Optimization of Well Patterns in Offshore Low-Permeability Thin Interbedded Reservoirs: A Numerical Simulation Study in the Bozhong Oilfield, China

Abstract

Offshore low-permeability thin interbedded reservoirs contain significant oil reserves and are crucial for future development. However, due to the high cost and operational challenges associated with offshore fracturing, large-scale fracturing common in onshore fields is uneconomical. Furthermore, offshore low-permeability reservoirs often have sparse well placement and wide well spacing, in contrast to onshore low-permeability fields, which leads to low recovery. Additionally, there is a lack of comprehensive theory on optimizing the well patterns and fracture networks to maximize net income, highlighting the need for further research. This study tackles these issues in a low-permeability thin interbedded reservoir in the Bozhong Oilfield by using reservoir numerical simulation. First, fracture parameters, including fracture half-length and conductivity, are optimized for different well patterns. Subsequently, well pattern optimization is conducted under fractured conditions, targeting maximum net income under various conditions. The results indicate that when fractures are confined to a single reservoir layer and the main reservoir layer accounts for less than 36% of the development section, fractured directional well patterns yield a higher net income. Conversely, when fractures penetrate all reservoir layers, fractured horizontal wells with closer fracture spacing a higher number of fractures are the most profitable option, particularly in offshore fields with large well spacing. The findings provide critical insights into optimizing well patterns and fracture network designs for offshore low-permeability thin interbedded reservoirs.

1. Introduction

Chinese offshore low-permeability oil and gas fields are extensive and large in scale, constituting key regions for future resource development [1,2,3,4]. However, given the late initiation of development, combined with the high costs and operational challenges associated with offshore projects, the current approach to developing these reservoirs focuses on achieving “high production with fewer wells” [5].

In contrast to offshore oilfields, onshore low-permeability oilfields have been under development for many years and have achieved effective production [6]. Horizontal wells with hydraulic fracturing, as the primary development method for low-permeability reservoirs, are widely applied in low-permeability oil and gas fields [7,8]. Key fracture parameters, including fracture spacing, half-length, and conductivity, significantly influence the productivity of hydraulically fractured horizontal wells [9,10,11,12]. The efficient development of onshore low-permeability reservoirs is attributed not only to the rapid advancement of horizontal well fracturing technology but also to the optimization of fracture parameters in coordination with well pattern design. A method for designing an integrated fracturing development plan that simultaneously optimizes fracturing well parameters and the initial well pattern for low-permeability reservoirs was introduced by Gan [13]. Building on the concept of optimizing both well patterns and fracture networks, Zhu Shiyan, Zhang Chenshuo, and Zhang Jianfeng employed numerical simulations to optimize fracture parameters and fracturing strategies within horizontal well patterns used in conjunction with vertical water injection wells [10,11,14]. Specifically, it is critical to avoid aligning fractures directly opposite injection wells or to reduce fracture lengths near the injection well ends to prevent premature water breakthrough, which could diminish production. Cao Zhenyi further advanced this research by using reservoir simulations to optimize the injection–production well spacing ratio in inverse seven-spot horizontal well patterns, specifically for gas injection to enhance energy supplementation in horizontal wells, while maintaining the same well pattern area for vertical well production [15].

