Zakhar Lanetc | Searcharxiv

arXiv2020

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

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.

physics.flu-dyn↗

arXiv2018

Relevance of analytical Buckley-Leverett solution for immiscible oil displacement by various gases

In order to generate the valid numerical simulation model, the sufficient amount of gathered data from the oil field is required. However, it is not always possible to acquire such data at the initial stage of project development. Buckley and Leverett (1942) developed the analytical solution allowing to assess the oil displacement efficiency. One of the main assumptions of this model is incompressibility of oil and injected fluid. For slightly compressible water and oil such assumption is rational. However, that is not always the case when the gas is injected. This research aims to identify the conditions at which the usage of the incompressible gas model is appropriate. Likewise, the cases when the model of compressible gas is required are also evaluated. To accomplish the goals of this research, the comparative analysis between the injection of compressible and incompressible gases was undertaken using the numerical solution of the correspondent reservoir engineering problem. The validation of the numerical model was undertaken showing that it matches the analytical Buckley-Leverett solution. The findings of this research indicate that the relative and absolute density change with the pressure of the injected gas has the profound impact on the convergence between two models under consideration. With the increase in the injection pressure, the discrepancy between the models of compressible and incompressible gas raises for all the considered injection fluids (CO2, CH4 and N2). Due to a steep slope of 'density-pressure' curve for CO2 at low initial reservoir pressure, the incompressible model cannot accurately predict the oil displacement efficiency by this gas at any reasonable injection pressure. All 1D results are also representative for 2D simulation. However, the mismatch between two models increases considerably for 2D simulation scenarios.

physics.flu-dyn↗