A new correlation for calculating carbon dioxide minimum miscibility pressure based on multi-gene genetic programming

Abstract

Miscible gas injection is one of the most efficient enhanced oil recovery (EOR) methods in petroleum industry. Minimum miscibility pressure (MMP) is a key parameter in any gas injection design project. Experimental Measurement of MMP is a costly and time-consuming method; so searching for a quick, not expensive and reliable method to determine gas-oil MMP is inevitable. This paper Present a fast and vigorous method using a new approach based on multi-gene genetic programming (MGGP) to determine carbon dioxide minimum miscibility pressure (CO₂ MMP) for carbon dioxide injection processes. Then, new correlations for MMP calculation of both pure and impure CO₂ streams using the MGGP, have been developed. Consequently, the MGGP models have been validated and compared with the other conventional model results, to evaluate different techniques. It was founded that the new developed correlations predict accurate values of CO₂ MMP compare with the experimental slim-tube CO₂ MMP test results, with the lowest average relative and absolute error and also higher correlation coefficient among all evaluated CO₂ MMP correlation results.

Introduction

In recent years, enhanced oil recovery (EOR) has been concerned worldwide. Enhanced oil recovery includes many techniques and miscible gas injection is one of the most widely used techniques. Among all gas injection processes, carbon dioxide is the most common gas which is used due to its lower cost, high displacement efficiency at low pressure and the potential for concomitant environmental benefits (Danesh, 2003).

An important concept associated with any miscible gas injection processes is the minimum miscibility pressure (MMP). The MMP is the lowest pressure at which the injected gas and the initial oil in place become multi-contact miscible and the displacement process become very efficient (Zuo et al., 1993, Mansoori et al., 1989, Jaubert et al., 2001). An inaccurate prediction of MMP may cause significant consequences such as decrease in the oil recovery rate (Mousavi Dehghani et al., 2008).

Several methods have been proposed for measurement of MMP, including experimental tests and Mathematical correlations. The widely used experimental methods include slim tube test, rising bubble apparatus test and vanishing interfacial tension technique (Flock and Nouar, 1983, Christiansen and Haines, 1987, Rao, 1997, Gu et al., 2013, Elsharkawy et al., 1996, Rao and Lee, 2002, Orr and Jessen, 2007, Rathmell et al., 1971). Since the Experimental determination of MMP is costly and prolong; its widespread applications have been hindered (Tatar et al., 2013).

Another Approach for calculating MMP is based on using mathematical correlations. These correlations relating the MMP to the oil physical properties and injection gas compositions and consists of empirical equations and equation of states (Zuo et al., 1993, Mansoori et al., 1989, Nasrifar and Moshfeghian, 2004, Benmekki and Mansoori, 1988, Fazlali et al., 2013). The empirical correlations for minimum miscibility pressure predictions in CO₂ injection have been studied by several investigators (Holm and Josendal, 1974, Holm and Josendal, 1982, Dunyushkin and Namiot, 1978, Lee, 1979, Yellig and Metcalfe, 1980, Johnson and Pollin, 1981, Alston et al., 1985, Orr and Silva, 1987, Dong et al., 2000, Sebastian et al., 1985, Eakin and Mitch, 1988). In CO₂ injection process, the MMP depends on the CO₂ purity, oil composition and reservoir temperature (Shokir, 2007, Emera and Sarma, 2004). It was founded that the injected CO₂ is not always pure and several impurities such as nitrogen, sulfuric acid and light hydrocarbons from a variety of sources, including natural reservoirs and process plant waste streams are available (Chen et al., 2013). The effect of the impurities on CO₂ injection has been studied in several investigation (Alston et al., 1985, Sebastian et al., 1985, Metcalfe, 1982, Bon et al., 2006).

In recent decades, the simulation of MMP of CO₂ injection using artificial intelligent include artificial neural networks (ANNs), adaptive neuro-fuzzy inference system (ANFIS) and support vector mechanism (SVM) have been reported in several studies, which good predictions have been achieved (Emera and Sarma, 2004, Huang et al., 2003, Nezhad et al., 2011, Zendehboudi et al., 2013, Shokrollahi et al., 2013, Sayyad et al., 2014, Rahimzadeh Kivia et al., 2013). However, these approaches suffer from structural dependency and sources of data efficiently, which affect their output results. Moreover, they do not usually give a definite function base on the input values, to calculate the MMP (Gandomi and Alavi, 2012a).

Recently, the Multi-gene genetic programming (MGGP) has been used successfully to modeling engineering problems. Contrary to artificial neural networks and many other soft computing tools, the MGGP provides constitutive prediction equations, therefore Instead of complex rules and mathematical routines, the MGGP is able to learn the key information patterns within the multidimensional information domain with high speed (Gandomi and Alavi, 2012a, Gandomi and Alavi, 2012b). This paper proposes a new approach based on MGGP to determine an accurate formula for minimum miscibility pressure (MMP) for pure and impure CO₂ injection process. A large experimental PVT data set is used to develop the new MMP equations by MGGP. Finally, the performance of the MGGP model is compared to the conventional methods by means of some statistical indices.