Numerical Simulation of the Effect of Reservoir Properties on Oil Production from the Low-Permeability Formation by Extended Reach Wells

Li, Yanlai

doi:https://doi.org/10.1155/2023/4994087

Geofluids

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Abstract Introduction Discussion and Analysis Conclusion Appendix Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

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Geomechanics of Deep Unconventional Oil and Gas Exploitation

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Research Article | Open Access

Volume 2023 | Article ID 4994087 | https://doi.org/10.1155/2023/4994087

Numerical Simulation of the Effect of Reservoir Properties on Oil Production from the Low-Permeability Formation by Extended Reach Wells

Yanlai Li¹

Academic Editor: Zhongwei Wu

Received22 Sept 2022

Revised13 Nov 2022

Accepted29 Nov 2022

Published03 Apr 2023

Abstract

At present, extended reach wells (ERWs) are widely applied on oil and gas exploitation in numerous reservoirs around the globe, and this is attributed to their superiority in the development of marginal oil and gas fields and cost-effectiveness. Identifying the effects of reservoir properties on production is significant to the operation of ERWs for oil and gas extraction. This work utilizes numerical modeling techniques to simulate the application of ERWs in low-permeability formations. The impacts of low permeability on the oil production and the pressure distribution of the reservoirs with different formation properties are analyzed, and the simulation results of the oil exploitation by ERWs are compared with the oil production and pressure distribution of that by horizontal wells (HWs). A test scheme is designed to analyze the effect of reservoir properties on oil extraction through ERWs and quantify the sensitivity of oil production to reservoir properties. The reservoir properties of formation rock compressibility, formation fluid compressibility, initial reservoir pressure, reservoir saturation pressure, formation porosity, and absolute permeability are studied through 66 ERW cases. The results illustrate that low permeability leads to a fast decrease of oil production rates and significantly uneven pressure distribution. The pressure is lower at the center of the ERW but is higher at both ends of the ERW, while the pressure is evenly distributed along the horizontal well in the HW cases. In addition, the oil production is in direct proportion with the initial reservoir pressure, formation rock compressibility, formation porosity, and formation fluid compressibility but is in an inverse ratio with the reservoir saturation pressure. Furthermore, the initial reservoir pressure has the largest impact on both the total cumulative oil production driven out by natural energy and the cumulative oil production after the development of ten years by natural energy; on the contrary, the absolute permeability has no effect on the total cumulative oil production driven out by natural energy.

1. Introduction

As the closed-loop drilling and the geo-steering drilling become more mature, ERWs have become an important way to develop oil and gas resources [1]. In terms of onshore shallow oil and gas exploration and exploitation, the horizontal displacement of the Zhuangxie 314 ERW drilled by the Shengli Oilfield in China in 1998 reached 2051.22 m, breaking the record of ERW length of 2000 meters (m) for the first time in China [2]. Later, China’s Shengli Oilfield drilled an exploratory ERW, Jinping 1, in Dongying sag of Jiyang depression. The well had overcome great difficulty to realize a long horizontal displacement, and its ratio of horizontal displacement to vertical depth reached 2.803 [3, 4]. On the aspect of offshore shallow oil and gas development, in 2004, China drilled an ERW with a measured depth of 6300 m and a vertical depth of 1229 m in the Liuhua Oilfield in the eastern South China Sea, where the environmental conditions were unfavorable to the drilling operation [5]. In 2010, China drilled five ERWs in the Bohai Sea, with the well depths ranging from 3393 to 4199 m and the horizontal displacement up to 3460 m [6]. Located in north Yamalo-Nenets Autonomous Okrug, the East Messoyakha field drilled an ERW combined with multilateral “fishbone” well techniques, which considerably enhanced the well productivity to the same level as that after hydraulic fracturing [7].

With regard to deep-water oil and gas field development, in 2002, the A-10 deep-water ERW was drilled in the Ursa Oilfield in the Gulf of Mexico basin, with a vertical depth of 5486 m and a horizontal displacement of 6096 m. The well was drilled from the Ursa tension leg platform (TLP) to the yellow sand reservoir in the Ursa Prince section of the Mars Ursa basin [8]. Brazil had drilled 47 ERWs in the Peregrino Oilfield from 2010 to 2017, with an average horizontal displacement of 1419 m [9]. In 2014, under the condition of an extremely narrow drilling margin window (no more than 0.06 g/cm³), shell Malaysia drilled ERWs through three depleted reservoirs to the target reservoir offshore Sabah [10].

