Automatic History Matching Method and Application of Artificial Intelligence for Fractured-Porous Carbonate Reservoirs

Abstract

Fractured-porous carbonate reservoirs, mainly composed of dolomites and crystalline rocks with various rock types and extremely poor initial porosity and permeability, are dominated by tectonic fractures and exhibit extreme heterogeneity. The fracture system plays a predominant role in hydrocarbon fluid transport. Compared with conventional sandstone reservoirs, fracture geometry and topological structure parameters are key factors for the accuracy and computational efficiency of numerical simulation history matching in fractured reservoirs. To address the matching issue, this paper introduces an artificial intelligence history matching method combining the Monte Carlo experimental planning method with an artificial neural network and a particle swarm optimization algorithm. Taking reservoir geological parameters and phase infiltration properties as the objective function, this method performs reservoir production history matching to correct the geological model. Through case studies, it is verified that this method can accurately correct the geological model of fractured-porous reservoirs and match the observed production data. This research represents a collaborative effort among multiple disciplines, integrating advanced algorithms and geological knowledge with the expertise of computer scientists, geologists, and engineers. Currently the world’s major oilfields history fitting is mainly based on reservoir engineers’ experience to fit; the method is applicable to major oilfields, but the fitting accuracy and fitting efficiency is severely limited, the fitting accuracy is less than 75%, while the artificial intelligence history fitting method shows a stronger applicability; intelligent history fitting is mainly based on the integrity of the field data, and as far as the theory is concerned, the accuracy of the intelligent history fitting can be up to 100%. Therefore, AI history fitting can provide a significant foundation for mine field research. Future research could further explore interdisciplinary collaboration to address other challenges in reservoir characterization and management.

1. Introduction

According to statistics, the global oil and gas reserves of fractured-porous reservoirs are 248 × 10⁸ t and natural gas reserves are 2681 × 10⁸ m³ [1]. The matrix of fractured-porous carbonate reservoirs, which are dominated by dolomite and metamorphic rocks, is dense and basically non-porous, and tectonic fractures and accompanying dissolution pores constitute the main storage space for hydrocarbons such as oil and gas, and the artificial compression fractures and natural fractures communicate with each other, which constitutes the main place for oil, gas, water, and other fluid transportation in the fractured-porous reservoirs. Artificial fractures and natural fractures communicate with each other, constituting the main place for oil, gas, water, and other fluid transport in fractured-porous reservoirs. According to Bratton [2] and Keith Schonberger’s [3] fractured reservoir division scheme, the fractured-porous reservoir belongs to class I, where fractures serve as both spaces for storing hydrocarbons and as the main channel for fluid flow during oil and gas extraction, making this a determining factor for reservoirs with industrial exploitation value. Under the combination of rock type, mineral composition, geomechanics and tectonic curvature, the reservoir fracture system shows remarkable randomness, complexity and multi-scale characteristics in spatial distribution, connectivity and topology.

Production history matching in the numerical simulation of reservoirs was an important part of correcting the geological model, reducing the uncertainty of geological understanding and thus improving the prediction accuracy. Therefore, selecting a fractured reservoir numerical model that meets the geological conditions and seepage patterns was the basis for ensuring the accuracy of history matching in this type of reservoir [4]. At present, the more mature fracture medium models mainly include the equivalent continuous medium model, dual medium model, discrete fracture model and embedded discrete fracture model [5]. Currently, the history fitting of fractured reservoirs is limited by two major aspects, namely, the accuracy of the fracture system portrayal and the accuracy of fluid description, and the traditional history fitting methods are mostly aimed at the correction of fracture permeability, and the correction is mostly based on the empirical method. With the advancement of geophysical and drilling technologies, the acquisition of fracture data is easier, and it is crucial to carry out intelligent fitting.

