Research on the Optimization of Continuous Gas Lift Production from Multiple Wells on the Platform

Abstract

As the development of oil and gas resources becomes increasingly complex, the traditional oil and gas well management model faces many challenges. Continuous gas lift technology has become an important means to improve oil and gas well recovery due to its high efficiency and adaptability. Because of the multi-well continuous gas lift process on the platform, there is mutual interference between wells, and the constraints of the total gas production of each well need to be greater than the critical liquid-carrying flow rate. (Under production conditions, when gas–liquid two-phase flow occurs, the minimum gas flow rate required when the liquid phase can be completely carried out of the wellhead by the gas phase). To achieve the optimization goal of maximizing gas production, an optimized gas distribution based on a particle swarm optimization algorithm is proposed. This method achieves the overall optimal allocation of resources through dynamic optimization. Through actual engineering case analysis, the feasibility of this method is verified, which is of great significance for improving the gas lift efficiency and economic benefits of the platform.

1. Introduction

Against the background of growing global energy demand and increasing pressure from climate change, the oil and gas industry is facing unprecedented challenges and opportunities. Improving oil and gas field exploitation efficiency, reducing production costs and improving resource utilization are the common goals pursued by various enterprises and scientific research institutions in the industry. Among many oil production technologies, the multi-well continuous gas lift process has become an important production method in modern oil and gas field development due to its high flexibility and adaptability.

The core principle of the continuous gas lift process is to reduce the density of the wellbore liquid by mixing gas and liquid and effectively lifting the liquid in the wellbore to the surface, thereby improving oil production efficiency. This technology is especially suitable for high-yield oil wells and liquid-producing gas wells. Through reasonable gas lift parameter settings and system design, the wellhead production can be significantly improved. However, with the deepening of oilfield development, the complexity and diversity brought about by multi-well operations on platforms have made the optimization of gas lift systems challenging. As shown in Figure 1 below, the main problems are the reasonable distribution of the gas injection volume of each well and the mutual interference between the output of each well.

First of all, the optimization of a multi-well gas lift on a platform involves many factors, including wellhead oil pressure, gas supply, fluid properties and the operating status of the gas lift system. How to efficiently allocate these elements and optimize output under limited resource conditions has become an important issue facing oil and gas production developers. Secondly, during the gas lift production process, the production characteristics and gas lift efficiency are different under different wellhead oil pressure conditions. Therefore, optimization using traditional rules of thumb makes it difficult to achieve the best results. In order to solve these problems, many researchers and engineers began to explore optimization methods based on modern information technology and intelligent algorithms. The representative works in this area are as follows.

In 1994, Martinez et al. [1] first applied a genetic algorithm to the problem of optimizing gas distribution. Given the total amount of gas injected on site, the optimal gas injection rate was individually assigned to each well in the block.

In 1994, Wang Qisheng et al. [2] proposed the use of nonlinear optimization theory to solve the optimal gas distribution mathematical model. However, the mathematical model established only considered the maximum value that the system could obtain for oil production.

In 1995, Liu Xiangping et al. [3] proposed a multi-objective optimization gas distribution mathematical model that can consider the maximum liquid production rate and the highest economic benefits of the block. Through field measurement data verification, its effect is the same as that of the single-objective optimization gas distribution model. The results are not significantly different.

In 1997, Liu Xiangping et al. [4] proposed a mathematical model with the maximum daily income of all gas lift wells in a gas lift system as the objective function and solved it using the SUMT external point method, but it only considered the minimum gas injection rate.

In 2002, Yang Youlin [5] proposed four constraints based on the actual production needs of Zhongyuan Oilfield. This was the first time that a mathematical model was established for optimizing gas distribution problems in China.

In 2002, Alarcón et al. [6] used a linear combination of functions to generate a new mathematical model that was able to fit field data of gas lift performance curves, and constrained nonlinear programming was then applied to gas lift allocation in each well they studied.

In 2003, Wang Lei et al. [7] established a mathematical model under limited gas supply and used analytical methods to perform numerical solutions. In the same year, Yu Lianjun et al. [8] conducted a technical and economic evaluation analysis on the application of gas lift-optimized gas distribution in Wendong Oilfield.

In 2005, Zhong Haiquan et al. [9,10] presented corresponding gas lift performance curves based on four different production states of gas lift wells and used the penalty function outer point method to solve the optimal gas distribution model. At the same time, a method for estimating the initial gas injection rate is given using the hybrid penalty function method.

