Optimization Algorithm and Genetic Coding Method for an Oilfield Development Plan Considering Production Constraints

Abstract

For heterogeneous reservoirs that develop due to water flooding, the increased degree of flooding will cause unbalanced displacement, and there are large areas of residual oil enrichment in the reservoir. In this paper, a genetic coding method for oilfield development plan optimization that considers production constraints is proposed. This method considers the constraints of well location, oil and water well type, the open horizon and its combination, water injection volume, and the liquid production index in the actual oilfield development design. On the basis of genetic algorithms and the individual quality inspection method, a program for regulating and optimizing the overall development index of reservoirs was developed. A comprehensive optimization calculation was carried out for the H block. In the process of executing the algorithm, invalid schemes of 16.6–20.2% were eliminated, crude oil recovery increased by 5.56%, and the water cut decreased by 1.81%. The research results show that, compared with a conventional oil and water well production and development plan for an oilfield, this program can greatly improve efficiency and promote the automatic optimization of the overall development index of the reservoir, which is in line with the actual situation of the oilfield.

1. Introduction

After entering the stage of high water cut development in water drive reservoirs, due to the difference in reservoir conditions, the deterioration of well conditions in the production process, and the implementation of a large number of reservoir reconstruction measures, problems such as a lack of improvement in injection production well networks, poor reserve control, severe interlayer interference, and large interlayer differences have been caused, with little oil remaining in the layers and contiguous zones [1,2,3,4]. There are significant differences in reservoir development effects, and the remaining oil in the reservoir exhibits local accumulation characteristics. This requires an adjustment and optimization of the development plan to achieve the goal of improving water drive control and balanced displacement.

The optimization of a block development plan is the research focus of development geology and oil and gas reservoir engineering. Conventional reservoir development plan optimization is based on reservoir engineering and numerical simulation methods combined with the current situation and experience of the block through manual analysis and continuous testing to find the optimal index. Therefore, many scholars solve this kind of problem by introducing intelligent optimization algorithms. Hageman et al. proposed a method combining the genetic algorithm with tabu search to improve the genetic algorithm, which enhanced the local search ability, but its timeliness was poor [5]. The optimization results of the algorithm proposed by Sarma et al. are more difficult to implement than the construction capacity highlighted in this study [6,7]. The disadvantage of the optimization algorithm proposed by Kumar et al. is that it finds the optimal solution locally [8]. Zhao et al. proposed the use of Latin hypercube sampling and axial orthogonal importance sampling as a finite sample data optimization method, but the calculation time was short and the accuracy was low [9]. Shukla et al. used binary coding in genetic algorithms to select feature subsets, which is difficult to accurately achieve [10]. At present, research on optimization methods for development plans generally focus on the optimization of a single development index, such as well location or liquid production, while the actual reservoir development indices are systematic, interrelated, and influenced by each other. A singular or a few indicators cannot be used as a factor to evaluate the overall displacement effect of the reservoir. The degree of displacement in different areas of the reservoir is different, and the oil saturation is different. It cannot guarantee the balance of displacement in the development process, which will make the remaining oil more dispersed and increase the degree of unbalanced displacement [11,12,13,14,15,16]. The actual developmental effect of oil fields is influenced by various factors.

This article takes the well location, oil and water well type, open layer and its combination, water injection rate, and liquid production rate as constraints and takes parameters, such as cumulative oil production, recovery degree, and comprehensive water content ratio, as objective functions. An “individual quality inspection” method is proposed to address the problems of slow convergence, a large number of solutions, and noncompliance with actual situations in traditional genetic algorithms. Based on the individual quality inspection, the genetic algorithm is improved. A genetic algorithm is used to generate the plan, and numerical simulation methods are used to calculate the objective function. A genetic algorithm is established to optimize oil field development plans considering production constraints. Coding methods for different indicator types and coding combinations for the overall plan are developed. Based on the completed history matching model of the H block, the automatic optimization scheme is generated, and the optimal development scheme is obtained by combining numerical simulation analyses.

2. Genetic Algorithm for Oilfield Development Plan Optimization Considering Production Constraints

The development optimization problems of water-flooding reservoirs must adopt an optimization solution [17,18,19]. Firstly, determine the variable system, establish a calculation model according to the mathematical and physical relationship between the objective function and the variables, and then set constraint conditions based on the actual situation of the field. Finally, comprehensively establish an mathematical optimization model. The variables that affect reservoir development are diverse and mutually influential. For example, the well location variable is a multidimensional array type, the production and injection well type is an integer type, and the solution space of water injection and liquid production is a continuous real number. Therefore, an optimization algorithm compatible with a multi-type variable system is needed to solve the optimization problem of oilfield development plans.