Compared with conventional sandstone reservoirs, fractured reservoirs are more heterogeneous. In particular, the stochastic and multi-scale characteristics of fracture development in reservoirs lead to poor convergence and more uncertain parameters in numerical solutions. The traditional manual parameter matching guided by experts’ experience is inefficient and the index matching error could not be quantitatively predetermined, which led to low computational efficiency and poor accuracy. Automatic history matching technology can not only greatly improve its matching efficiency but also reduce the intervention of human subjective factors and provide an accurate and quantitative description of the matching effect. It has been the focus of many researchers in the past. The rise in artificial intelligence algorithms such as machine learning has provided new solution ideas for solving the complex nonlinear process of oil and gas reservoir development and has been successfully applied in the field of exploration and development, such as seismic inversion, fracture identification, well logging interpretation, production capacity prediction, and residual oil characterization. Jung et al. [6] (2017), in response to the problem of matching the description of reservoir parameters for different types of fluvial reservoirs, proposed a method based on the Comprehensive Kalman filter method to match the reservoir production relations of the new matching description method. Smith et al. [7] (2021) proposed a new parameter optimization method based on deep learning for the current complex reservoir model, which relied heavily on the Kalman filter method of the phase model history matching technology to improve the accuracy of history fitting. Zhang et al. [8] (2020) proposed a deep learning automatic history matching method based on ensemble smoothing for large-scale inversion modeling of reservoirs with complex geological conditions and applied it to fluvial reservoirs with complex geometries. Sun et al. [9] (2021) proposed a new crack opening prediction algorithm based on an integrated learning algorithm by taking the fracture parameters of core observation, imaging logging, etc., as the training data and applied it to a fractured oil reservoir. Anne et al. proposed an integrated learning method based on the Kalman filtering method to improve the history matching accuracy of a fractured reservoir. Anirbid et al. [10] (2022) analyzed and summarized the application of machine learning and artificial intelligence in the oil and gas industry for the many challenges of data analysis in the oil and gas field process and promoted the application of different machine learning methods in the field of oil and gas field development [11].

In this paper, we carried out research on the history matching of fractured-porous reservoirs. Based on the problems of poor accuracy and long processing times of history matching, we carried out research on the artificial intelligence history matching method. Innovatively, we adopted the Monte Carlo experimental planning method to randomly sample and combine the geological, phase flow, and other parameters of the orthorectified historical data. We used artificial neural network downscaling to optimize the main controlling factors, a particle swarm optimization algorithm to invert the historical data, and artificial neural network upscaling to restore the original parameters. Finally, we achieved the artificial intelligence automatic history matching of fractured-porous reservoirs. By restoring the original parameters, we obtained a high-precision geological model, which finally achieved the artificial intelligence automatic history matching for fractured-porous reservoirs.

2. Methodology

The history matching of reservoirs refers to the process of obtaining geological parameters required for the numerical simulation of reservoirs based on existing production data, well logging data, and other actual mineral data [12,13,14,15]. Compared with conventional reservoirs, the history matching of fractured-porous reservoirs is more complicated. To address this problem, this paper proposes an artificial intelligence history matching method based on the Monte Carlo experimental planning method combined with an artificial neural network and a particle swarm optimization algorithm.

2.1. Mathematical Model of Artificial Intelligence Automatic History Matching for Fractured-Porous Reservoir

Fractured-porous reservoirs are predominantly determined by the fracture system. Consequently, numerical simulation of such reservoirs mainly focuses on the fracture system. This study, which is based on the analysis of actual mine data, aims to establish a mathematical model relating the geological model parameters required for the numerical simulation of reservoirs to the real production data.

$$P_{real}=P_{sim}+\mathsf{\Delta }P$$

(1)

where P_real is the actual production data, m³/day; P_sim is the numerical simulation forecast data, m³/day; and ΔP is the error of production data, m³/day. (Production error values can be positive or negative.)

Figure 1 shows the complex fracture characteristics of fractured reservoirs. In the numerical simulation process, different parameters set within the geological model cause a significant deviation in production data. Therefore, this study focuses mainly on the physical properties of fractures. Through the intelligent history matching method, the preferred selection of parameters such as the nature of fracture pore permeability, openness, orientation, and dip angle was achieved. In this study, based on the Monte Carlo laboratory planning method combined with real data, several sets of geological models of fractured-porous reservoirs were randomly generated.

Length:

$$L=L_{\min }+random(L)\cdot (L_{\max }-L_{\min })$$

(2)

Fracture opening:

$$w=w_{\min }+random(w)\cdot (w_{\max }-w_{\min })$$

(3)

Fracture permeability is related to fracture opening:

$$K_f={\displaystyle \frac{w^2}{12}}$$

(4)

Towards:

$$\theta =0+random(\theta )\cdot (\pm 180°-0)$$

(5)

Inclination:

$$\alpha =0+random(\alpha )\cdot (\pm 180°-0)$$

(6)

Fracture density:

$${\rho }_l=0+random({\rho }_l)\cdot (\pm 180°-0)$$

(7)

where L_min and L_max are the known maximum and minimum fracture lengths, m; K_f is the fracture permeability, mD; w_min and w_max are the known fracture widths (opening), m; θ is the fracture strike (divided into two categories); α is for the fracture inclination, °; and ρ_l is the fracture density, with ρ_lmin and ρ_lmax as the known maximum and minimum unit densities of fracture, number/m.