In 2006, Nakashima and Camponogara [11] developed a low-cost, high-efficiency dynamic programming (DP) algorithm that solved the optimization problem of maximizing the profit obtained from a cluster of oil-producing wells operating in gas lift mode. The solution takes into account the available gas injection rate constraints and can handle multiple gas lift well performance curves (WPCs).

In 2009, Luo Yinfu et al. [12] used piecewise linear functions to model single-objective and multi-objective optimal gas distribution problems and used an improved non-dominated sorting genetic algorithm to solve the optimal gas distribution problem.

In 2012, Garcia and Rosa [13] conducted a study on 16 oil wells with gas lift, taking into account the limited compressor capacity, used a genetic algorithm to optimize oil production and finally found out which well should be shut down to obtain maximum production.

In 2013, Ghaedi et al. [14] proposed a hybrid genetic algorithm (HGA) for solving the gas lift optimization gas distribution problem. They applied the algorithm to an oilfield with nine wells in southwestern Iran using different numbers of natural gas that can be used for natural gas distribution, and the results demonstrate the superiority of the algorithm. In the same year, Wei Ruiling et al. [15] established a multi-objective model of oil production and economic benefits and used the Kuhn–Tucker method for a numerical solution. The application effect was good, but it only considered the maximum and minimum values of the gas injection rate.

In 2014, Ghaedi et al. [16] applied the ant colony algorithm (ACO) to the gas lift optimization problem for the first time. They applied the algorithm to three different oilfields with different numbers of wells, and the results showed the feasibility of the method.

In 2018, Aoun et al. [17] used commercial simulation software to model four wells in a gas lift well group and conducted sensitivity analysis to establish a gas lift performance curve. Then, a new gas lift performance curve was fitted with the generated gas lift performance curve and then the optimized gas distribution model was solved using the genetic algorithm and gray wolf optimization algorithm.

In 2019, Miresmaeili et al. [18] compared the Bayesian regularized (BR) artificial neural network (ANN) with the Levenberg–Marquardt (LM) backpropagation training algorithm in gas lift optimization gas distribution modeling. In terms of model solving, the teaching-based optimization algorithm (TLBO) and the genetic algorithm (GA) were compared in terms of performance based on the convergence speed and optimal solution. The results show that the BR model is more robust and effective than the LM model, and, for the optimization algorithm, the TBLO is better than the GA for gas distribution mapping of continuous gas lift systems. In the same year, Namdar [19] used the water cycle optimization algorithm to solve the optimal gas distribution model. The results show that under a lower liquid production target, the water circulation optimization algorithm has better convergence and performance than the genetic algorithm in solving the minimum gas injection rate required for gas lift wells.

In 2020, Khoshkbarchi et al. [20] established an optimized gas distribution mathematical model that comprehensively considered the reservoir, gas lift wells, gas lift valves and other equipment and used the derivative-free optimization technology of grid adaptive direct search (MADS) to solve the problem. This solution method can solve the optimal value when some discontinuities or possible faults occur in the optimized gas distribution mathematical model, such as flow pattern changes in the oil jacket annulus and oil pipes, obstructions in the gas lift valve and critical fluids in the injected gas.

In 2020, Bondarenko, A.V. et al. [21] studied the process optimization problem of temporary plugging and fracturing of gas wells to avoid reservoir damage, which can improve the inflow and recovery rate of gas wells.

In 2022, Merzoug et al. [22] modeled multiple gas lift wells through a multinomial steady-state simulator and performed sensitivity analysis on the gas lift injection rate in the model to refit the gas lift performance curve (GLPC) and then created a mathematical model of production costs. Then, the genetic algorithm (GA) and gray wolf optimization algorithm (GWO) were used to solve the model. In the same year, Carpenter et al. [23] evaluated the feasibility of using genetic algorithm (GA) technology to optimize continuous gas lift injection rate distribution in the Middle East oilfield network through numerical modeling and simulation studies.

In 2023, Janatian et al. [24] proposed a robust model of predictive control with a constraint correction function to solve the gas lift optimization distribution model. The method is based on the worst-case implementation of uncertainty with constraint modifications. The mismatch between the measured and predicted outputs is used directly to modify active constraints in the optimization problem. Compared with other robust optimization methods (such as traditional min-max and multi-level MPC), this method is less conservative and requires less computing time.

In 2023, Han Lu [25] and others proposed a robust optimization gas distribution model that can avoid the influence of reservoir pressure changes and limited liquid production and used a differential evolution algorithm to solve it.