A genetic algorithm is a global optimization algorithm established by simulating the genetic and evolutionary processes of organisms in nature. Starting from a set of randomly generated solutions, dominant individuals are selected in the iterative process, and the individual dominant genes are transmitted to the next set of solutions through genetic operations. The genetic process is repeated until the solution that meets the correct conditions is obtained [20,21,22,23]. Unlike other traditional methods, genetic algorithms do not search from a single point; rather, they search from multiple points. Each iteration calculates all the individuals simultaneously. When the global optimal solution is very complex, the parallel operation search speed is fast, which may generate many local optima. In this case, the genetic algorithm can use its advantages to find the global optimal solution to the problem. A genetic algorithm is applied to the optimization of oilfield development. A specific single development plan can be used for a genetic individual. A group of development plans forms a population. A computer program is used to call the numerical simulation black oil model to simulate the prediction result as the objective function. The genetic algebra or convergence precision condition is set as the termination condition of the genetic cycle.

Over a long period of development, engineers can gain a clear understanding of the injection–production well pattern, reserve control, inter-well and inter-layer interferences, and reservoir residual oil enrichment in water-flooding reservoirs [24,25]. Transforming the understanding of the expert system into constraints can effectively combine the algorithm with the current research results. For example, the upper limit of the production capacity is limited by the level of oil production technology; the maximum value of water injection is limited by water source conditions; and the new drilling deployment area is limited by the degree of well network perfection. In addition, if the plan parameters are not limited, the unrealistic variable values generated in the genetic process will significantly increase the computational complexity of the objective function-solving process. If the genetic generation plan includes two wells with very small well spacing or wells located at the boundary of the work area, this will increase the risk of convergence problems in the numerical simulation, resulting in more calculations and a longer calculation time.

To meet the actual application conditions of the mine, these production constraints are incorporated into the optimization process of the development plan. This article improves the classic genetic algorithm by adding the ‘individual quality inspection’ process to the classical genetic algorithm, and an oilfield development plan optimization algorithm and genetic coding method considering production constraints are established. Whether it is in the generation of the initial individual or the subsequent cross-mutation to generate new individuals, the individual quality test is performed on the new individuals; that is, to check whether the new individuals meet the production constraints. If they are not met, the genetic process enters the previous step until the individuals that meet the constraints are generated. By introducing the individual quality inspection process, the following roles are implemented: 1. the convergence risk during the objective function-solving process is reduced, and computational efficiency is improved. 2. By pre-excluding some incompatible individuals, the optimization time is shortened. 3. The currently existing research results and knowledge are effectively combined. The oilfield development plan optimization algorithm and genetic coding method considering production constraints can be expressed as follows:

IGA = (C, F, P_i, S, ϕ, C₀, M₀, K, T),

(1)

where C is the individual coding plan, F is the individual fitness evaluation function, P0 is the initial population, S is the population size, ϕ is the selection operator, C₀ is the crossover operator, M₀ is the mutation operator, K is the individual quality inspection, and T is the termination condition of the genetic algorithm.

The process of the oilfield development plan optimization algorithm and genetic coding method considering production constraints is shown in Figure 1. The implementation steps for specific reservoir optimization problems are as follows:

(1) Under the production constraints, a certain number of initial plans are generated, which form the initial plan group.

A single development plan is an individual. In the plan, well location, production and injection well type, the open horizon and its combination, water injection, and liquid production rate are involved in genetic coding as parameter systems. The initial plan group is used as the initial population.

(2) The numerical simulation is called the black oil model prediction plan.

By calling the numerical simulation the black oil model, the prediction of a single plan is completed. The prediction results are regarded as individual fitness, and the simulation results of all plans in the plan group are regarded as population fitness.

(3) The next set of plans is generated through genetic operations.

The genetic manipulation of the well points includes selection, crossover, and mutation. According to the type of production constraints, the constraints that limit the types of production and injection wells are reflected in the genetic operation process rather than the individual quality inspection process. For example, the production constraints mean that the type of production and injection wells cannot be changed. In the process of crossover and mutation, the gene sequence that characterizes the current well type remains unchanged in genetic operations.