Based on Figure 1 and Figure 2, there is some variability in the fracture system, and its dip orientation, etc., seriously affects reservoir development. Fractured-porous reservoirs are important for production and development. As there is an obvious difference between the fracture system and the porous medium, there are more obvious flow processes between the two. Thus, the physical parameters of the pore system also affect the accuracy of the fractured pore reservoir history matching. Therefore, this study also needs to invert the relevant physical properties of the matrix reservoir. The physical characteristics of the reservoir pore system can be well characterized based on core and logging techniques. Figure 2 shows the fracture variability combined with logging data to give the theory of stochasticity to carry out the parameter description.

$$K_m=K_{\min }+random(K)\cdot (K_{\max }-K_{\min })$$

(8)

$${\phi }_m={\phi }_{\min }+random(\phi )\cdot ({\phi }_{\max }-{\phi }_{\min })$$

(9)

where K_min and K_max are the known minimum and maximum permeability of bedrock, mD; and ${\phi }_{\min }$, ${\phi }_{\max }$ are the known minimum and maximum porosity, respectively.

In the process of the numerical simulation of a reservoir (fluid system), the properties of reservoir fluid also affect the accuracy of the history matching of the reservoir model. Therefore, this study also considers the relevant physical properties of fluid and conducts intelligent history matching based on the value of the end point of relative permeability, aiming to obtain the optimal fluid parameters.

$$Sor=So{r}_{\min }+random(Sor)\cdot (So{r}_{\max }-So{r}_{\min })$$

(10)

$$Swc=Sw{c}_{\min }+random(Swc)\cdot (Sw{c}_{\max }-Sw{c}_{\min })$$

(11)

$$Swx=Sw{x}_{\min }+random(Swx)\cdot (Sw{x}_{\max }-Sw{x}_{\min })$$

(12)

where Sor, Swc, and Swx are fluid residual oil saturation, irreducible water saturation and isotonic point saturation, respectively; and S_min and S_max are the known minimum and maximum saturation, respectively.

Based on the analysis of relevant parameters obtained through a series of methods such as actual field seismic logging and drilling sampling, according to the variational inference theory [16,17,18], the relationship between reservoir production data and required geological parameters is as follows [19]:

$$\begin{array}{c}\ln p\left(x_i\right)=D_{KL}\left(q(z)\Vert p\left(z\mid x_i\right)\right)-{\displaystyle {\int }_{z}q}(z)\ln {\displaystyle \frac{q(z)}{p\left(z,x_i\right)}}dz=\\ D_{KL}\left(q(z)\Vert p\left(z\mid x_i\right)\right)+L(q(z))\end{array}$$

(13)

where x_i represents the reservoir production data; z represents the geological parameters and the end point value of fluid relative permeability; $p\left(z\mid x_i\right)$ is the posterior probability of production data x for geological parameter z; in which q(z) is $p\left(z\mid x_i\right)$ approximate replacement, which is used to solve the problem of high-dimensional density; and D_KL is divergence, which measures q(z) and $p\left(z\mid x_i\right)$. The difference between probabilities, and the greater the divergence, the more obvious the difference.

A probability distribution model based on Gaussian mixture model probabilities was developed to combine probability distribution and likelihood model solutions for reservoir geological models [20,21,22].

$$p\left(z\mid x_i\right)={\displaystyle \sum _{i=1}^N{\alpha }_i\varphi (x_i\mid z_i)}$$

(14)

where N is the number of Gaussian models, i = 1, 2, 3, …, k, …, N; ${\alpha }_k$ is the probability that the production data belong to the sub model—note ${\displaystyle \sum _{i=1}^N{\alpha }_i=1}$; $\varphi (x\mid z_k)$ Gaussian distribution density function, $z_k=({\mu }_k,{\sigma }_k^2)$, $z=({\mu }_k,{\sigma }_k,{\alpha }_k)$. Among them, ${\mu }_k,{\sigma }_k,{\alpha }_k$ are the expectation, covariance, and probability of sub model k, respectively.

According to the abovementioned Gaussian mixture model, the log-likelihood function is used to estimate the geological parameters and the value of end point z of the fluid permeability, and the expression of log-likelihood function and production data is constructed with the help of posterior probability [19]:

$$\log L(z)={\displaystyle \sum _{i=1}^N\log }P\left(x_i\mid z\right)={\displaystyle \sum _{i=1}^N\log }\left({\displaystyle \sum _{k=1}^N{\alpha }_i}\varphi \left(x\mid z_k\right)\right)$$

(15)

Note: In the formula, each sub model has a position, ${\mu }_k,{\sigma }_k,{\alpha }_k$, which needs to be solved by the iterative method.