As for offshore marginal oil and gas field development, ERWs have also been successfully applied on the Xijiang 24-1 marginal oilfield, which is 8000 m away from the Xijiang 24-3 production platform. In the Pearl River Mouth basin, the XJ24-1 marginal oilfield located in Xijiang of the South China Sea was discovered as early as 1985, but it was shelved due to its remote location. The commercial exploitation of the XJ24-1 marginal oilfield was not realized until the application of ERW technology in 2003 [11]. The drilled Xijiang 24-3-A20 ERW had a vertical depth of 2851.24 m and a horizontal displacement of 7825.51 m [12]. In 2007, ExxonMobil drilled an ERW with a vertical depth of 2336 m and a horizontal displacement of 9059 m off the coast of California, setting a new record for the global offshore ERW [13]. Chenghai 1 area of Dagang Oilfield in China utilized Chenghai 1 offshore artificial island to develop a marginal oilfield 5500 m offshore with ERWs, among which the maximum horizontal displacement reached 5454 m, and the maximum ratio of horizontal displacement to vertical depth was 5.41 [14, 15].

Furthermore, it is noteworthy that ERWs can significantly reduce the cost to develop marginal oilfields [16, 17]. In the Pedernales Oilfield in California, the Statfjord Oilfield in Norway, and the Oseberg Oilfield in Norway, the investment had been reduced by 3.2 to 100 million dollars applying the ERW technology; the Wytch Farm Oilfield in the south of the UK implements the existing artificial island to carry out offshore and onshore oil production for marginal oilfields using ERWs, which reduced the cost of 150 million dollars and realized early production [16]. Besides, the application of ERW techniques can extend the exploratory range and allows for more oil output. For instance, the well 34/10-A36 drilled in the North Sea in June 1992 discovered an extra oil-bearing block and thus added a substantial amount of oil to the total reserves of that oilfield [18]. It can be seen that the ERWs can be used for various kinds of reservoirs.

On another aspect, numerous studies had been conducted on low-permeability reservoirs, but few focused on the application of ERW in low-permeability reservoirs [19–22]. Cui et al. [19] developed a method to determine the response time of waterflooding in low-permeability reservoirs under the assistance of numerical modeling techniques and applied this method to analyze the effect of reservoir properties and production parameters on the response time. They found out that permeability had the largest impact on the response time. On the basis of the pore structure characteristics, Vafaie et al. [20] introduced a permeability prediction model for the tight shale gas reservoir. This approach cut the cost and saved the time spent on permeability measurement.

Based on the above issue, this work focuses on the reservoir of low permeability and applies the numerical modeling techniques on the oil extraction by ERWs. The effect of low permeability on the oil production and the pressure distribution of the reservoirs with different formation properties are explored. Following that, the simulation results of the reservoir development by ERWs are compared with that by HWs. Furthermore, this work identifies the patterns in which different low-permeability reservoir properties affect the oil amount extracted by ERWs and quantifies the sensitivity of oil production to these properties to provide a theoretical basis and guidance for the application of ERWs on the practical exploitation of low-permeability reservoirs.

2. System Description

2.1. Physical Model

The schematic for a low-permeability reservoir model with an extended reach well (hereinafter referred to as the “ERW Base Case”) is demonstrated in Figure 1(a). The properties of the low-permeability reservoir model are listed in Table 1. The sizes of the ERW Base Case in the and directions are m, and the reservoir thickness is 100 m. The reservoir is vertically divided into 4 layers, and the pores contain only the oil phase. The ERW lies in the middle of the reservoir and extends along the -axis from the top (the 1^st layer) of the reservoir on one side to the bottom (the 4^th layer) of the reservoir on the other side. To better simulate the low-permeability property of the reservoir, the reservoir absolute permeability is set as 5 mD and no more than 7.5 mD in the test scheme in the following section. Isothermal conditions are applied on the numerical simulation, and the bottom hole pressure of these two cases is the same as the reservoir saturation pressure .

(a)

(b)

A low-permeability reservoir model with a horizontal well (HW Case) is also established for comparison, in which a HW is in the middle (the 2^nd layer) of the reservoir and parallel to the -axis, as shown in Figure 1(b). The reservoir size of the HW Case is the same as that of the ERW Base Case.

2.2. Mathematical Model

In this work, the mass conservation equation is given by where is the concentration of the component (mol/m³), is the current timestep (sec), is the mass averaged velocity vector (m/s), and , , and refer to the three interperpendicular orientations in the three-dimensional reservoir model. In Equation (1), is defined as where is the fluid velocity in direction , is the reservoir pressure (MPa); is the absolute permeability (mD), is the fluid viscosity (mPa·s), and is the gravity vector (m/s²).

