Brazilian Journal of Chemical Engineering TOWARD PREDICTIVE MODELS FOR ESTIMATION OF BUBBLE-POINT PRESSURE AND FORMATION VOLUME FACTOR OF CRUDE OIL USING AN INTELLIGENT APPROACH

Accurate estimation of reservoirs fluid properties, as vital tools of reservoir behavior simulation and reservoir economic investigations, seems to be necessary. In this study, two important properties of crude oil, bubble point pressure (Pb) and formation volume factor (Bob), were modelled on the basis of a number of basic oil properties: temperature, gas solubility, oil API gravity and gas specific gravity. Genetic programming, as a powerful method, was implemented on a set of 137 crude oil data and acceptable correlations were achieved. In order to evaluate models, two test datasets (17 data for Pb and 12 data for Bob) were used. The squared correlation coefficient (R) and average absolute relative deviation (AARD %) over the total dataset (training + test) are 0.9675 and 8.22% for Pb and 0.9436 and 2.004% for Bob, respectively. Simplicity and high accuracy are the advantages of the obtained models.


INTRODUCTION
Thermodynamic quantities of crude oil are a set of important features in order to determine technical specifications of oil production process equipment.Designing plenty of systems such as upstream and underground devices, surface operation equipment, etc., requires adequate and accurate information about oil parameters which are achieved, in many cases, from experimental tests along with mathematical correlations and formulas.
Laboratory tests are usually expensive and sometimes difficult and time-consuming.However, the application of correlations is economically advantageous and increases the speed of works.Furthermore, the other great use of the correlations is to determine oil future specifications and changes taken into great consideration in reservoir simulators.
Various pressure-volume-temperature (PVT) properties of crude oil can be estimated by means of equations of state or oil PVT analysis, if a complete set of variables of the oil including temperature, pressure and fluid composition are available.But in many cases, the composition of reservoir fluid is not predetermined, especially in the primary stages of recovery processes.Thus, some correlations are required to be functions of a number of readily available reservoir parameters in order to be used by engineers and scientists in this area.
In fact, the main aim of this project was to provide simple and accurate models for prediction of bubble point pressure (P b ) and bubble point formation Brazilian Journal of Chemical Engineering volume factor (B ob ) solely as functions of simple and quickly accessible live crudeoil parameters.The parameters are temperature (T), gas solubility (R s ), oil API gravity and gas specific gravity (γ g ).
In a hydrocarbon system at constant temperature, whether single-component or mixture, the bubble point pressure is the maximum pressure at which the first gas bubbles appear (Ahmed, 2010).The state of the system in this condition is called "saturated liquid".
The oil formation volume factor (FVF) is the ratio of the specific volume of oil at its natural temperature and pressure to the specific volume of the oil at standard conditions (i.e.P = 1 atm and T = 60 ˚F).If B o is measured in the bubble point condition, it will be the bubble point oil formation volume factor (Bob).
There are several correlations and methodologies developed and proposed so far for prediction of P b and B ob .Methods of Standing (1947), Vasquez andBeggs (1980), Glaso (1980), Marhoun (1988) and Petrosky and Farshad (1993), as famous correlations, have been introduced in the literature (Ahmed, 2010).Elsharkawy and Alikhan (1997) presented a set of correlations for gas solubility, oil compressibility (C o ) and B ob .Their relation for B ob is as follows: ) (1) in which, γ g is gas specific gravity.
Some presented correlations or algorithms are based on consistencies of a number of oil components or assays, which should be predetermined (Elsharkawy, 2003;AlQuraishi, 2009;Bandyopadhyay and Sharma, 2011;Farasat et al., 2013).However, the composition-based models have some limitations in their uses in preliminary reservoir investigations and simulations.
There are also several methods using the artificial neural network (ANN) technique to predict P b and B ob (Rasouli et al., 2008;Asadisaghandi and Tahmasebi, 2011).Adaptive network-based fuzzy infer-ence system (ANFIS) is another new approach that has been applied in this area (Shojaei et al., 2014).
Different procedures and methodologies can be used for model development.Artificial neural network (ANN), generalized regression neural networks (GRN), imperialist competitive algorithm (ICA), particle swarm optimization (PSO), adaptive network-based fuzzy inference system (ANFIS), genetic programing (GP), etc. are applied as famous methods in various fields, especially for optimization and prediction purposes.In the present study, a genetic programming based multi-gene symbolic regression algorithm called "GPTIPS" (Searson, 2009) was applied.This is an approved method used by the authors in some projects (Abooali and Khamehchi, 2014).
The application of genetic programming for developing simple-to-use correlations for P b and B ob seems novel.Moreover, applying natural ranges of bubble point pressure, bubble point formation volume factor, temperature, gas solubility, oil API gravity and gas specific gravity has increased the applicability and accuracy of the new developed models.

Data Set
The total dataset includes 137 training sets of data from 137 oil samples.Each set includes temperature, solution gas ratio, oil API gravity, gas specific gravity, oil bubble point pressure and formation volume factor.The data were collected from different geographical zones.
In order to determine the predictive capability of the models and also to implement a comparison between the new developed models and other correlations, two additional sets -one for P b including 17 sets of data and the other for B ob which has 12 sets of data -were applied.The data of the additional sets known as "test sets" were gathered from several papers and reference books (Ahmed, 2010; McCain,  1990; Shojaei et al., 2014).The ranges of all parameters are presented in Table 1.))    These comparisons demonstrate the superiority of the correlations developed in the present project among proposed models.
The experimental values of all dataset along with predicted data have been provided in the supporting materials and information.

CONCLUSIONS
By application of genetic programing methodology, two new models have been achieved for estimation and prediction of bubble point pressure and bubble point formation volume factor, as functions of a number of rapidly measurable oil parameters.One of the useful applications of this kind of model is prediction of oil properties in the future during the reservoir lifetime that is very important, especially for economic studies as well as effective uses in reservoir simulators.A comparison between the new proposed models and some other correlations shows the greater accuracy of the proposed models over previous works. Figure

Figure
Figure 4: P correlation co

Table 4 : C Method Standing Glaso Marhoun Petrosky and AUT Present study
Toward Predictive Models for Estimation of Bubble-Point Pressure and Formation Volume Factor of Crude Oil Using an Intelligent Approach 1089 Brazilian Journal of Chemical EngineeringVol.33, No. 04, pp.1083 -1090, October -December, 2016