Handling of Phase Change in Thermal Simulators
Authors: Abou-Kassem J.H. , Aziz K. 
Published: December 2007

Summary
The problems associated with handling phase change in thermal simulators are considered. A new set of pseudo equilibrium ratios (PER's) is introduced and pseudo equilibrium ratios (PER's) is introduced and implemented in a steam model. The proposed approach is compared with the variable substitution (VS) method and is shown to be an efficient, simple method of handling phase change. phase change.

Introduction
In a thermal recovery process, any of the three phases (oil, water, and gas) may disappear or appear under certain conditions. For example, the gas phase may disappear in undersaturated reservoirs or in a saturated reservoir undergoing repressurization, forcing the steam to condense and the hydrocarbon components to dissolve in the oil. Also, a large pressure drop in the injection block may cause the water to evaporate, leading to the formation of super-heated steam and the vaporization of hydrocarbon gas from the oil. The oil phase also may disappear in a block because of cracking or because of its movement to other areas of the reservoir if the residual oil saturation is zero. Therefore, proper handling of the disappearance and appearance of various phases is very important in a thermal simulator. The problem of phase change normally is handled either by the VS method or by the use of PER'S. The first method requires complicated logic for its implementation, while the second method has not been fully validated. The concept of PER was introduced by Crookston et al. This is a technique whereby the disappearance and appearance of either the oil or water phase can be handled without resorting to the VS logic in the numerical solution procedure of an in-situ combustion process. It should be noted, however, that the Crookston et al. ratios succeed because the gas phase never disappears in an in-situ combustion process because inert gases (nitrogen, for example) are present. In contrast, in a steamflooding process it is common for the gas phase to disappear and to reappear. Therefore, VS is the usual method used to handle this problem in steam models. Another procedure to solve the gas phase problem, which is not as successful as the VS procedure, is the artificial generation of small amounts of an inert gas in the system through a low-temperature cracking reaction. Forsyth et al. have reported that this procedure sometimes converges to a nonphysical solution. They have recommended adding a "penalty source" term instead of a reaction term in the inert gas equation to solve the gas phase problem.
Proposed Scheme Proposed Scheme We propose new PER's that allow the use of the same equations and constraints regardless of the phases present. In other words, the disappearance and appearance of present. In other words, the disappearance and appearance of either the oil, water, or gas phase can be handled without resorting to the variable substitution logic in the simulator. Therefore, the implementation of the proposed method in a compositional simulator is proposed method in a compositional simulator is straight forward. The new PER's are expressed as
................... (1)
where
............................. (2)
............................ (3)
.................................... (4)
and, and are small numbers, of the order of . If is set to 1, then Eqs. 1 through 3 reduce to the PER's introduced by Crookston et al. The functions X, X, and X are nearly 1.0 except when S, S, or Sg approaches zero-i.e., near phase diappearance. The values of these functions are nearly 1.0 for all saturations greater than 10–3. As the gas saturation decreases from 10–3 to 10–5, the function Xg doubles in value. Further decrease in gas saturation results in an increase in Xg by more or less the same order of magnitude. Therefore, as shown by Eq. 1, the PER's behave in a fashion similar to the function Xg. The physical interpretation of this behavior can be summarized as follows.
JPT
p. 1661