The In-situ Upgrading Process (IUP) involves very complicated multi-phase 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 up-scale the simulation results to the full field scale using superposition techniques. Because of non-symmetric pattern configuration and time delay of developing patterns sequentially, inter-pattern 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) where 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 inter-pattern flow will be dampened quickly within only a few patterns, and a repetitive “pseudo-steady state” of inter-pattern flow develops, where the energy and mass fluxes from the previous pattern to the current pattern are the same as those from to the current pattern to the next pattern, except for the delay time. Using a 1D heat transfer model, we analytically prove that the pseudo-steady state and therefore the HBCs hold for a long strip of patterns. A practical procedure to implement these HBCs in numerical simulation is developed, where the state variables (pressure, temperature and fluid composition) are iteratively updated in grid blocks on both edges of a sector model that is composed of two patterns. This iterative approach to impose HBCs has been 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 impact 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 inter-pattern time delay, which also validates the pseudo-steady state of inter-pattern flow for a more complicated IUP model. The two-pattern sector model with the HBCs converges in 3-4 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. Using the 1D example, we also analytically prove the convergence of our numerical implementation of HBCs.
In terms of clock-time used, it is possible to achieve 5N time speed-up through application of the HBCs, where N is the number of patterns in a field-scale model. Therefore, the new approach is proven a key enabler for field-scale IUP pattern optimization. Provided that the inter-pattern pressure communication that is induced by the pattern delay time is not too severe, we expect that HBCs can be also applied to simulation of other field scale thermal processes, such as the In-situ Conversion Process and steam floods.