The genetic selection operation process adopts the proportional selection method. By analyzing the simulation prediction results of each plan, the better the prediction index, the greater the probability that the plan is selected to participate in the heredity. The calculation formula for the probability of scheme selection is as follows:

$$P_{\mathrm{i}}=\frac{{\mathrm{f}}_{\mathrm{i}}}{{\displaystyle \sum _{K=1}^M{\mathrm{f}}_{\mathrm{k}}}},$$

(2)

where M is the number of plans; f_i is the prediction result of plan i.

The crossover operation provides two different options: single-point crossover and multi-point crossover. Considering the production constraints, the crossover point is generated outside the frozen gene sequence, and the frozen gene sequence remains unchanged during the crossover operation.

The purpose of the mutation operation is to give the individual a random disturbance so that the individual has a certain probability of jumping out of the local optimum. Like the crossover process, the genes that require freezing under production constraints do not participate in the mutation.

(4) Individual quality inspection.

If the genetic algebra is set to N and the population size of each generation is M, a total of M × N prediction plans are simulated. The larger the value of M, the more likely it is to avoid falling into the local optimum. The larger the value of N, the more likely it is to ensure the accuracy of the optimization results, but this will lead to a large number of calculations. At the same time, unreasonable plans will lead to a large number of convergence problems in the process of calling numerical simulation prediction, resulting in a large number of invalid calculations and unreliable prediction results. By introducing the individual quality inspection process, individuals who meet the production constraints will participate in the next generation of genetic operations, which greatly reduces the amount of calculation without affecting the optimal solution.

For the production constraint system, including well location, production and injection well type, open layer and its combination, water injection, and liquid production index, individual quality inspection is reflected in the following aspects:

The requirements for well location are as follows: 1. To meet the set of new drilling or old well conditions, the new drilling well location is variable; the old well location is not variable. 2. The well location is within the scope of the reservoir. 3. In the plan, the well spacing between all wells and adjacent wells meets the given well spacing range.

The requirements for the type of well are as follows: Meet the requirements of the plan for the specified type of injector or productor wells.

The requirements for the open horizon and its combination are as follows: 1. To meet the setting of the specified open horizon of the well. 2. To meet the open horizon in the reservoir range.

The requirements for water injection rate and liquid rate indicators are as follows: 1. The value of a single-well water injection rate or liquid rate is within the scope of the program requirements. 2. The water injection or liquid production value of the well group or the whole area is within the range required by the plan. 3. The water injection rate and liquid rate in the whole area meet the special setting of injection–production balance in the plan.

(5) Stopping condition.

The operation of the algorithm is terminated when it reaches any of the following conditions: when it achieves a given number of evolutions; when the variables in the plan group are similar; and when the prediction results of each plan are close.

(6) Decoding.

After the algorithm reaches the termination condition, it reads the saved optimal plan encoding and enters the decoding program. Then, the black oil model is called again to calculate the decoded plan, and the optimal plan prediction data are obtained.

3. Processing of Production Constraint Problem

3.1. Characterization of Constraints

In the process of individual quality inspection, the individuals who meet the production constraints are classified as effective. When all individuals in the population are classified as effective individuals, the population becomes effective. When production constraints require the parameters in the variable system to be frozen, they remain unchanged and cannot be randomly generated. If the parameters are variable, these parameters are generated by genetic operations within the production constraints. If the production constraints contain m variables and n constraints, the constraints of the optimization model can be expressed as follows:

$$f_i\left(r\right)\le 0,i=1,2,\dots ,m,$$

(3)

$$r=\left(r_1,r_2,\dots ,r_n\right)\in R,$$

(4)

$$R=\{\left(r_1,r_2,\dots ,r_m\right)\mid a_i\le r_i\le n_i,i=1,2,\dots ,m\},$$

(5)

$$MA=\left(a_1,a_2,\dots ,a_m\right),$$

(6)

$$MI=\left(n_1,n_2,\dots ,n_m\right),$$

(7)

where R is the solution space; MA and MI are the bounds of the variables.

3.2. Effect of Crossover Operator Base on Production Constraints

The production constraints mentioned in this paper can be divided into two types. One is the explicitly specified parameter values. The values of such parameters are fixed throughout the genetic process and can be regarded as genes frozen during the crossover process. Secondly, the range of parameters is specified. The values of such parameters can be generated by genetic processes, but they are required to be within the correct range and can be regarded as genetically variable during the crossover process. The crossover operation is an important part of the genetic process. The crossover operator of the classical genetic algorithm randomly generates crossover points in all individual gene sequences. In the design of the OOCP crossover operator, the crossover points are generated outside the frozen gene sequence, and the frozen gene sequence remains unchanged in the crossover operation.