2.2. Automated History Matching Method for Artificial Intelligence in Fracture-Porous Carbonate Reservoirs

Based on the complexity of the reservoir geological model, it is often necessary to obtain the reservoir geological parameters and fluid phase permeability parameters through a variety of testing and analytical methods, and the obtained parameters often have spatial variability, so it is difficult to accurately determine the physical parameters of the reservoir in the underground reservoir, which makes it difficult to meet the expected requirements for production matching [23]. Moreover, due to the complex geological and fluid properties of fractured-porous reservoirs, the deviation of numerical simulation results is large. In addition, the grid of reservoir geological models constructed by numerical simulation of reservoirs has reached the level of millions, and the grid of some complex reservoirs even reaches the level of tens of millions, which shows that the intelligent history matching is particularly important [24,25,26,27,28,29,30].

In this study, a composite artificial intelligence history matching method is proposed for the series of difficulties faced in history matching of fractured-porous reservoirs, which optimizes the matching based on the complex geological characteristics and phase infiltration properties of fractured-porous reservoirs, and ultimately meets the simulation requirements.

The matching process is divided into four main parts [30,31,32,33,34]:

① Firstly, incorporate the above variable parameters and input them into the numerical simulator, define the minimum variable level, randomly extract the forward production data with different parameters based on the Monte Carlo experimental planning method, set the minimum matching rate threshold, and determine and output the satisfied parameters and the corresponding intervals.

② Based on the above output parameters combined with the actual production data using an artificial neural network method for parameter dimensionality reduction processing and based on the type of input parameters, set the number of neurons in the hidden layer and the number of times of deep learning and other hyper-parameters and the final output of the high correlation parameter and nonlinear mapping relationship.

The above dimensionality reduction process is mainly based on the weights and influencing factors to realize the data iteratively; in addition, it is based on the artificial neural network system also realizing the data dimensionality in the above dimensionality reduction process in the implicit layer so it can obtain the nonlinear mapping relationship between the variables and variables, and variables and historical production data. Based on the dimensionality reduction in the obtained high correlation parameter and the nonlinear mapping relationship, it can be conducted to realize the parameter dimensionality and ultimately to obtain the data required by the geological model. This process is similar to the decoder and encoder process of the artificial neural network system, but the process is carried out in two steps [35]. As shown in Figure 3, the method mainly starts with dimensionality reduction followed by dimensionality enhancement to the same dimension.

The Monte Carlo experimental method is mainly a screening method for data analysis. After the data set is determined, screening excerpts are set, and the data are randomly screened based on the Monte Carlo method for the initial history fitting, and the fitting rate is assessed, which is mainly implemented to analyze each data and make clear the significance of each crack data, which is successively coordinated with the later analytical methods.

$$x,y\underset{\mathrm{decode}}{\stackrel{\mathrm{encode}}{\rightleftharpoons }}\widehat{x},y(x),x(\widehat{x})$$

(16)

where x is the input parameter; y is historical production data; $\widehat{x}$ is a high correlation parameter; y(x) is the nonlinear mapping relationship between input parameters and production data; and $x(\widehat{x})$ is the nonlinear mapping relationship between high correlation parameters and input parameters.

③ Based on the high correlation parameters combined with the particle swarm optimization algorithm, the optimal parameter solution is inversed, the initial population is divided according to the input high correlation parameters, and super parameters such as inertia weight, sociality and elasticity coefficient are defined. The position and speed of each particle are defined, then different particles are randomly selected for history matching, the matching rate is determined, the particles are updated, the lowest matching rate is met, and the optimal parameter solution is output.

④ Based on the nonlinear mapping relationship of the output in ② and the optimal parameters in ③, the parameter dimension is increased by combining with the neural network system, and the optimal solution of the input parameters is obtained. This process and the process ② are mutually inverse processes. Based on the above process, the high-precision history matching of reservoir numerical simulation is realized, and the high-precision geological model is obtained. The method flow and technical route are shown in Figure 4.

This study focuses on the smart history fitting study of fractured reservoirs, and the assumptions of this method are as follows:

(1)

The fluid is mainly oil, gas, and water in three phases;

(2)

The fluids flow simultaneously in the matrix rock mass and the fracture grid and satisfy Darcy’s law;

(3)

The reservoir temperature is a constant condition;

(4)

Rock compressibility is not considered and pore penetration evolution is neglected;

(5)

Neglect the effect of gravity.