With the advancement of intelligent algorithms, their application has become increasingly prevalent in the optimization of well patterns and fracture networks in low-permeability oil and gas reservoirs, like polynomial regression models (PRMs), which are used in oil production prediction using Volve field datasets [16], predicting and optimizing the time of water breakthrough during water injection [17], and assessing the impact of well placement on oil recovery [18]. Onwunalu utilized well-by-well perturbation (WWP) and particle swarm optimization (PSO) to optimize well patterns of various sizes [19]. Jahandideh developed a hydraulic fracturing optimization method under compressible geospatial variability using a Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm, maximizing shale gas recovery [20]. Xu et al. combined embedded discrete fracture models (EDFMs) with intelligent algorithms to optimize fracture parameters in fractured horizontal wells, achieving higher returns than the traditional local grid refinement (LGR) method [21]. Kim integrated the particle swarm optimization algorithm into the convolutional neural network (CNN) to rapidly optimize complex well patterns [22]. Feng Qihong developed a hierarchical optimization method for multistage fractured horizontal wells in tight oil reservoirs using embedded discrete fractures and intelligent optimization algorithms [23]. Ma Jialing applied a synchronous perturbation stochastic approximation algorithm and employed reservoir simulation to automatically optimize both well patterns and fracture networks in gas reservoirs, obtaining an optimal well pattern that aligns with the geological conditions [24]. Wang et al. employed a stochastic simplex approximation gradient and the steepest ascent algorithm to optimize multi-well, multistage fractured horizontal well patterns, focusing on maximizing economic returns [25]. Polynomial regression models and artificial neural network (ANN) models have been coupled with genetic algorithms for infill well placement at the onset of foam injection, which offers superior optimization efficiency, by Nwanwe [26]. In recent years, with the further development of onshore low-permeability oil and gas fields, well pattern optimization has made significant progress. Zhao et al. optimized coalbed methane well patterns by incorporating the geological characteristics of the reservoir and determining the optimal well spacing based on permeability [27]. Yong used an integrated geology–engineering–economy approach to optimize horizontal well patterns in shale gas reservoirs [28]. Wu optimized well placement in conglomerate reservoirs by considering sedimentary sources and the orientation of in situ stress, achieving an optimal water injection well arrangement [29]. He et al. conducted a numerical simulation study to optimize well spacing and gas injection pressure in horizontal well patterns for water and gas co-flooding secondary development [30]. Nasir proposed a two-stage optimization strategy, enabling the rapid, efficient, and high-return optimization of large well populations [31]. Shengli Oilfield employed numerical simulation to optimize well patterns under the premise of pressure drive development in low-permeability reservoirs [32]. He Yonghong optimized well patterns for shale oil development in the Ordos Basin by considering interlayer thickness and overall reservoir thickness, achieving large-scale economic development [33]. Meng combined sedimentary facies analysis and effective sand body distribution with ecological data and engineering parameters using interference well testing for the qualitative analysis of well connectivity and interference probability [34]. This approach identified critical well spacing density and produced an intersection map of gas abundance and well density to optimize the well pattern.

Although significant progress has been achieved in developing onshore low-permeability oilfields, offshore oilfields face unique challenges that hinder the implementation of dense well patterns similar to those used onshore. The large well spacing and limited number of wells necessitate well patterns’ optimization tailored to offshore conditions [4,5]. Unlike onshore reservoirs, offshore low-permeability reservoirs are predominantly characterized by interbedded and thin interbedded layers. Currently, the injection–production well patterns in offshore fields are suboptimal, resulting in low recovery efficiency. Moreover, only a small number of wells have undergone hydraulic fracturing treatments, and the production performance of these wells declines rapidly due to insufficient reservoir energy supplementation [4]. This study focuses on the Bozhong Oilfield, a representative thin interbedded low-permeability reservoir. Using reservoir numerical simulation, this research investigates the optimization of fracture parameters. Subsequently, this study conducts well spacing and well type optimization to maximize net revenue. The findings provide theoretical guidance for the development of thin interbedded low-permeability reservoirs in offshore oilfields.

2. Overview of the Study Area

The Bozhong Oilfield is located in the southern Bohai Sea, with low- and extra-low-permeability reservoirs primarily distributed in the Shahejie Formation’s second and third members (Sha-2 and Sha-3). The reservoirs lie at depths of −3200 to −3900 m. The Sha-2 member has an average porosity of 15.8% and permeability ranging from 5 to 20 mD, placing it between conventional low-permeability and extra-low-permeability reservoirs, and it exhibits some productivity during the initial production phase. In contrast, the Sha-3 member exhibits an average porosity of 13.9% and permeability below 5 mD, classifying it as an extra-low-permeability reservoir requiring hydraulic fracturing to achieve economically viable production. Currently, the Sha-2 member is developed using irregular well patterns combined with hydraulic fracturing, with injection–production well spacing ranging from 370 to 560 m, yielding certain development successes [35]. However, the Sha-3 member remains in the exploratory development stage. Efforts in this interval include a fractured directional well drilled in 2007 and two multistage fractured horizontal test wells drilled in 2016. Both attempts fell short of expectations due to insufficient reservoir energy supplementation, leading to rapid production decline [4,35]. The Sha-3 member in the BZ25-1 Block 5 area represents a typical thin interbedded extra-low-permeability reservoir, as shown in Figure 1. Well log interpretation data for a fractured well in this zone indicate reservoir thickness ranging from 0.8 to 7.6 m and interlayers of 1.1 to 10.4 m. These characteristics result in poor vertical connectivity. While directional wells with multistage perforations can target multiple thin layers, horizontal wells without hydraulic fracturing have low vertical development efficiency but can control significantly larger reservoir areas. Hydraulic fracturing in horizontal wells could potentially connect multiple reservoir layers, further enhancing reservoir drainage efficiency. Therefore, it is essential to explore and define the optimal well type and pattern for developing thin interbedded extra-low-permeability reservoirs such as those in the Sha-3 member of the Bozhong Oilfield.

