A novel multi-objective estimation of distribution algorithm for solving gas lift allocation problem

Highlights

• We employ a novel multi-objective optimization algorithm for solving gas lift optimization problem.

• The optimization algorithm is based on Bayesian networks and Gaussian kernel functions.

• The gas lift allocation problem can be viewed as a multi-objective problem with conflicting criteria.

• As the number of the dimensions of the optimization problem increases the efficiency of proposed algorithm becomes more apparent.

Abstract

Gas lifting is a common practice in the oil industry. Using an appropriate gas lift injection rate can ensure that the desired oil production rate would be achieved. In the case of an oil field, the problem of distributing a certain amount of the available gas among a number of wells is formally known as a gas lift allocation problem. In this paper, a multi-objective optimization algorithm, based on the Gaussian Bayesian Networks and the Gaussian kernels, is proposed in order to determine the best injection points, considering multiple objective functions. Firstly, the problem is solved in a similar approach to the previous literature with similar gas lift data and similar function approximation method, to compare the performance of the proposed algorithm with the older ones. Thereafter, an extended problem is discussed, with minimizing the water production as a new optimization criterion. The developed multi-objective scheme is capable of handling and optimizing a gas-lift problem with several constraints and conflicting objectives such as controlling the gas usage and increasing the oil production, whereas in the conventional single-objective optimizations, any alteration in the constraints demands a new optimization process and often there is no place for considering an additional objective in the gas-lift allocation problem. The results obtained by the proposed optimization algorithm significantly overcame those reported in the previous similar literature. For a single-objective fifty-six well problem, the results exhibited 16.24% improvement in the total oil production.

Introduction

The demands for high oil production rate leads to a gas lift operation, which consists of injecting a certain amount of high-pressure gas through the tubing, and consequently, lowering the hydrostatic pressure difference along the tube. However eventually, at some points, the increase in the friction pressure loss offsets the hydrostatic pressure reduction which, in turn, limits the increase in the production rate and yields in the convexity of the gas lift performance (GLP) curve. Determining the optimum injection rates in a multiple well production network is known as the gas lift allocation problem. Many researchers have tackled this problem from different points of view by using a wide range of optimization techniques, from the quasi-Newton (Nishikiori et al., 1989) to the genetic algorithm (Martinez et al., 1994). Alarcón et al. (2002) improved the quasi-Newton optimization algorithm and offered a new mathematical model to fit the field data. Ray and Sarker (2007) challenged the problem as a bi-objective problem through maximizing the oil production level and minimizing the gas usage rate as the optimization criteria. They suggested a variant of multi-objective genetic algorithm called, the non-dominated sorting genetic algorithm II (NSGA-II) as the optimization tool. Other approaches, such as mixed-integer programming (Kosmidis et al., 2005) and dynamic programming (Camponogara and Nakashima, 2006), explored the additional aspects of the problem, including the activation of wells and their interactions. Wang and Litvak (2008) provided a heuristic method and considered the long-term reservoir developments by incorporating a reservoir simulator. They also used a multi-objective scheme to reduce the rate oscillations besides maximizing the oil production. However, the nature of the local search does not even guarantee to find local solutions. Furthermore, Sukarno et al. (2009) extended the operational condition to the case of a dual gas lift system. Zerafat et al. (2009) presented a comparison of different methods to the Genetic Algorithm and examined the capabilities of the algorithms in solving the uni-objective gas-lift optimization problem with the constraints on the lift-gas injection rates. They also proposed a variant of Ant Colony Optimization to deal with the problem. It can be witnessed that with the exception of two cases (Ray and Sarker, 2007, Wang and Litvak, 2008), the literature has chiefly focused on the single objective optimization of the gas lift problem.

In this study, it is aimed to confront the problem as a multi-objective problem and expand the idea of multiple criteria optimization, since the presence of constraints in the real gas-lift problems is an inevitable fact. In the conventional single objective approach, for every update in the constraints, the process of gas lift allocation problem should be re-solved. For example, if the amount of the available gas or the capacity of compressors changes, a new solution is needed by the single objective approach. On the other hand, the multi-objective approach provides a set of solutions for different criteria, which makes it easier to compare several production strategies altogether. In a multi-objective approach, it is possible to simultaneously handle several conflicting objectives in the optimization process.

For instance, by a multi-objective method, it is likely to optimize the total oil production rate and minimize the number of required wells at the same time, but through a single objective method, the number of wells should be assumed as a constraint for the problem.

Hence, since it is necessary to compare different scenarios for the gas lift design, a multi-criteria optimization approach is an efficient tool for solving such a multi-dimensional problem with different constraints. The proposed optimization algorithm is an estimation of the distribution algorithm (EDA) based on the Gaussian Bayesian networks (P. Larrañaga et al., 2000) and the Gaussian kernels (Socha and Dorigo, 2008). The general idea of an EDA is to construct probabilistic models based on a set of promising solutions, and guide the search process by sampling the probabilistic models. Furthermore, in order to adjust the algorithm for solving the multi-objective problems, the concept of non-dominating sorting (Deb et al., 2002) has been employed. The obtained results from the EDA are compared with those reported by using the multi-objective genetic algorithm (Ray and Sarker, 2007) due to the evolutionary nature of both algorithms and lack of any other similar multi-objective optimization algorithm in the literature on the topic of gas lift optimization. It should be pointed out that in the field of petroleum engineering, very few works have ever employed any variant of the estimation of distribution algorithms. For instance, Abdollahzadeh et al. (2013) utilized an EDA-BOA (Bayesian Optimization Algorithm) for history matching. To the best of the authors' knowledge, there exists no study on applying any multi-objective EDA in the literature of petroleum engineering.