3. Case Applications

The study area is located in Basin G in the Middle East. The buried depth of Formation XX of the main oil-bearing layer system ranges from 2800 to 3200 m, and the average sedimentary thickness is approximately 70 m [35,36]. The location and geomorphologic features of the study area are detailed in Figure 5. According to the core observation, lithologic assemblage characteristics, and electrical characteristics, the lithologic matrix is mainly composed of micritic dolomite and bioclastic dolomite. Among them, the bioclastic dolomite in the bioclastic shoal microfacies is a favorable reservoir rock type [37]. Core analysis shows that the average matrix porosity of Formation XX is 8.72%, and the average matrix permeability is 2.6 × 10⁻³ μm² [38]. Microscope thin sections and imaging logging interpretation indicated that the reservoir space in Formation XX had fractures and also developed secondary pores generated by dissolution, including intergranular dissolved pores, moldic pores, organism cavity pores, etc., forming a fracture-pore type reservoir. Production practice shows that fractures are important factors affecting oil well productivity and water cut increase.

In this paper, we take the well area A of the fractured-porous reservoir of Formation XX in the Basin G oilfield as the research object, construct an arithmetic pore-fracture dual medium model based on the information obtained from the well area test, and carry out the study of automatic artificial intelligence history matching by combining it with the historical production data of the A well area.

3.1. Overview of Reservoir

The well area A studied in this paper is a typical fractured-porous carbonate reservoir, with an area of about 12.9 km², underground crude oil reserves of about 6.93 × 10⁶ m³, and a total of 42 wells drilled in the well area (39 existing production wells), with a cumulative oil production of 9.25 × 10⁵ m³ and a recovery degree of about 13.35% since the start of the production in January, 2002, and an oil production of 9.25 × 10⁵ m³ and 13.35% since the start of the production in January, 2002, respectively. After core sampling and testing, it can be seen that the reservoir pore system in well area A is mostly dolomite and chert, with a porosity of about 0.59~7.32% and a permeability of about 0.3~3.6 mD; the porosity of the fracture system ranges from 5.6~27.8% and permeability from 0.6~143.4 mD, with a fracture openness of about 2.8~46.7 μm and a fracture density of 0.53~2.26/m², and the fractures are of small and medium scale, and the fracture density is of 0.53~2.26/m². The fractures are mainly small- and medium-scale fractures, and the length of the fractures are mainly about 0.5~72.6 m. The relevant physical parameters of the reservoir are summarized in

Table 1. Statistics of reservoir physical parameters in well area A.

Reservoir Physical Parameters	Value
Well area	12.9 km2
Crude oil reserves	6.93 × 106 m3
Porosity (matrix system)	0.59~7.32%
Permeability (matrix system)	0.3~3.6 mD
Porosity (fracture system)	5.6~27.8%
Permeability (fracture system)	0~2204.4 mD
Fracture density	0.53~2.26 pieces/m2
Fracture length	0.5~72.6 m

. Comparing the geological and physical parameters of the pore and fracture systems, it can be seen that the fracture system is the main storage space and flow medium in the A well area.

According to the seismic test and logging interpretation, the reservoir in Well A can be divided into two big layers and five small layers based on geological structure and oil content, of which the upper reservoir is the main reservoir. In addition, there are 14 faults in the reservoir of Well A, which are mainly distributed in the middle and south of the well area, and the strike is mainly northeast-southwest, in which normal and reverse faults are staggered, and drilling in the well area is mainly distributed near the faults. Reservoir geological characteristics of well area A are shown in Figure 6, and well area A belongs to a typical backslope nasal fracture reservoir.

According to the core displacement test, the viscosity of underground crude oil in this reservoir is about 3.42 mPa·s, the bound water saturation is about 0.25~0.37, the relative permeability (K_ro) of oil phase corresponding to bound water is about 0.75~0.93, and the critical water saturation is about 0.30~0.35. The residual oil saturation is about 0.25~0.35, and the relative permeability (K_rw) of water phase corresponding to the residual oil is about 0.49~0.62. Based on the experimental tests, the phase infiltration curves associated with fractured reservoirs were plotted, and the curves are detailed in Figure 7.

Based on the complex fracture geological characteristics of fractured-porous reservoirs in the Asmari group of the G oilfield, the numerical simulation history matching accuracy of this type of reservoirs was lower. Moreover, it was difficult for the numerical simulation accuracy of the reservoirs to accurately guide later production. Aiming at the above problems, this paper adopted a composite artificial intelligence history matching method to solve the difficult matching problem of fractured-porous reservoirs. An application was carried out with well area A as an example. The reservoir matrix system was relatively homogeneous. This paper mainly discussed the fracture reservoir inversion method to realize the research on fracture reservoir construction.

