Dew point pressure model for gas condensate reservoirs based on multi-gene genetic programming approach

doi:10.1016/j.asoc.2016.05.049

Applied Soft Computing

Volume 47, October 2016, Pages 168-178

https://doi.org/10.1016/j.asoc.2016.05.049 Get rights and content

Abstract

One of the most critical parameters in characterization of gas condensate reservoirs is dew point pressure (DPP), and its accurate determination is a challenging task in development and management of these reservoirs. Experimental measurement of DPP is a costly and time consuming method. Therefore, searching for a quick, reliable, inexpensive, and robust algorithm for determination of DPP is of great importance. In this paper, first, a new approach based on multi-gene genetic programming (MGGP) to determine DPP of gas condensate reservoirs is presented. Then, a correlation for DPP calculation using MGGP has been developed for gas condensate reservoirs. Finally, the efficiency of the proposed DPP model has been validated by comparing its predictions with the results of other conventional models. It is found that the correlation developed in this work is capable of predicting more accurate values of DPP, with the lowest average relative and absolute errors with respect to the experimental results, and also higher correlation coefficient among the results of all the evaluated DPP correlations. Therefore, it is suggested that the proposed model can be applied effectively for DPP prediction for a wide range of gas properties and reservoir temperatures.

Graphical abstract

Introduction

Gas condensate reservoirs exhibit complex phase and flow behaviors due to formation of condensate bank near the wellbore region and dynamic changes in composition of each phase. Natural production from these reservoirs leads to reservoir pressure drop which causes gas condensation, and liquid drops out in the pore space of the reservoir (see Fig. 1). This phenomenon occurs primarily in the vicinity of the wellbore, and then, propagates in a cylindrical form within the entire drainage volume of the well. The most important effect of liquid condensation is reduction of gas relative permeability and, consequently, loss of production. Therefore, efficient production from gas condensate reservoirs is very sensitive to accurate determination of dew point pressure [1].

In general, there are three methods to calculate the dew point pressure (DPP). The first approach is experimental measurement of DPP of collected laboratory samples. The widely used experimental methods for this purpose include constant composition expansion (CCE) [2] and constant volume depletion (CVD) [3] tests. Although experimental measurement of DPP is very accurate and reliable, it is very costly and time consuming especially in lean gas condensate reservoirs [4].

The second method of dew point pressure calculation is use of empirical correlations. Empirical correlations for DPP predictions have been studied by several investigators [5], [6], [7], [8], [9], [10], [11], [12], [13], [14]. The third approach is iterative estimation of DPP using any equation of state (EOS) [15], [16]. This approach has convergence problems because matching parameters of selected EOS should be tuned with some experimental data by least squared method. In addition, the EOS approach does not generalize to unseen data, and usually memorizes the data that were used to develop it [17].

In recent decades, the DPP estimation using artificial intelligent techniques such as artificial neural networks (ANNs), adaptive neuro-fuzzy inference system (ANFIS) and support vector machine (SVM) has been investigated in several studies and good predictions have been reported [17], [18], [19], [20], [21], [22], [23], [24]. Despite the acceptable performance of ANNs, there is no efficient procedure to select the structure to build such networks. Hence, many trials should be performed to obtain an appropriate configuration. Moreover, the mentioned approaches do not usually give a definite function, in terms of the input values, to calculate the DPP [25], [26], [27]. The generated prediction equation can be incorporated in commercial engineering software or applied to any reservoir engineering calculation cases without any difficulty.

Recently, the multi-gene genetic programming (MGGP) has been applied successfully to model various complex engineering problems. MGGP is a modified genetic programming (GP) approach for model structure selection combined with the least square technique (LST) for parameter estimation. The MGGP models are validated using experimental data that were not used during the training process. The MGGP-based equations can reliably be used for pre-design purposes. MGGP does not require simplifying assumptions to develop the models. Contrary to artificial neural networks and many other soft computing tools, the MGGP provides constitutive prediction equations. MGGP is able to learn the key information patterns within the multidimensional information domain with high speed, instead of complex rules and mathematical routines [28], [29], [30], [31].

This paper proposes a new approach based on MGGP to determine an accurate formula for DPP of gas condensate reservoirs. A large experimental PVT data set of a giant gas condensate field is used to develop the new DPP equation by MGGP. Then, the performance of the MGGP model is compared to the conventional methods by means of some statistical indices. Moreover, the results obtained by MGGP are compared with other artificial learning techniques such as standard GP, ANFIS, and artificial neural network models.

