ISSN 0104-6632 Printed in Brazil

www.abeq.org.br/bjche

Vol. 33, No. 04, pp. 1083 - 1090, October - December, 2016 dx.doi.org/10.1590/0104-6632.20160334s20150374

*To whom correspondence should be addressed

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

D. Abooali1 and E. Khamehchi2*

1School of Chemical Engineering, Iran University of Science and Technology, (IUST), Postal Code, 16765-163, Tehran, Iran.

2Faculty of Petroleum Engineering, Amirkabir University of Technology, Hafez Avenue, 15914, Tehran, Iran. Phone: + 98 (21) 64545154; Fax: + 98 (21) 64543528

E-mail: khamehchi@aut.ac.ir

(Submitted: June 14, 2015 ; Revised: September 1, 2015 ; Accepted: September 2, 2015)

Abstract - 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 (R2) 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. Keywords: Crude oil; Bubble point pressure; Formation volume factor; Genetic programming.

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 mathemati-cal correlations and formulas.

Laboratory tests are usually expensive and some-times difficult and time-consuming. However, the application of correlations is economically advanta-geous and increases the speed of works. Further-more, 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) prop-erties 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 re-quired to be functions of a number of readily availa-ble reservoir parameters in order to be used by engi-neers and scientists in this area.

In fact, the main aim of this project was to pro-vide simple and accurate models for prediction of bubble point pressure (Pb) and bubble point formation

1084 D. Abooali and E. Khamehchi

Brazilian Journal of Chemical Engineering

volume factor (Bob) solely as functions of simple and quickly accessible live crudeoil parameters. The parameters are temperature (T), gas solubility (Rs), oil API gravity and gas specific gravity (γg).

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 ra-tio of the specific volume of oil at its natural tem-perature and pressure to the specific volume of the oil at standard conditions (i.e. P = 1 atm and T = 60 ˚F). If Bo 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 Pb and Bob. Methods of Standing (1947), Vasquez and Beggs (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 compressibil-ity (Co) and Bob. Their relation for Bob is as follows:

( ) ( )( ) ( )

( )( )

5 5ob s

5

s g o

B 1 40.428 10 R 63.802 10

T – 60 0.78 10

R T – /60

− −

−

= + × +

× +

× γ γ

(1)

in which, γg is gas specific gravity. Khamehchi et al. (2009) also proposed three models for Pb, Rs and bubble point oil viscosity (μob). They called the achieved models “AUT”. Their Pb correlation is given below:

0.9129 0.666 0.2122 1.08b s gP 107.93 R T API− −= ×γ × × (2)

Some presented correlations or algorithms are

based on consistencies of a number of oil compo-nents or assays, which should be predetermined (El-sharkawy, 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 Pb and Bob (Rasouli et al., 2008; Asadisaghandi and Tah-masebi, 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 net-work (ANN), generalized regression neural networks (GRN), imperialist competitive algorithm (ICA), particle swarm optimization (PSO), adaptive net-work-based fuzzy inference system (ANFIS), genetic programing (GP), etc. are applied as famous methods in various fields, especially for optimization and pre-diction purposes. In the present study, a genetic pro-gramming based multi-gene symbolic regression al-gorithm called “GPTIPS” (Searson, 2009) was ap-plied. This is an approved method used by the authors in some projects (Abooali and Khamehchi, 2014).

The application of genetic programming for de-veloping simple-to-use correlations for Pb and Bob 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 applicabil-ity and accuracy of the new developed models.

MATERIALS AND METHODS 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 grav-ity, oil bubble point pressure and formation volume factor. The data were collected from different geo-graphical zones.

In order to determine the predictive capability of the models and also to implement a comparison be-tween the new developed models and other correla-tions, two additional sets – one for Pb including 17 sets of data and the other for Bob 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 parame-ters are presented in Table 1. Table 1: The range of parameters in the dataset of present study.

Quantity Range Temperature (˚F) 85 – 306 Solution gas oil ratio (SCF/STB) 83 – 2217 Oil API gravity 21.143 – 124.054 Gas specific gravity (air = 1) 0.216 – 1.872 Bubble point pressure (psia) 350 – 5152 Bubble point formation volume factor (bbl/STB)

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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 Engineering Vol. 33, No. 04, pp. 1083 - 1090, October - December, 2016

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 methodol-ogy, two new models have been achieved for estima-tion and prediction of bubble point pressure and bub-ble 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 pre-diction of oil properties in the future during the reser-voir lifetime that is very important, especially for economic studies as well as effective uses in reser-voir simulators. A comparison between the new pro-posed models and some other correlations shows the greater accuracy of the proposed models over previ-ous works.

NOMENCLATURE AARD% average absolute relative deviation

percentage ANN artificial neural network API oil API gravity ARD% absolute relative deviation percent bbl STB-1 barrel(s) per standard barrels Bo oil formation volume factor Bob bubble point oil formation volume factorCo oil compressibility at constant

temperature FVF formation volume factor GP genetic programing GRN generalized regression neural networks ICA imperialist competitive algorithm n number of samples in the dataset Pb bubble point pressure PSO particle swarm optimization PVT pressure – volume – temperature R2 squared correlation coefficient RMSD root-mean-square deviation Rs gas solubility SCF STB-1 standard cubic feet of solution gas per

standard barrels of oil T temperature

cal.iy predicted dependent variable of

component i

exp.iy experimental dependent variable of

component i exp.

y average of experimental dependent variables

γg gas specific gravity γo oil specific gravity μob oil bubble point viscosity

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