For example, Well A and Well B are two wells that have been put into production in the reservoir. The plan means that the type and well location of these two wells remain unchanged during the adjustment process. Then, the crossover operator is only generated in the variable gene sequence during the execution process, and the crossover process is only performed in the variable gene segment. The gene coding fragments of the two example plans are shown in

Table 1. The gene coding fragments of the example plans.

	Well A			Well B
	Production Well or Injector Tag	Location	Production	Production Well or Injector Tag	Location	Production
Plan I gene fragment	01	101001	10010	01	101010	01001
Plan II gene fragment	01	101101	11001	01	100111	10100
Gene fragment status	Freezed	Freezed	Unfreezed	Freezed	Freezed	Unfreezed

.

The execution process of the gene fragment crossover operator of Well A and Well B in Plan I and Plan II is shown in Figure 2. In the previous generation, the gene fragments determining the type and location of wells were frozen, and the crossover points were only generated in the gene fragments that determine the variable production allocation index; only the variable gene fragments were involved in the crossover operation.

4. Genetic Coding Types

The deployment of adjustment wells, the open layer and its combination, the design of the production rate, and the water injection rate are the key points of the oilfield development adjustment plan. OOCP is based on the accurate coding of actual events. The following process is used to complete the coding process for the oilfield development plan: 1. Understand the reservoir object of the study and clarify the current situation and existing problems of reservoir development. 2. Analyze the factors that affect reservoir development and establish a variable system. 3. Select the appropriate coding method according to the numerical characteristics of the characterization variables. 4. Unify the coding combination of the variable system and establish individual plan coding. The coding process is shown in Figure 3. The program uses the C # language and is implemented using Visual Studio 2019. The required basic data comprise a model that has completed history matching. This model is compatible with the Eclipse reservoir model data format.

5. Example

5.1. Reservoir Profile

Taking an actual reservoir as an example, the optimization test of the adjustment plan is carried out. Figure 4 shows the remaining oil saturation distribution of the numerical model of the H2 reservoir work area. The plane grid number of the numerical simulation model of the H2 reservoir is NX = 153, NY = 136, with one layer in the longitudinal direction; the step size of the plane mesh is DX = DY = 10 m. From January 2003 to June 2022, the geological reserves of the reservoir were 32.16 × 10⁴ t. The average porosity of the model is 0.164, and the average permeability is 120 × 10⁻³ µm². The average injection–production well spacing is 600 m, and the area is 2 million square meters. At present, there are five oil wells and three water injection wells in the block. The current production parameters are shown in

Table 2. The current production mode parameters of the block.

Well Number	Well Type	Oil Rate (m3/d)	Water Rate (m3/d)	Water Injection Rate (m3/d)
H2-5	Production well	0.6	10.6	0
H9X-5	Production well	1.2	13.4	0
H2-8	Production well	1.2	12.3	0
H2-12	Production well	2.7	0.7	0
H2X-13	Production well	1.2	6	0
H2X-1	Injection well	0	0	21
H2X-2	Injection well	0	0	10
H2-6	Injection well	0	0	10

. A computer program to realize OOCP is compiled. Firstly, the program is designed according to the variable system to realize the genetic coding and decoding of the plan. The next-generation population is generated according to the genetic rules of the algorithm, and the black oil model is called to complete the plan prediction and the calculation of the objective function.

5.2. Plan Design and Prediction

Six development plans are prepared for this area: Plan 1 maintains the current status of the reservoir. Plan 2 adopts the method of manual analysis and deployment. Through the reservoir engineering analysis, two oil wells and one crystal are deployed, and the well location coordinates of each well are determined. Additionally, a plan to optimize the injection and production parameters of five old wells through dynamic analysis is established. Plans 3–6 are optimized by OOCP, and the five old wells and three new wells deployed in Plan 2 are optimized as a whole. Different well location and well type constraints are set for each plan. Plan 3 limits the well types of new and old wells, while Plan 4 only limits the well types of new wells, Plan 5 only limits the well types of old wells, and Plan 6 does not limit all well types. At the same time, according to the reservoir development history, the water injection rate of a single well is limited to no more than 20 m³/d, and the liquid production rate of a single well is limited to no more than 30 m³/d. The detailed parameter setting table for the adjustment plan is shown in

Table 3. Plan parameter adjustment comparison table.