3.2. Cases Studied

Case 1: Single-well matching

This paper analyzed the production wells in Well A and took the typical Well A-9 as an example to conduct research on artificial intelligence history matching. This research utilized the tNavigator numerical simulator for numerical simulation. Well A-9 is located in the southwest of Well A in the oil reservoir. The fault-fracture system around the well was well developed, and the geological characteristics were complex. Since it was put into production in 2002, the cumulative oil production of this well had been 1.02 × 10⁵ m³. As it was the main production well in Well A, the matching of the production history of this well was particularly important. Geologic characteristics of well A-9 are detailed in Figure 8.

According to the analysis, the control area of Well A-9 was about 0.38 km², and the underground crude oil reserves were about 6.48 × 10⁵ m³. According to the seismic logging analysis, there were two faults near the well, most of which were reverse faults. A large number of small- and medium-sized fractures were developed around the well and around the faults, with complicated geological characteristics. Conventional seismic and logging interpretation data could not accurately describe the nature of the fractures. As a result, there were some differences in the construction of the geological models, which could not accurately describe the real geological properties of the oil reservoirs. As a result, the matching of reservoir history took a long time and the matching accuracy was poor, which seriously restricted the simulation progress of subsequent reservoir development.

Based on the data obtained from seismic, logging, and core experiments, it was known that the porosity of bedrock around Well A-9 was about 1.3~3.9% and the permeability was about 0.4~3.6 mD. The fracture permeability was about 0~2035.7 mD, and the fracture opening was about 42~155.9 μm. The fracture density was about 0.62~1.85 pieces/m². Based on the buried depth of the reservoir and the structural origin, most of the fractures in the well area were high-angle fractures, with the fracture inclination ranging from 65~85° and the fracture length ranging from 0.5~72.6 m. The fracture trend was complex, and the fracture system was the main seepage channel in this well area. Reservoir fluid properties were as described above. Reservoir geological characteristics parameters of A-9 well are shown in

Table 2. Well A-9 reservoir physical parameters statistics.

Reservoir Physical Parameters	Value
Well area	0.38 km2
Crude oil reserves	6.48 × 105 m3
Porosity (matrix system)	1.3~3.9%
Permeability (matrix system)	0.4~3.6 mD
Permeability (fracture system)	0~2035.7 mD
Fracture density	0.62~1.85 pieces/m2
Fracture length	0.5~72.6 m

. Based on the reservoir geology and reservoir fluid data of the above typical wells and the production history data of Well A-9, the artificial intelligence history matching test was carried out.

The permeability property field of the fracture system was constructed based on the above parameters. Firstly, the data obtained from the pre-simulation test were divided into interval values. In order to ensure that the obtained data could accurately reflect the real data, the data interval could be appropriately expanded and contracted, that is, from 0.8 times the minimum value to 1.2 times the maximum value.

Firstly, the data obtained from the pre-simulation test were divided into intervals, and in order to ensure that the data obtained could accurately reflect the real data, the data intervals could be expanded and contracted appropriately, i.e., 0.8 min~1.2 max. At this time, the matching intervals of the fracture attribute parameters of typical wells were obtained and combined with the historical production data of the typical wells, and the orthogonal history matching was carried out based on the Monte Carlo experimental planning method. Before matching, the Monte Carlo value interval limit (the value interval limit was set to 0.01) and the maximum number of Monte Carlo simulations were set, and then N groups of matching models were randomly generated. Fracture attribute parameters were closely related to fracture permeability attributes, and this study mainly inverts the fracture reservoir permeability attribute field.

The parameters of each type and historical data were input into the parallel solver for solution and the related calculation results were output. The matching threshold was set based on the Monte Carlo experiment (the matching threshold was 75%), and then the best model parameter groups were output. In this simulation experiment, the maximum number of matching times was set to be 5000. Based on the Monte Carlo experimental planning algorithm, 5000 a priori models were randomly generated, with a uniform grid step size of 50 × 50 m and a longitudinal grid step size of 2 m as the unit of division. The model construction was carried out based on the above design. The fracture model permeability property fields associated with well A-9 for different parameter characterization lines are shown in Figure 9.

Parameters were optimized according to the above history matching accuracy threshold. If the matching accuracy is greater than 75% (threshold), the corresponding model parameters will be output. The history matching results are shown in Figure 10. The Monte Carlo history matching results of Well A-9 are shown in Figure 11.