3. Numerical Model

Based on the well log interpretation results shown in

Table 1. Log interpretation results of a development interval of a directional well in the Bozhong oilfield.

Reservoir Number	Reservoir Thickness (m)	Permeability (mD)	Porosity
1	1.6	2.5	0.168
Interlayer	1.3	0.0001	0.00001
2	1.8	1.3	0.149
Interlayer	1.1	0.0001	0.00001
3	5.4	1.8	0.158
Interlayer	3.4	0.0001	0.00001
4	0.8	3.3	0.172
Interlayer	10.4	0.0001	0.00001
5 (main reservoir layer)	7.6	1.5	0.148
Interlayer	1.5	0.0001	0.00001
6	1.5	1.1	0.139
Interlayer	4	0.0001	0.00001
7	4	1.9	0.152
Interlayer	3	0.0001	0.00001
8	2.8	0.8	0.129
Interlayer	7	0.0001	0.00001
9	4.5	0.8	0.135

, this study utilizes the reservoir simulation software tNavigator (v20.1), which offers superior computational efficiency and a user-friendly interface compared to other simulation tools to construct two optimization models. The first model focuses on optimizing fracture parameters for various well patterns while the second explores well pattern optimization under different proportions of the main reservoir layers. In the latter model, the main reservoir layers are defined as those targeted by horizontal well placement. These models aim to identify the most effective development strategies for thin interbedded reservoirs by integrating hydraulic fracturing design and well patterns’ optimization.

3.1. Fracture Parameter Optimization Model

Based on the well log interpretation results presented in Table 1, the Sha-3 member of the Bozhong Oilfield features interlayer thicknesses predominantly around 2 m, with reservoir thicknesses ranging from 0.8 to 7.6 m and individual layer thicknesses also typically around 2 m. Using these characteristics, an optimization model for fracture parameters under different well patterns was developed. A schematic of the model is shown in Figure 2. In this model, production wells are hydraulically fractured, while injection wells remain unfractured. Fractures are simulated using a local grid refinement approach, with the model parameters and reservoir fluid properties detailed in

Table 2. Reservoir oil of PVT.

Oil Phase Pressure (MPa)	Oil Formation Volume Factor	Viscosity (cp)
0	1.037	3.626
0.5	1.0367	3.382
1.053	1.0339	3.796
1.605	1.033	3.833
2.158	1.0326	3.851
2.711	1.0323	3.862
3.263	1.0321	3.869
3.816	1.032	3.874
4.921	1.0319	3.881
6.579	1.0317	3.886
8.789	1.0316	3.891

,

Table 3. Oil–water relative permeability meter.

Water Saturation	Water Relative Permeability	Oil Relative Permeability
0.3480	0.0000	0.9995
0.3668	0.0084	0.9709
0.3856	0.0168	0.9424
0.4044	0.0251	0.9138
0.4232	0.0335	0.8853
0.4420	0.0414	0.8581
0.4608	0.0491	0.8317
0.4796	0.0571	0.8035
0.4985	0.0698	0.7580
0.5173	0.0909	0.6841
0.5361	0.1162	0.5962
0.5549	0.1409	0.5102
0.5737	0.1642	0.4272
0.5925	0.1877	0.3435
0.6113	0.2094	0.2661
0.6301	0.2278	0.1996
0.6489	0.2443	0.1398
0.6677	0.2565	0.0948
0.6865	0.2714	0.0411
0.7053	0.2800	0.0082

and

Table 4. Numerical model parameters for fracture parameter optimization model.