Section snippets

Background

DPP correlations have been studied by several investigators. Eilerts and Smith [6] developed four correlations relating dew point pressures to temperature, composition, molar average boiling point and oil-to-gas volume ratio. Olds et al. [7] studied the behavior of reservoir fluids of Paloma field, and the influence of composition change on the DPP. They indicated that removal of the intermediate molecular weight components from the mixture resulted in a significant increase in DPP. Olds et al.

Multi-gene genetic programming

MGGP belongs to the class of symbolic regression which makes an explicit relation between one or more inputs and an output using mathematical symbols, functions and variables. Symbolic regression is different from conventional regression where the coefficients/functions are not calculated. The equations are found based on an extensive continuously improving guided search in an evolving search space.

In order to understand the notion of MGGP, first, Genetic programming (GP) is discussed in brief

Data acquisition

DPP determination of gas condensate reservoirs has been extensively studied and various correlations have been proposed to estimate it. According to previous investigations [16], [32], [33], [34], [35], reservoir temperature (T_R), gas composition and molecular weight of C₇₊ (M_C7+) are the most effective parameters in prediction of DPP. However, retrograded gases were mixtures of widely-ranged components. In order to obtain a simplified MGGP equation with less input variables, gas composition

Results and discussions

Since MGGP is a stochastic algorithm that can offer different solutions in different runs, several runs were performed in order to find the optimum MGGP model. Table 4 shows three typical examples of the formulas found by their algorithm and performance in training data set. According to the trained MGGP model, the following formula which has the best performance in predicting the DPP, has been developed: $DPP = 0.661 \times [M_{C 7 +}^{2} - M_{C 7 +} - X_{C 7 +} (1 - X_{vol})] + \frac{0.239}{X_{vol} (X_{vol} + X_{C 7 +})} + \frac{0.0297 M_{C 7 +}}{1 - X_{int} X_{C 7 +} - X_{_{C 7 +}}^{2}} + 1.884 X_{}$

Sensitivity analysis of the mean

In this section, the sensitivity analysis on the mean is established. This process shows the relative importance of inputs of the MGGP model and illustrates how sensitive a model output is to any change in an input while keeping other inputs constant. For this purpose, in the MGGP trained models, the first input was changed between its mean ± a definite number of standard deviations, and the model output was computed while other inputs were fixed at the irrespective means. The standard deviation

Conclusion

In this study a new model based on MGGP has been developed to estimate the DPP of gas condensate reservoirs. Values of reservoir temperature, gas composition (i.e., volatile fractions (C₁, N₂), intermediate fractions (C₂–C₆, H₂S), and heavy fraction (C₇₊)) as well as molecular weight of C₇₊ (M_C7+) were selected as the input data and DPP data of CVD tests were selected as the output data in training the MGGP model.

This paper demonstrates that the predictive capability of formulation by MGGP can

Acknowledgment

The authors would like to gratefully thank National Iranian Oil Company (NIOC) for their technical support.

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Dew point pressure model for gas condensate reservoirs based on multi-gene genetic programming approach

Abstract

Graphical abstract

Introduction

Section snippets

Background

Multi-gene genetic programming

Data acquisition

Results and discussions

Sensitivity analysis of the mean

Conclusion

Acknowledgment

PVT and Phase Behavior of Petroleum Reservoir Fluids

Experimental investigation of retrograde condensation in porous media at reservoir conditions

SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers

Retrograde condensation in porous media

SPE J.

Characterization of gas condensate mixtures

Specific Volumes and Phase Boundary Properties of Separator-Gas and Liquid-Hydrocarbon Mixtures

The volumetric and phase behavior of oil and gas from Paloma Field

AIME

Volumetric and viscosity studies of oil and gas from a San Joa-quin Valley Field

AIME

Volumetric behavior of oil and gas from a Louisiana field

AIME

A correlation of dewpoint pressure with fluid composition and temperature

AIME

Improved Correlations for Retrograde Gases. MS Thesis

Predicting the dewpoint pressure for gas condensate reservoir: empirical models and equations of state

Fluid Phase Equilib.

Evolving smart approach for determination dew point pressure through condensate gas reservoirs

Fuel

A new multi-gene genetic programming approach to non linear system modeling. Part II: geotechnical and earthquake engineering problems

J. Neural Comput. Appl.

Evolving an accurate model based on machine learning approach for prediction of dew-point pressure in gas condensate reservoirs

Chem. Eng. Res. Des.