The corresponding fracture permeability model is shown below, as follows:

Based on the above analysis of the fracture attribute model, it can be seen that the fracture permeability around well A-9 was relatively low, the fracture was underdeveloped, and the fracture permeability attribute was relatively affected by the fracture length, fracture opening, and fracture density. Combined with the cubic law and fracture system permeability model to invert the fracture property parameters of the A-9 well zone, please refer to

Table 3. A-9 parameter table of typical well optimization model.

Fracture Length /m	Fracture Opening /μm	Fracture Dip Angle/°	Fracture Density /Pieces/m2	Fracture Azimuth /°
3–50	58–149	69–75	0.6~1.2	0~150

for specific parameters.

The uncertainty of the fractured reservoir history fitting was mainly based on the fracture data, and the uncertainty analysis and sensitivity analysis were mainly the fracture data. Based on the above Monte Carlo experimental planning method, the generalized typical well prior model was obtained. By combining it with the history matching precision setting threshold screening, the high-precision matching prior model was obtained, and the parameter interval of the model was determined. Then, according to the matching results and the prior model, deep training was conducted based on the artificial neural network method to obtain the nonlinear mapping relationship between each parameter and the history matching accuracy. The number of iterations for the artificial neural network training was set to 2000. The number of neuron nodes was adaptive based on the input parameters. Parameter dimensionality reduction was carried out based on the mapping relationship, thereby obtaining the high-correlation parameters of history matching and realizing parameter dimensionality reduction.

Based on the deep learning of the artificial neural network method, it can be seen that the fracture length (L), fracture width (openness) (W), and fracture density (ρ_l) of the three variables for the high correlation parameters, fracture inclination, direction of the secondary parameters, and the matching weight were low. The sensitivity results are detailed in Figure 12. In order to simplify the amount of computation in this paper, high correlation parameters were preferred for the subsequent intelligent history matching operation.

$$R\propto {(L,W,{\rho }_l)}^b$$

(17)

where R is the matching rate, %, and b is the matching index.

Based on the highly correlated parameters optimized by deep learning of the artificial neural network combined with the particle swarm optimization algorithm as mentioned above, inversion optimization for history matching was performed. Aiming at the Monte Carlo preferred prior model parameters and the nonlinear mapping relationship constructed by deep learning of the artificial neural network, particle swarm optimization was carried out in combination with the production data. The initial population number was set at 20, parameter particles were initialized, and the corresponding positions and velocities of parameter particles were defined. Then, the abovementioned preferred prior parameter model was optimized. Subsequently, history matching was conducted based on the particle update criterion. The matching accuracy threshold was set at 90%, (see Figure 13a) and the corresponding model was output when the threshold requirements were met.

Based on the model obtained from the particle swarm optimization algorithm for the A-9 typical well, subsequent dimension increase treatment was conducted. The secondary parameters were optimized using the artificial neural network method, and ultimately, a numerical model of the A-9 typical well that satisfied the historical production situation was constructed. The optimized geological model of well A-9 is shown in Figure 13b. This process was mainly realized through the abovementioned optimization model and nonlinear correlation mapping relationship.

The artificial intelligence history matching method based on multi-algorithm superposition achieved high-precision history matching of the A-9 typical well and addressed the challenging problem of history matching for fractured reservoirs in bedrock buried hills. The history matching method of the dual media model based on multi-algorithm superposition artificial intelligence was innovatively proposed.

Case 2: District-wide History Matching

With a focus on the matching results and process of Case 1, an AI-driven automatic history matching study was undertaken in well area A. Relying on the previously mentioned lateral drilling logs and seismic interpretation data of well area A, an intelligent history matching test was implemented across the entire area. The analysis indicates that the fracture system in well area A was highly developed, and there existed substantial uncertainty in the history matching when considering the geological features, specifically the fracture development characteristics. Consequently, the history matching study was conducted using the artificial intelligence history method featuring multi-algorithm superposition. Firstly, the test data set that was randomly divided based on the Monte Carlo model parameters to generate numerous a priori models. Given the complexity of the fracture system in the well area, fracture parameters and the remaining parameters were sampled separately. The Monte Carlo interval of 0.001 (for the fracture system) was set to randomly generate a priori models. By integrating the area of the work area and the production dynamic data of the entire area, a matching model was constructed. At this juncture, based on the Monte Carlo experimental planning algorithm, 8000 a priori models were randomly generated. In combination with the production data of well area A and utilizing the tNavigator numerical solver, the forward matching study was carried out. The grid step parameter settings of this matching model were identical to those previously mentioned. A portion of the permeability field of the orthotropic matching model is depicted in Figure 14.