Parameter	Value
Ij-plane cell size (m)	10 × 10
Thin reservoir thickness (m)	2
Thick reservoir thickness (m)	5
Interlayer thickness (m)	2
Initial formation pressure (MPa)	54
Bottom hole pressure of production well (MPa)	34
Bottom hole pressure of injection well (MPa)	64
Fracture conductivity (D·cm)	20
Fracture spacing of horizontal well (m)	100
Fracture number	5

.

To comprehensively assess the impact of fracture parameters on cumulative production, the following assumptions are made during the simulation:

(1)

This study adopts a water injection strategy for reservoir development. Consequently, the impact of stress sensitivity on reservoir properties is disregarded in the simulation. Additionally, as the focus of this research is on tight sandstone reservoirs, the effects of fine migration and velocity sensitivity on reservoir properties are also excluded from the analysis.

(2)

Fractures remain open throughout the simulation period, with no proppant embedment or changes in fracture dimensions and conductivity.

(3)

For horizontal well patterns, when the fracture spacing exceeds 20 m, the stress shadow effect has a negligible influence on fracture geometry [37]. Therefore, stress shadow effects are not considered for fracture spacing greater than 20 m in this study.

Using the established models, this study examines the influence of fracture parameters, specifically fracture half-length and fracture conductivity, which remain fundamental and critical to the analysis even when employing machine learning techniques to optimize fracture parameters [38], on cumulative production under different well configurations and varying production well spacings.

3.2. Well Pattern Optimization Model

To evaluate the applicability of different well patterns for thin interbedded reservoirs, this study develops well pattern optimization models based on the well log interpretation results in Table 1. Reservoir 5 is selected as the main reservoir layer for horizontal well placement, with various combinations of additional layers included to construct models with different main reservoir layer proportions. The main reservoir layer that accounted for 49% comprises Reservoirs 3–6, as shown in Figure 3a. The main reservoir layer that accounted for 36% comprises Reservoirs 2, 4, 5, 6, and 7, as shown in Figure 3b. The main reservoir layer that accounted for 29.8% comprises Reservoirs 1 through 8, as shown in Figure 3c. The main reservoir layer that accounted for 23.5% comprises Reservoirs 1 through 9, as shown in Figure 3d. The fluid properties, reservoir parameters, and production well parameters are consistent with those used in the fracture parameter optimization model. Additional model parameters are listed in

Table 5. Numerical model parameters for well pattern optimization model.

Parameter	Value
Ij-plane cell number	180 × 180
Ij-plane cell size (m)	10 × 10
Initial formation pressure (MPa)	54
Bottom hole pressure of production well (MPa)	34
Bottom hole pressure of injection well (MPa)	64
Fracture half-length (m)	100
Fracture conductivity (D·cm)	20
Fracture spacing of horizontal well (m)	50/100
Fracture number (fracture spacing 50m)	9
Fracture number (fracture spacing 100m)	5

. To fully investigate the impact of primary layer proportion on the performance of fractured well patterns, the same assumptions from the previous section are applied: fractures remain open with no proppant embedment or conductivity changes during the simulation, and stress shadow effects are ignored when fracture spacing exceeds 20 m.

Based on the numerical models developed, this study investigates the variations in net income for fractured well patterns under different well configurations, primary layer proportions, and well spacings. The net income calculation considers the drilling and completion costs for production wells, the drilling and completion costs for injection wells, and hydraulic fracturing expenses, for which costs related to platform construction and unquantifiable risk factors were excluded from the analysis. The parameters used in the net income calculations are detailed in

Table 6. Net income calculation parameters.

Parameter	Value
Oil price (USD/m3)	507.93
Reservoir depth (m)	3800
Directional well drilling costs (USD/m)	1781.53
Directional well completion costs (USD/m)	150,744.82
Horizontal well drilling and completion costs (USD)	13,704,074.22
Fracturing cost (USD/time)	328,897.78

.

