Robust Fuzzy Timestep Selector for a Fully Implicit Reservoir Simulator

Crumpton, Paul (Saudi Aramco)

OnePetro 

Abstract

The objective of this work is to avoid wasteful timestep cuts of the reservoir simulator by developing a timestep-selector that controls the linear and non-linear iterations as well as the physical quantities. Using a Fuzzy logic framework, a non-linear timestep selector has been developed that reduces run time, and increases robustness for challenging nonlinear simulations.

From a linear analysis standpoint a fully implicit reservoir simulator has no stability limit on the size the timestep. However, in practice the non-linearity prevents arbitrary timestep size being chosen. Without any theory to guide us the timestep choice it is left to heuristics, usually based on physical engineering constraints such as the previous time steps, maximum pressure and saturation changes. This can be very effective, but can lead to many timestep cuts, and sometimes lead to failure of the simulator. This is especially common for highly non-linear dual-porosity, dual-permeability reservoirs which are very common in the Middle East. Here a Fuzzy logic framework is used to construct a non-linear timestep selector which takes many inputs (linear and non-linear convergence data as well as pressure and saturation changes) and breaks down the complexity. Firstly fuzzification of the inputs into fuzzy sets (e.g. High medium and low) then applications of rules (e.g. if linear high then timestep is low) and de-fuzzification into a crisp timestep to be used for the next iteration. This process provides us with a powerful framework to construct various strategies for controlling the timestep. In contrast, traditional timestep controllers use crisp logic, this is difficult to blend multiple conflicting inputs to a timestep selector.

To demonstrate the effectiveness of this approach results are presented on a suite of cases, covering a wide range of models including compositional and dual-porosity cases. For some cases a dramatic 3x improvement is observed, however, what is more important, is on average the new timestep selector significantly improves performance, especially for the slow challenging cases; by reducing the time steps wasted due to timestep cuts. Perhaps what is most impressive is that the fuzzy controller did achieve the goals of the fuzzy rules to keep the non-linear and linear iterations under control, which had the benefit of reducing total failures of the simulator.

A fuzzy logic framework is applied to timestep selection of a fully implicit reservoir simulator. A combination of convergence data as well as physical quantities are used as inputs which has led to a robust and extendable timestep selector.