approach was tested and validated by simulation results of an IUP model that is composed of 59 patterns. Our results show that the full-field boundary conditions only affect the production-rate profiles of the first and the last patterns. Production-rate profiles generated from all other patterns are almost identical except for the interpattern time delay, which also validates the pseudosteady state of interpattern flow for a more-complicated IUP model. The two-pattern sector model with the HBCs converges in three to four iterations. The production-rate profiles of oil, gas, and water generated by the sector model with HBCs are almost identical to those produced from one of those inner patterns in the 59-pattern model. With the 1D example, we also analytically demonstrate the convergence of our numerical implementation of HBCs.
In terms of clock-time used, it is possible to achieve 5N time speedup through application of the HBCs, in which N is the number of patterns in a field-scale model. Therefore, the new approach is proved a key enabler for field-scale IUP pattern optimization. Provided that the interpattern-pressure communication that is induced by the pattern delay time is not too severe, we expect that one can also apply HBCs to the simulation of other field-scale thermal processes, such as the in-situ conversion process and steamfloods.