4. Results and Discussion

4.1. Optimization Results of Fracture Parameter

4.1.1. Fracture Half-Length

This study begins by optimizing the fracture half-length for different well patterns with different production well spacings (300 m and 500 m) using the model setup described in Figure 2. When the production well spacing is 300 m, the simulated fracture half-length ranges from 60 m to 140 m, with an increment of 20 m. For a production well spacing of 500 m, the fracture half-length is simulated from 60 m to 180 m, with a 20 m increment. All simulations are conducted over a production period of 10 years, and the results are presented in Figure 4 and Figure 5.

For the 300m well spacing, as shown in Figure 4, the cumulative production demonstrates a clear dependency on the fracture half-length across all well patterns. The five-spot pattern and inverse nine-spot pattern display diminishing cumulative production as the fracture half-length increases beyond a critical value (fracture half-length 120 m), likely due to early water breakthrough and interference between adjacent fractures. The horizontal well pattern shows a moderate production improvement with longer fractures, but the cumulative production begins to plateau with a fracture half-length longer than 120 m. For the 500 m spacing, as shown in Figure 5, the production trends resemble those observed for the horizontal well pattern under the 300 m spacing. However, unlike the 300 m well spacing scenario, the optimal fracture half-length increases with the larger production well spacing, reaching a value of 160 m. Increasing fracture half-length significantly boosts cumulative production initially, but the rate of increase flattens when the fracture length exceeds a critical threshold, which indicates that beyond a certain fracture length, the additional stimulated reservoir volume contributed less to overall production.

4.1.2. Fracture Conductivity

Fracture conductivity, similar to fracture half-length, is a critical parameter influencing hydraulic fracturing performance. Using the model depicted in Figure 2 and considering a well spacing of 300 m, this study examines cumulative production variations under different fracture conductivity values for both directional well networks (five-spot and inverse nine-spot patterns) and horizontal well networks. The simulations are conducted with a fixed fracture half-length of 120 m, which is the best fracture half-length optimization in Section 4.1.1, and the fracture conductivity ranges from 10 to 70 D·cm in increments of 5 D·cm. All simulations are performed over a 10-year production period, with the results presented in Figure 6.

For both directional and horizontal wells, increasing fracture conductivity positively correlates with cumulative production. As shown in Figure 6, for a production well spacing of 300 m, higher fracture conductivity results in a steeper increase in cumulative production during the early stages, followed by a gradual stabilization as production progresses. Within the directional well pattern, cumulative production exhibits a diminishing marginal benefit as fracture conductivity increases, suggesting that production enhancement becomes less pronounced beyond a certain conductivity threshold (60 D·cm). Similarly, in the horizontal well pattern, although the impact of fracture conductivity on production is more substantial, it also shows signs of saturation at higher conductivity levels.

Offshore fracturing operations are constrained by platform space, load capacity, and material transportation limitations, resulting in relatively small-scale treatments. As shown in

Table 7. Fracturing well construction parameters and post-fracturing interpreted fracture half-length in Bozhong Oilfield.

Well Name	Proppant Volumes (m3)	Pumping Rate (m3/min)	Fracture Half-Length
A4	29	3.2	78
A20	23.3	3.2	81
A22	35.7	3.2	90
C25	35.6	3.2	73

, the current fracturing scale in the Bozhong Oilfield is relatively modest. Proppant injection volumes range from 29 to 36 m³, with a pumping rate of approximately 3.2 m³/min. The post-fracturing interpreted fracture half-length is around 100 m, and the average fracture conductivity is approximately 20 D·cm, as illustrated in Figure 7. Given these operational constraints, the fracture design parameters during the optimization of well networks in thin interbedded reservoirs are set to a fracture half-length of 100 m and a fracture conductivity of 20 D·cm.

4.2. Optimization Results of Well Pattern of Thin Interbed

4.2.1. Optimization Results of Non-Penetrating Well Pattern with Hydraulic Fracturing

Vertical fracture propagation across multiple reservoir layers is essential for the effective development of offshore low-permeability thin interbedded reservoirs. However, this process is significantly influenced by stress contrasts between reservoir and barrier layers [36,39]. When the stress contrast between these layers is large, fractures may be confined within a single reservoir, preventing connectivity across multiple layers [36]. Based on this understanding, the well pattern optimization model shown in Figure 3 is used to perform numerical simulations for different well spacings, focusing on scenarios where fractures do not penetrate the main reservoir layer. The objective of these simulations is to maximize net income for different well spacings. The simulation results are illustrated in Figure 8 and Figure 9.

