Thermal compositional reservoir simulation with a large number of hydrocarbon components is computationally intensive, especially as the number of variables treated implicitly increases. The Fully IMplicit method (FIM) treats all the variables implicitly; it is unconditionally stable (even with possibly large timesteps), but it is computationally expensive. In contrast, the IMPEST (IMplicit Pressure, Explicit Saturations and Temperature) method is computationally inexpensive, but only conditionally stable; the allowable stable timestep of IMPEST for large-scale heterogeneous models may be extremely small. AIM (Adaptive IMplicit method) offers a balance between FIM and IMPEST by treating a subset of the primary variables implicitly.

The challenge with AIM is to find robust and sharp stability criteria that can be used to choose an optimal timestep size and devise an efficient switching algorithm to dynamically label variables in grid blocks implicit or explicit. The switching algorithm aims to maximize the timestep size at which a stable solution for explicit saturation, temperature, and compositions in a grid block is guaranteed. In this paper we apply the thermal stability criteria to both the traditional percentage-based switching algorithm as well as a variable-based switching algorithm. This Thermal AIM (TAIM) framework was implemented in Stanford's General Purpose Research Simulator (GPRS).

The TAIM stability criteria are obtained using von Neumann approach. The derivation of the criteria is done using a comprehensive linear stability analysis that takes into account complex physics including mass and heat convection, heat conduction, capillary mixing and compressibility. We found the stability criteria to be sharp, i.e. small violation of the criteria leads to unstable solutions. The presence of heat conduction does not impose restrictive stability conditions on time steps due to the explicit treatment of temperature. Variable-based switching leads to a more efficient TAIM solution as compared to a percentage-based strategy.

You can access this article if you purchase or spend a download.