In 2023, Van Thang et al. [26] studied the complex optimization problem of the gas lift well production rate, wax deposition and removal cycle.

In 2024, Belousov, A et al. [27] investigated the complex optimization problems related to jet throttling flow in gas wells.

From the above research, it can be seen that by establishing mathematical models and computer simulations, a comprehensive analysis of multi-well gas lift systems can be carried out and dynamic optimization can be achieved using data-driven methods. This method can not only respond to various changes in the production process in a timely manner but also make optimized decisions based on real-time data, with higher efficiency and accuracy. Despite this, most studies focus on the optimization of oil wells, with the optimization target being oil production. There are few systematic studies on the overall optimization of continuous gas lift for gas wells, especially platform gas wells. Therefore, this article will conduct a systematic analysis and discussion on the optimization method of the multi-well continuous gas lift process on the platform. By elaborating on the basic principles of multi-well gas lift optimization, analyzing its production characteristics and challenges and combining practical cases, we conduct in-depth research on multi-well optimization strategies. The research content will include the design principles of the gas lift system, the algorithm implementation process, application effect evaluation, etc., and strive to provide theoretical support and practical guidance to improve the operating efficiency of oil and gas fields and reduce production costs.

2. Platform Continuous Gas Lift Optimization Model

2.1. Problem Description

At present, the optimized gas distribution of multiple wells on the platform for continuous gas lift still requires manual adjustment. The adjustment is cumbersome, the workload is large and linkage coordination is difficult. With continuous gas lift on the platform, the production of each well is not only affected by its own conditions but also by factors such as gas output, gas injection rate and fluid characteristics of adjacent wells. In addition, in order to avoid liquid accumulation at the bottom of the well, the sum of the injected gas rate and the well gas production rate in the liquid-filled well should be greater than or equal to the critical liquid-carrying flow rate; that is, the minimum total gas production rate must be greater than the critical liquid-carrying flow rate. The goal of optimized gas distribution for multi-well continuous gas lift on the platform is to ensure normal and stable production (normal drainage) in all wells and maximize total gas production.

2.2. Mathematical Modeling

2.2.1. Establish Optimization Model

According to the objectives and constraints of gas distribution optimization for multi-well continuous gas lift on the platform, the mathematical model is established as follows:

$$\left\{\begin{array}{l}Des{t}_{Fitness}={\displaystyle \frac{{\displaystyle \sum _{i=1}^n{q}_i\left(q_{gi}\right)}}{Q_{\mathrm{SumMax}}}}\\ Q_{gTotal}={\displaystyle \sum _{i=1}^n{q}_{gi}}\\ q_{critical}-q_{gpro}=q_{gi\mathrm{m}\mathrm{i}\mathrm{n}}\le q_{gi}\le q_{gi\mathrm{m}\mathrm{a}\mathrm{x}}\\ p_s=P_s\end{array}\right.$$

(1)

In the formula, $q_{critical}$ is the critical liquid-carrying flow rate, 10⁴ m³/d; $q_{gpro}$ is the gas production rate of the gas well, 10⁴ m³/d; $q_{gi\mathrm{m}\mathrm{i}\mathrm{n}}$ is the minimum gas injection rate, 10⁴ m³/d; $q_{gi\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum gas injection rate, 10⁴ m³/d; $P_s$ is the set separator pressure, MPa; $p_s$ is the separation device pressure, MPa; $Q_{gTotal}$ is the total gas distribution rate, 10⁴ m³/d; $q_{gi}$ is the gas distribution rate (gas injection rate) of each well, 10⁴ m³/d; $q_i\left(q_{gi}\right)$ is the corresponding gas production rate of each well under the gas injection rate (excluding gas injection rate), 10⁴ m³/d; $Q_{\mathrm{SumMax}}$ is the total maximum limit gas production rate, 10⁴ m³/d; $Des{t}_{Fitness}$ is the target fitness (dimensionless).

2.2.2. Basic Calculations

(1)

Critical liquid-carrying flow calculation model

A commonly used droplet model is used to calculate the critical liquid-carrying flow rate of a gas well. Taking the Li Min method as an example, the calculation model is as follows:

$${\mathrm{V}}_c = 2.5{\left({\displaystyle \frac{({\rho }_1-{\rho }_g)\sigma }{{{\rho }_g}^2}}\right)}^{0.25}$$

(2)

In the formula, ${\mathrm{V}}_c$—critical liquid-carrying flow rate, m/s; ${\rho }_1$—density of liquid, kg/m³; ${\rho }_g$—natural gas density, kg/m³; $\sigma$—gas–liquid surface tension, N/m.

