A salinity cut-off method to control numerical dispersion in low-salinity waterflooding simulation

Abstract

Low-salinity or controlled salinity waterflooding (LSWF) is a promising enhanced oil recovery (EOR) technique. In simulations of this process, numerical dispersion smears saturation fronts, causing errors in the results. The objective of this work is to control these effects in LSWF simulation. We examine the impact of numerical dispersion on simulated LSWF performance. The low-salinity (LS) front is smeared even at unfeasibly fine grids. The velocities of the water fronts are altered. A numerical mixed zone forms around the interface between the injected and resident brines. This mimics a typical physical mixing effect. In reservoir simulation, threshold salinities are defined where the low salinity effect (LSE) is first encountered. It has been suggested that numerical dispersion effects can be corrected by imposing effective thresholds. We demonstrate that existing methods to evaluate these effective salinities do not accurately predict the salt front movement especially when dispersion is significant. We propose a simple simulation-based approach to evaluate the effective salinities based on the conservation of volumes of the resident and injected brines in the reference and upscaled solutions. After comparing analytical and corrected coarse-grid solutions in one-dimension, the effectiveness of the approach is demonstrated in multi-dimensional systems. A method is proposed to control the numerical mixed zone to replicate a physical longitudinal mixing effect. This method is demonstrated in one-dimension and does not require a fine-grid numerical solution as a benchmark. We investigate the effects of effective thresholds on the modeled transverse mixing or dispersion. A method to model transverse dispersion in simulations with an effective longitudinal component is suggested. This method is extended to the explicit modeling of physical dispersion in systems with transverse flows. We can now simply evaluate the effective salinities for a simulation grid; and control its numerical dispersion effects to representative physical mixing or dispersion.