Plan	New Well	Old Well	New Well Location	New Well Type	Old Well Type	Perforating Parameter	Injection–Production Parameters
1	None	None	None	None	None	Unchanged	Unchanged
2	Three wells	Five wells	Areal pattern	Two injection wells	Three injection wells	Manual adjustment	Manual adjustment
3	Three wells	Five wells	By artificial	1 production well	Two production wells	OOCP 1- Optimization	OOCP- Optimization
4	Three wells	Five wells	OOCP-Optimization	Two injection wells	Three injection wells	OOCP- Optimization	OOCP- Optimization
5	Three wells	Five wells	OOCP- Optimization	One production well	Two production wells	OOCP- Optimization	OOCP- Optimization
6	Three wells	Five wells	OOCP- Optimization	Two injection wells	OOCP- Optimization	OOCP- Optimization	OOCP- Optimization

¹ OOCP: Optimization algorithm of oilfield development plan considering production constraints.

.

The constraint conditions of the algorithm are inputted by the calculation program. In the process of program execution, in addition to inputting the parameter system, constraint conditions, termination conditions, and other information related to the optimization plan, it is also necessary to set the calculation parameters related to the genetic algorithm, such as the selection of genetic operators, mutation probability, crossover mode, the number of crossover points, etc. These parameters are entered through the program interface.

Plan 1 and Plan 2 are directly predicted using numerical simulation as a non-adjustment plan and an artificial optimization plan, respectively, as a comparison reference. The OOCP program is used to perform automatic optimization in the input algorithm program of Plans 3–6, and the cumulative oil production of the block is used as the fitness index. The statistical results of the parameters performed by the program are shown in

Table 4. Algebra and fitness of an optimal individual in Plans 3–6.

Plan	Total Number of Invalid Individuals	Algebra of Optimal Individual	Fitness of Optimal Individual
3	415	3	180,300
4	463	23	184,200
5	478	47	183,700
6	506	14	183,900

. The optimal parameters of Plans 3–6 after genetic optimization are decoded, the numerical simulation module is called to complete the prediction, and the prediction data of all six plans are obtained.

5.3. Analysis of the Effect

The following section will analyze and discuss the results from two aspects: execution efficiency and production effect. In terms of execution efficiency, the total number of individuals in each plan from Plans 3 to 6 is 2500, and the total number of invalid individuals is between 415 and 516, which indicates that the invalid plan of 16.6–20.2% is filtered out using the method of production constraints, which greatly reduces the simulation workload. Considering the convergence problem that may be caused by the participation of invalid plans, the computational efficiency of this method may be higher.

In terms of the production effect, from the perspective of the final recovery degree of each plan, when optimizing the reservoir development plan, it is not only necessary to consider the recovery degree of crude oil but also the utilization rate of water injection. As shown in Figure 5, among the six prediction plans, the final recovery degree of the unadjusted plan is 46.8% (Plan 1). The final recovery degree of the plan optimized by OOCP is 2% (Plan 3) and 3% (Plans 4–6) higher than that of the unadjusted plan, respectively. The predicted recovery degree of Plans 4–6 is 1.1% higher than that of manual optimization (Plan 2). In fact, this advantage is more obvious in the early stages of the implementation of the program (fifth to tenth years). From the ratio curve of the water content and the recovery degree of each plan, as shown in Figure 6, the water content of Plans 3–6 is lower than that of Plans 1–2 under the same recovery degree. Among them, the manual optimization plan (Plan 2) experiences a phenomenon where the water content rises rapidly in a short time after a sharp decline when the crude oil recovery is 0.422. The reason for this is the reduced water content. After an expert analysis, a production well with a water content exceeding 0.95 was closed. Although it has a certain effect on reducing the water content, it still was not able to achieve the desired effect. Plan 3 and Plan 5 did not produce significant fluctuations, and the overall trend was relatively stable. Combined with the decrease in the water cut, the optimal scheme is Plan 5, which is shown in Figure 5 and Figure 6. These figures show that OOCP optimization can effectively improve the cumulative yield and reduce the water content, which is also better than the manual optimization method.

6. Conclusions

• Through the analysis of the constraints of the key indicators affecting the development effect of water-flooding reservoirs, the coding process and the coding combination of reservoir development plans, which can be used as the basic coding method for the optimization of multivariate development plans, were proposed.
• An individual quality test method is proposed to solve the practical constraints in the optimization process and realize the control of multiple constraints in the genetic process.
• An optimization algorithm for the oilfield development scheme considering production constraints is established. In the process of algorithm execution, 16.6–20.2% of invalid schemes are eliminated using the individual quality inspection method, which greatly reduces the number of calculations. The crude oil recovery rate improves by 5.56%, and the water content is reduced by 1.81%. Based on the algorithm, the calculation program can realize the automatic optimization of the reservoir block development plan.