Negative Saturation Approach for Non-Isothermal Compositional Two-Phase Flow Simulations

Abstract

This article deals with developing a solution approach, called the non-isothermal negative saturation (NegSat) solution approach. The NegSat solution approach solves efficiently any non-isothermal compositional flow problem that involves phase disappearance, phase appearance, and phase transition. The advantage of the solution approach is that it circumvents using different equations for single-phase and two-phase regions and the ensuing unstable procedure. This paper shows that the NegSat solution approach can also be used for non-isothermal systems. The NegSat solution approach can be implemented efficiently in numerical simulators to tackle modeling issues for mixed CO 2 -water injection in geothermal reservoirs, thermal recovery processes, and for multicontact miscible and immiscible gas injection in oil reservoirs. We illustrate the approach by way of example to cold mixed CO 2 -water injection in a 1D geothermal reservoir. The solution is compared with an analytical solution obtained with the wave-curve method (method of characteristics) and shows excellent agreement. A complete set of simulations is carried out, which identifies six bifurcations. The two main bifurcations are (1) when the most downstream compositional wave is replaced by a compositional shock and (2) when an extra Buckley-Leverett rarefaction appears. The plot of the useful energy (exergy) versus the CO 2 storage capacity shows a Z -shape. The top horizontal part represents a branch of high exergy recovery/relatively lower storage capacity, whereas the bottom part represents a branch of lower exergy recovery/higher storage capacity.

Predicting Fluid Properties in the MUFITS Reservoir Simulator with User-Supplied Modules

“…It can only change Φ i for a given P, T, and c tðjÞ . Since the number of phases np is not changed, the reported saturations s i and concentrations c iðjÞ and c tðjÞ are allowed to take negative or larger-than-one values [19]. If Mode = 1, then the initial guess is not specified.…”

“…The saturation distribution is governed by the Buckley-Leverett solution [22]. This analytical solution consists of the leading displacement front S, at which s 1 is discontinuous, and the trailing Riemann wave, in which s 1 changes continuously, reaching s 1 = 1 at X = 0 m. One can show that for Equation (19) and specified phase viscosities μ 1 and μ 2 , the shock propagates at a velocity of 0.8 m/day. Thus, S is exactly at X = 80 m at t = 100 days.…”

Extending the persistent primary variable algorithm to simulate non-isothermal two-phase two-component flow with phase change phenomena

“…To handle this, Abadpour and Panfilov (2009) proposed the negative saturation method, in which saturation values less than zero and bigger than one are used to store extra information of the phase transition. Salimi et al (2012) later extended this method to the non-isothermal condition, and also taking into account the diffusion and capillary forces. By their efforts, the primary variable switching has been successfully avoided.…”

Non-isothermal compositional liquid gas Darcy flow: formulation, soil-atmosphere boundary condition and application to high-energy geothermal simulations

“…Another strategy to avoid the switch of variables is based on the extension of some physical quantities such as the phase molar fractions like in [23] using component fugacities, or the phase molar fractions and pressures like in [3,28]. Let us also mention the negative saturation formulations [1,37] belonging to this family. A comparison between some of these formulations can be found in [41,28] in the case of isothermal compositional Darcy flows.…”