The calculation formula for the critical liquid-carrying flow rate of the droplet model is

$${\mathrm{q}}_c=2.5\times {10}^8{\displaystyle \frac{Ap{V}_c}{ZT}}$$

(3)

In the formula, $q_c$—critical liquid carrying flow rate, m³/d; ${\mathrm{V}}_c$—critical liquid-carrying flow velocity, m/s; A—cross-sectional area of oil pipe, m²; P—pressure, MPa; T—temperature, K; Z—gas compression factor under conditions of T and p.

When the gas production of the gas well is less than the critical liquid-carrying flow rate, it is considered that liquid accumulation will occur in the gas well. To simplify the consideration, it is assumed that the accumulated liquid will be discharged quickly after continuous gas lift injection and the impact of the platform system caused by the liquid accumulation process will be ignored. Then, it is necessary to supplement at least the minimum gas rate required for the total gas production to reach the critical liquid-carrying flow rate. If the gas injection rate is too high, the gas injection rate can be increased appropriately based on the optimized gas distribution results of the well group.

(2)

Performance calculation of gas well inflow

The inflow performance of a gas well can be described by the gas production index, the liquid production index and liquid-gas ratio, or by the gas production index and liquid production index. This article chooses the liquid production index and liquid–gas ratio to describe the performance. The specific equation is

$$Q_L=J\cdot (p_r-p_{wf})$$

(4)

In the formula, $p_r$—formation static pressure, MPa; $Q_L$—gas well liquid production, m³/d; $p_{wf}$—bottom flow pressure, MPa; $J$—gas well liquid production index, m³/d/MPa.

The gas production is

$$Q_g=Q_l/LGR$$

(5)

In the formula, $Q_g$—gas production rate of gas well, m³/d. $LGR$—gas well output liquid–gas ratio, m³/m³.

(3)

Gas well gas lift performance curve

As shown in Figure 2 below, the gas lift performance curve of the gas well’s continuous gas lift gas production is drawn based on the gas well parameters. When the gas injection rate increases, the bottom hole flow pressure decreases. In this process, the gas well gas production rate also increases, so the decrease in bottom hole flow pressure is also due to the increase in gas production. Therefore, it is necessary to iteratively solve the final coordinated bottomhole flow pressure and gas production.

2.3. Optimization Algorithm

In order to solve the above model, the particle swarm optimization algorithm (PSO) is used for optimization. The generated gas distribution plan for multiple wells on the platform is one of the particles, which is optimized according to the particle swarm optimization algorithm. The optimization method is shown in Figure 3 below. According to the inflow performance parameters and wellbore structure configuration, the gas lift performance curve under different wellhead oil pressures can be calculated. Based on the surface pipeline network configuration parameters, the corresponding outflow performances under coordinated wellhead oil pressures can be calculated for each well.

The most critical calculation is the calculation of the fitness of each particle. The calculation method of particle fitness is as follows:

The corresponding gas production and liquid production under the gas injection rate of each well, considering the mutual interference between gas lift wells, can be solved by using the gas lift performance curve according to the principle of node analysis. For example, assume there is a gas lift well production system consisting of n wells and a separator, as shown in Figure 4.

Considering surface gathering and transportation pipelines, there is mutual interference between wells. The separator pressure is constant as a boundary condition. When the surface gathering and transportation pipeline pressure fluctuates, it will affect the gas production and liquid production of the gas well. The relationship can be represented by the relationship curve between wellhead pressure and gas production under different gas injection rates, as shown in Figure 5. According to the principle of node analysis, this curve is the inflow curve with the wellhead as the node.

For a system, according to its flow method, its output aggregation process is calculated as follows:

(1)

Draw the inflow curve of each well with the wellhead as the node under different gas injection rates.

(2)

For any solution ($q_{g1}$, $q_{g2}$,..., $q_{gn}$), use the interpolation method to find the wellhead inflow curve of each gas lift well. The fluid at node A comes from wells 1 and 2. For well 1, take a series of points on the inflow curve, calculate to node A according to the multiphase pipe flow theory and obtain the inflow curve of well 1 for node A. In the same way, the inflow curve of well 2 to node A can be obtained, as shown in Figure 6.