Threshold optimization was carried out for the matching results of the Monte Carlo experimental planning method, and the orthogonal matching threshold was set to 75%, outputting a highly adaptive a priori model, and outputting a series of models that met the matching constraints based on the matching threshold. The results of this partial orthogonal matching experiment are shown below. Figure 15 shows the fitting results based on the Monte Carlo experimental planning method, where the blue curve meets the fitting threshold, starting from the corresponding model will be optimized in the next step.

The current production history fitting accuracy of fractured reservoirs was relatively low; we took the pre-fitting results of well area A and compared them with the AI history fitting method, which was mainly reflected in the improvement of simulation accuracy; compared with the current existing numerical simulation method/intelligent numerical simulation method, the accuracy was improved by about 20%.

Based on the typical well matching curves in Figure 15, it can be seen that wells with large variations in single-well production capacity have relatively low matching rates, and their periwell fracture systems were relatively difficult to characterize, e.g., A-10, A-14.

A number of a priori models were combined with the production data to carry out deep training learning based on the artificial neural network method, and the nonlinear correlation mapping relationship between the fitted model parameters and the production data was constructed. Based on the strength of this mapping relationship, high correlation parameters were screened to realize the dimensionality reduction in the fitted parameters.

Based on Figure 16, it can be seen that the fracture properties in well area A had a greater impact on the matching of the production data, of which the fracture length (L), fracture inclination (α), fracture width (W), and fracture density (ρ_l) were highly correlated parameters, of which fracture density was the main controlling factor, and the rest of the matching parameters had a relatively small impact on the matching accuracy; therefore, a follow-up AI automatic history matching study was carried out for the above high correlation parameters.

Based on the Monte Carlo experimental planning method and artificial neural network method, the preferred model parameter set and production data were used to carry out the artificial intelligence automatic history matching research, and based on the particle swarm optimization algorithm, the history matching inversion research was realized. For the preferred parameter model of well area A, the initial population was divided into 100 based on the parameter base, the number of iterations was set to 2000, the learning factor was set to 2, the inertia weight was set to 0.95, the parameter particles were initialized, and the corresponding positions and velocities of the parameter particles were defined so as to optimize the preferred a priori parameter model mentioned above and carry out the study of history matching inversion based on the solver; the threshold of matching was set to 85% for particle swarm optimization. The matching threshold was set at 85%, and the corresponding parameter model was output to meet the threshold. The results of the particle swarm algorithm optimized history of the fit are shown in Figure 17, where the red data is the history and the blue curve meets the fit threshold.

Similarly, the preferred parameter model for the above particle swarm algorithm was upscaled and based on the historical data combined with the nonlinear mapping relationship obtained by the artificial neural network for bedrock attributes and its remaining secondary parameters, it was upscaled to obtain the matching parameter model of the fracture system of submerged fractured reservoirs (see Figure 18a) to realize the complex reservoir artificial intelligence history matching. Artificial intelligence fitting methods are mainly based on efficiency and fitting accuracy, while this paper shows the accuracy of intelligent history fitting based on case studies. Compared with the traditional methods, the accuracy can reach more than 80% (see Figure 18b), which is unsolvable for the traditional methods.

4. Conclusions

The simulation in this paper is of high practicality and the method used is applicable to most historical history fitting studies of fractured reservoirs. In contrast to the traditional history fitting methods, the present method uses the fracture parameters as optimization parameters for optimal fitting, making the method highly practical.

(1)

In this paper, a multi-overlapping AI history method based on the Monte Carlo experimental planning method, combined with an artificial neural network and a particle swarm optimization algorithm was proposed. By this method, the automatic matching of AI history for complex fractured reservoirs was realized and engineering technical problems such as the difficulty in matching such reservoirs and the low matching accuracy were solved.

(2)

Based on the method, the influence of uncertain parameters on the history matching of fractured reservoirs during most seismic and drilling logging processes was discussed. Combined with the actual production data, the nonlinear mapping relationship between the parameters and production data was obtained, and the parameters with higher correlation were selected so as to realize the identification and analysis of the main control factors of fractured reservoir history matching.

(3)

In addition, for the massive data in high-precision history matching, this paper proposed the method of gradually reducing the parameter dimension and increasing the parameter dimension. This alleviated the shortcomings of artificial intelligence such as parameter redundancy in the process of automatic history matching to a certain extent. The feasibility of the program was verified with examples. However, the method was constrained by well data, and there was some difficulty in history matching for large oil and gas reservoirs. Finally, this thesis provided some technical guidance and solutions for the study of high-precision history matching in submerged fractured reservoirs.

The method is mainly suitable for fractured reservoir history fitting, for the rest of the reservoir history fitting needs to be based on example analysis.