The numerical scheme splitting along the coordinates in models of hydrocarbon migration based on Darcy flow concept and the mass conservation law

TL;DR

This paper introduces a coordinate-splitting numerical scheme that significantly reduces computational time in hydrocarbon migration modeling based on Darcy flow, maintaining accuracy while enabling more efficient basin simulations.

Contribution

The authors develop and validate a coordinate-splitting numerical scheme that drastically decreases computational time in hydrocarbon migration models without compromising accuracy.

Findings

Computational time reduced by approximately 1000 times.

Number of time steps decreased by about 300 times.

Model accuracy remains unaffected by the NSS-method.

Abstract

One of the most sophisticated and significant stages of basin modelling is hydrocarbon (HC) migration. In order to scrutinize this issue, it is expedient to utilize already available numerical reservoir simulation tools. Such tools are typically based on the Darcy flow model and are used to identify the structural features of the formation and estimate the production profile. Likewise, the migration of HCs can also be modelled allowing to clarify the possible location of HC deposits with higher accuracy. Despite all the advantages of this approach, there are some significant drawbacks, including the long computational time required to simulate the hydrodynamic process of HC migration. This issue cannot always be resolved by increasing computational power due to its technological scarcity. Thus, the authors suggest using a method of the numerical scheme splitting along the coordinates (further called NSS-method), allowing to significantly reduce the computational time when modelling HC migration. Explicit and implicit numerical models are created and scrutinized for the purpose of this research. The validity of these models is verified by their comparison with the available analytical solutions and by analyzing the stability of numerical schemes. As a result, the influence of NSS-method on the calculation accuracy was insignificant, allowing to decrease the computational time and number of time steps approximately by three orders of magnitude and 300 times, respectively.