Calculation of Parachors for Compositional Simulation
Authors: Fanchi J.R. 
Published: December 2007

Summary
Linear regression analysis has been used to develop an expression for the calculation of parachor values from the critical temperature and critical volume of a fluid. The expression has applicability in compositional calculations where parachor values for components or pseudocomponents are needed.

Introduction
One of the advantages of compositional simulation relative to black-oil simulation is the ability of the compositional simulator to model the flow performance of the hydrocarbon components that constitute the hydrocarbon liquid and vapor phases. On the other hand, additional computational labor is required. A set of pseudocomponents is used commonly to minimize the additional labor. pseudocomponents is used commonly to minimize the additional labor. The use of pseudocomponent data sets is illustrated in the SPE comparative compositional problem. Each set of pseudocomponents should be designed to be equivalent to a full compositional analysis of the problem, but should require less computational labor. There is no "best" method for constructing a reliable pseudocomponent data set. Some different pseudoization techniques pseudocomponent data set. Some different pseudoization techniques have been described by Hong. Among the problems of pseudoization is the determination of fluid properties. This paper focuses on the calculation of parachors for use with pseudocomponent data sets. Parachors are used in the Macleod-Sugden correlation to Parachors are used in the Macleod-Sugden correlation to calculate the interfacial tension (IFT) between the hydrocarbon liquid and vapor phases. This is important in a compositional simulation of a miscible or partially miscible displacement process. Actual implementation of the IFT effect is through the calculation of relative permeabilities. (For an example, see Coats) First, however, the parachors for each component or pseudocomponent must be known. In the following, the results of a regression analysis provide a relatively simple equation for the calculation of provide a relatively simple equation for the calculation of parachors from known component or pseudocomponent properties. parachors from known component or pseudocomponent properties. Parachor Calculation Parachor Calculation Amyx el al. present the parachors for a number of pure substances. Attempts to correlate the parachor with fluid properties have been made. These methods were primarily properties have been made. These methods were primarily applicable to relatively small molecules and generally are not suited to complex hydrocarbon systems. To avoid this difficulty, regression analysis was used to develop a relationship between parachor and known fluid properties. Among the fluid properties that are parachor and known fluid properties. Among the fluid properties that are known, either before or after pseudoization, are the critical volume (V), critical temperature (T), and critical pressure (p) of individual components or pseudocomponents. After trying a number of functional relationships, I found that the parachor values listed by Amyx et al. and shown in Table 1 are represented best by the following expression:
(1)
where H denotes Herzog's parameter and is defined by
(2)
The regression coefficients a ... a have the values
These equations require values of V and T with units of liters per gram mole and Kelvin, respectively. Results of the regression per gram mole and Kelvin, respectively. Results of the regression analysis and regression statistics are shown in Table 2. Significance of regression statistics is discussed generally in Ref. 6. For this case, a reasonably good match of the actual parachors is obtained with Eqs. 1 and 2, and the regression coefficients. The magnitude of the maximum deviation of the calculated parachor from the actual parachor is less than 1%, and the average of the absolute values of the deviation is approximately 0.3%.

Discussion
The use of pseudocomponents in a compositional simulation presupposes the selection of a mixing rule-such as mole-fraction presupposes the selection of a mixing rule-such as mole-fraction weighting. Mixing rules are prescriptions for combining pure component properties to determine pseudocomponent properties, such as V and T. The pseudocomponent values of V and T should be substituted directly into Eqs. 1 and 2.
JPT
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