The results show that the performance of different well patterns, particularly horizontal well patterns, varies significantly depending on the main reservoir ratio and well spacing. The findings highlight the advantages of horizontal well patterns in scenarios with high main reservoir ratios and large well spacings, while directional well patterns show superior performance under tighter well spacings and lower main reservoir ratios. Horizontal well patterns exhibit clear economic advantages in scenarios where the main reservoir layer accounts for a higher proportion (e.g., 49%) and the well spacing is large, with a well spacing greater than 450 m. The extended lateral length of horizontal wells enables greater contact with the high-quality reservoir, maximizing productivity and boosting net income, as shown in Figure 9a. Conversely, in scenarios where the main reservoir ratio decreases (e.g., to 36%), the performance of horizontal wells declines due to reduced reservoir contact and diminished drainage efficiency, as shown in Figure 9b–d. Directional well patterns, on the other hand, show better economic performance in conditions of tighter well spacing and lower main reservoir ratios, where their localized targeting capability ensures efficient drainage even in heterogeneous reservoirs with lower main reservoir ratios. Their ability to target specific zones allows for more effective resource exploitation in geologically complex reservoirs like thin interbedded reservoirs when the main reservoir layer proportion is low.

4.2.2. Optimization Results of Penetrating Well Pattern with Hydraulic Fracturing

When the stress contrast between reservoir layers is low, fractures are able to propagate vertically and connect multiple layers, enabling the more efficient development of offshore low-permeability thin interbedded reservoirs [36]. In such cases, the thickness of the connected reservoir layers plays a crucial role in overall recovery. To analyze this, the established well pattern optimization model is used to simulate various well patterns where fractures penetrate the main reservoir layer and connect all layers, with the goal of maximizing net income across different well patterns and well spacings. The simulation results are shown in Figure 10 and Figure 11.

The results show the critical role played by fracture communication in enhancing the production performance of reservoirs, particularly in scenarios involving various well patterns and spacing configurations. Horizontal wells demonstrate a marked economic advantage in scenarios with larger well spacings (>450 m). The net income curves, as shown in Figure 10, reveal that as the well spacing increases, horizontal wells maintain superior production performance and net income, leveraging their extended lateral reach and optimal fracture utilization. This is primarily attributed to their ability to effectively exploit extensive reservoir areas through fractures penetrating through multiple layers, ensuring efficient drainage, as shown in Figure 11. Moreover, the influence of fracture spacing is particularly significant in horizonal wells. As fracture spacing decreases, the economic efficiency of horizontal wells increases due to higher connectivity, making proper fracture spacing critical for maximizing their advantages. Conversely, directional wells exhibit better economic performance in smaller well spacing configurations (≤450 m). At closer well spacing, directional wells effectively access the reservoir with limited fracture requirements, reducing development costs while maintaining production rates. This makes directional wells a cost-effective choice for high-density well patterns in reservoirs with limited fracture penetration.

5. Conclusions

This study presents a comprehensive optimization of well patterns for offshore thin interbedded low-permeability reservoirs, with a focus on maximizing net income. The key conclusions are as follows:

(1)

The optimal fracture half-length is closely related to production well spacing rather than well pattern type. For extra-low-permeability reservoirs, the best fracture half-length is 120 m at a well spacing of 300 m and 160 m at 500 m.

(2)

Under current operational constraints, offshore fracturing treatments are limited, with a fracture half-length around 100 m and conductivity approximately 20 D·cm. Enhancing proppant volumes within the constraints of platform space, load capacity, and material transportation is recommended to achieve a greater fracture half-length and conductivity.

(3)

For thin interbedded reservoirs where fractures cannot vertically connect multiple layers, directional well patterns are preferred unless horizontal wells target more than 36% of the main reservoir layers.

(4)

Extra-low-permeability thin interbedded reservoirs are pivotal for the future economic development of offshore oilfields. In scenarios where large well spacings (>450 m) and fewer wells are required, fractured horizontal wells with fracture spacing no greater than 50 m are the optimal development strategy.