Modelling Physical Dispersion in Miscible Displacement-Part 1: Theory and the Proposed Numerical Scheme

Abstract

Physical dispersion, comprising molecular diffusion and mechanical dispersion, is one of the primary fluid mixing mechanisms in reservoir processes dominated by compositional change. Its effect controls the characteristics and magnitude of oil recovery by miscible displacement. Standard compositional simulators used to model miscible displacement generally do not include physical dispersion effects and solve the governing equations by first order finite-difference scheme with singlepoint upstream weighting of mobilities. This approach leads to unphysical smearing of fronts (known as numerical dispersion), which is assumed to compensate for the physical dispersion. Unfortunately, this assumption is valid only for one-dimensional problems under very restrictive conditions and can lead to erroneous results in multiple dimensions. The incorporation of physical dispersion in geologically complex models, such as the ones described by non-orthogonal corner-point grids, requires the use of advanced techniques of flux approximation to retain both physical and numerical accuracy. The use of the tensorial form of the permeability or dispersion coefficient becomes a necessity for convective or dispersive transport when flows are not aligned to the principal coordinate axes, which is almost always the case in practical reservoir simulation. In this paper, a new dispersive flux-continuous scheme based on a multi-point control volume procedure is developed to allow the inclusion of the full tensor form of physical dispersion into compositional simulation of miscible displacement on 3-dimensional hexahedron structured corner-point grids. Introduction Gas injection into oil reservoirs results in a number of physical mechanisms that help in mobilizing and extracting the oil. Depending on the pressure, temperature, and the compositions of reservoir oil and the injected gas, immiscible or miscible displacements occur. The mobility ratio of displacing to displaced fluids and the gravity and capillary forces determine the extent of viscous fingering that would take place in a gas displacement process. Often the mass transport is affected by dispersion in different directions due to varying velocity gradients. The oil recovery in a miscible displacement process depends on the size of the mixing zone between the injected fluid and the reservoir oil. For maximum oil recovery at breakthrough to occur, the mixing zone should remain small compared to the reservoir volume so that the oil produced is not diluted by the injected fluid. Ideally in a reservoir with a small mixing zone, for complete oil recovery, slightly more than one reservoir pore volume of injection fluid is required. However, if the mixing zone is large, several reservoir pore volumes of injection fluid may be needed to achieve complete recovery(1). On the other hand, the mixing due to diffusion and dispersion can dampen out viscous fingers in an unstable displacement, leading to increased sweep efficiency. Dispersive mixing is caused by molecular diffusion and mechanical dispersion and is the main part of the mixing in miscible displacements(2). Molecular diffusion is a phenomenon whereby the transport of mass of a species (component) occurs within a single fluid phase from one point to the other in the direction of decreasing concentration.

Modeling of physical dispersion using script environment in Petrel

“…This paper is a continuation of the previous works of the author [11,12,14,17,26] within the framework of which a reservoir simulator was built (through modification of the BOAST reservoir simulator [7]) correctly taking into account the phenomenon of fluid mixing. Modifications of the simulator concerned implementation of the hybrid method of minimizing numerical dispersion (mobility with multi-point upstream weighting [27] and double discretization grid [1]) and extension of standard saturation equations with additional terms of physical dispersion with control parameters [15,18,20,22,23]. These changes were tested on both simplified simulation models (in which fixed size of blocks, homogeneous reservoir parameters and stationary flow of reservoir fluids were assumed) and the actual formation model (selected natural gas reservoir model).…”

Simulation modeling of physical dispersion phenomenon observed in experimental data

“…This paper is a continuation of the previous statutory papers of the Department of Hydrocarbon Reservoir and UGS Simulation (Miłek et al, 2013;Szott and Gołąbek, 2014;Szott, 2015a, 2015b;Gołąbek and Szott, 2017) within the framework of which a reservoir simulator was built (through the modification of an open code BOAST reservoir simulator (Fanchi et al, 1982) correctly taking into account the phenomenon of mixing of gases. Modifications of the simulator concerned implementation of the hybrid method of minimizing numerical dispersion (mobility with multi-point weighing in the direction of inflow (Tood et al, 1972) + double discretization grid (Audigane and Blunt, 2003) and extension of standard saturation equations with additional term describing physical dispersion and control by specific parameters (Redlich and Kwong, 1949;Soave, 1972;Peaceman, 1977;Kreft and Zuber, 1978;Shrivastava et al, 2005). These changes were tested on simplified simulation models (in which fixed size of blocks, homogeneous reservoir parameters and stationary flow of reservoir fluids were assumed) and the real formation model (selected natural gas reservoir model).…”

A 3D compositional miscible gas flooding simulator with dispersion using Element-based Finite-Volume method

“…Later Chang et al (1994) investigated the formation of viscous fingering for different dispersivity scenarios of CO 2 injection. Shrivastava et al (2005aShrivastava et al ( , 2005b presented a similar approach as proposed by Chang et al (1994) to incorporate physical dispersion in a fully implicit compositional reservoir simulator.…”