(3)

When the pressure of node A is P_Ai, the gas flow rates q_1i and q_2i of well 1 and well 2 flowing into node A can be obtained from Figure 6. The gas rate of node A is q_Ai = q_1i + q_2i. In this way, a series of (P_A1, q_A1), (P_A2, q_A2)... (P_Am, q_Am) can be obtained. That is, the inflow curve of node A is obtained. See Figure 7.

(4)

According to the above method, the inflow curve of each node and the inflow curve with the separator as the node can be further obtained, as shown in Figure 8. According to the set separator pressure, the total gas production and liquid production can be obtained from the inflow curve of the separator. That is, the solution of the optimized gas distribution plan of the platform is divided by the maximum gas production of the system to obtain the fitness of the particle.

3. Example Calculation Analysis

3.1. Basic Parameters of the Platform

(1)

Ground pipe network parameters of the platform

Taking four wells on a platform in an oilfield as an example, the pipeline network connections and configuration parameters of the platform are shown in Figure 9 below.

(2)

Basic parameters of each well

The basic parameters of each well are shown in

Table 1. Basic parameters of each single well on the platform.

Well Name		Well 1	Well 2	Well 3	Well 4
Static pressure	MPa	20–34
Production gas index
Production liquid index or LGR
Oil pipe inner diameter	mm	62	62	62	62
Deep oil pipe	m	3967.78	3967.78	3976.36	4038.54
Casing inner diameter	mm	114.3	114.3	114.3	114.3
Formation temperature	°C	142	141	140	40
Surface temperature	°C	15	15	15	15
Relative density of formation water	-	1.02	1.02	0	0
Natural gas relative density	-	0.7	0.7	0	0
Wellhead oil pressure	MPa	1.7	1.65	1.64	1.66
Wellhead casing pressure	MPa	2.49	2.44	2.41	2.86
Gas production rate	m3/d	27,710	13,085	16,164	20,013
Liquid production rate	m3/d	1	1	1	2

below.

3.2. Basic Calculations

(1)

Calculation of bottom hole flow pressure of each well

The bottom hole flow pressure is predicted based on the production parameters (wellhead oil pressure, liquid production rate and liquid–gas ratio) as follows (Figure 10, Figure 11, Figure 12 and Figure 13).

(2)

Calculation of gas production index of each well

The well gas production index is fitted according to the bottom hole flow pressure and gas production rate as follows (Figure 14, Figure 15, Figure 16 and Figure 17).

(3)

Gas lift performance curve drawing

Based on the above single well parameters, the gas lift performance curves under different gas injection rates and gas injection pressure conditions are drawn as follows (Figure 18, Figure 19, Figure 20 and Figure 21).

3.3. Optimize Calculation Results

The particle swarm algorithm is used to optimize based on the established model and set parameters. The separator pressure is 0.5 MPa. The simulation results are shown in Figure 22 and

Table 2. Simulation calculation of optimized gas distribution for circulating gas lift of four wells.

Well Name	Pressure of Wellhead/MPa	Injection Gas Rate/103 m3/d	Production Gas Rate (Excluding Injection Gas Rate)/103 m3/d
Well1	1.1746	1	28.813
Well2	1.1754	1	14.258
Well3	1.1758	2	17.455
Well4	1.1757	3	20.873

below. It can be seen that compared with the total gas production without gas injection (Table 1), the gas production increases in a manner close to the optimal gas distribution, the overall production efficiency is significantly improved and the optimization goal is achieved. From the results, it can be seen that the wellhead pressure varies among different wells, but, due to the close distance, the production of liquid and gas is not particularly high, so the difference in the wellhead oil pressure is not significant.

4. Conclusions

Because of the centralized management of all platforms by the field information center at present, there is a large amount of real-time processing information for each well and achieving synchronous and rapid real-time processing for each well in the optimization calculation is challenging. Therefore, the oilfield is trying to use the platform as a terminal, installing information processing equipment and only optimizing the platform’s own wells. This greatly reduces the amount of information, commonly known as edge computing. However, there are still many issues that need to be studied. Therefore, this paper proposes an optimized gas distribution and liquid drainage method suitable for the continuous gas lift of multiple wells on a platform.

First, a dynamic optimization model of the multi-well production system on the platform is established and then the particle swarm algorithm is used to solve the problem. Calculations through examples show that this method can improve the efficiency of optimized gas distribution of platform gas wells. Taking into account the interference between wells, optimization can improve the production efficiency of gas wells, reduce production costs and provide good support for the sustainable development of oil and gas fields.