The continuity equation for a homogeneous reservoir with single-phase flow is where is the source and sink term (m³/s) and is the comprehensive compressibility of rock and fluid (1/MPa). In Equation (3), is defined as where is the formation fluid compressibility (1/MPa), is the formation rock compressibility (1/MPa), and is the formation porosity, fraction.

The initial condition of the ERW reservoir model is where is the initial reservoir pressure.

The condition of the inner boundary is and the condition of the outer boundary is where is the cross-section area of the wellbore perpendicular to the wellbore axis (m²), is the pressure at the differential area , is the bottom hole pressure, and is the normal vector of the boundary surface, dimensionless.

In this work, the total cumulative oil production of the reservoir that can be driven out by natural energy is calculated by where is the total cumulative oil production that can be driven out by natural energy (m³), is the total reservoir volume, and is the reservoir saturation pressure (MPa). The cumulative oil production after the production period of is computed by where is the cumulative oil production driven by the natural energy after the production period of (m³) and is the average reservoir pressure at timestep ( is larger than or equal to the reservoir saturation pressure ) (MPa).

In this paper, the finite element method is applied to solve the flow equations, and the oil production is computed by the mass balance equation. The simulations of all the models in this paper are computed by the COMSOL software.

3. Discussion and Analysis

3.1. Comparison between the ERW Base Case and the HW Case

The cumulative oil production after the production period of and the pressure distribution after the development of 10 years for the ERW Base Case and the HW Case are shown in Figures 2 and 3, respectively. The slope of the cumulative oil production curves in Figure 2 drops markedly before 750 days. This is attributed to the depletion of near-well oil reserves, whereas the oil flow about 1000 meters away from the ERW is hampered by the low-permeability reservoir property. Apart from the above phenomenon, it can be seen from Figure 2 that grows as the oil development progresses, while the slope of this curve gradually decreases. This is due to the reason that the pressure around the ERW drops down as time passes (as shown in Figure 3(a)), resulting in smaller differential pressure for oil production. Therefore, the rise of slows down by degrees with its value reaching m³ at the end of the 10^th year. The cumulative oil production of the HW Case is similar to that of the ERW Base Case, but the former is higher after the 10-year development.

(a)

(b)

With regard to the pressure distribution, as illustrated in Figures 3(a) and 3(b), the changes of pressure occur only around the ERW and HW, which also indicates that only the fluids near these two wells have flown into the wellbore after 10 years of development, and the fluids farther barely move. And this is again due to the low permeability of the reservoir, which severely hinders the fluid flows.

Based on the comparison in Figure 3, it is noted that in the ERW Base Case, the blue strip is wider at the center of the reservoir but is narrower at two ends of the reservoir around the ERW. This indicates that the pressure is lower at the center of the ERW but is higher at both ends of the ERW. This is caused by the fact that the ERW is at the bottom of the reservoir at 0 m on the -axis, and thus at this position, it is difficult for the oil in the upper two layers of the reservoir to flow into the ERW. At 4000 m on the -axis, the circumstance is just the opposite; that is, the fluid in the lower two layers of the reservoir flows slower into the ERW than the oil in the same layers at 2000 m on the -axis. Therefore, the average oil production rates at both ends of the ERW are lower than that at the center of the ERW, resulting in higher pressure at both ends of the ERW and lower pressure at the center of the ERW.

In contrast, in the HW Case, the width of the blue strip stays unchanged along the HW. This is due to the reason that the HW is parallel to the -axis, contributing to evenly distributed oil production rates and pressure along the HW. Besides, the flow rates of the oil are symmetrically equal at the upper two layers and the lower two layers of the reservoir; thus, the cumulative oil production of the HW Case is higher than that of the ERW Base Case.

3.2. Effect of Reservoir Properties on Oil Production

For the purpose of quantifying the effect of the reservoir properties on the development of low-permeability reservoirs by ERWs, a sensitivity analysis is implemented on the reservoir properties in Table 1, including formation rock compressibility, formation fluid compressibility, initial reservoir pressure, reservoir saturation pressure, formation porosity, and absolute permeability. A test scheme including a total of 66 ERW cases is designed as shown in Tables 2 and 3. When the simulations are completed, the cumulative oil production after the production period of 10 years () and of each case are calculated by Equations (8) and (9) and are recorded in Tables 2 and 3. The curves of oil production rates, , and average reservoir pressure for cases with different reservoir properties are illustrated in Figures 4–6, respectively.

(a)

(b)

(c)

(d)

(e)

(f)

(a)

(b)

(c)

(d)

(e)

(f)

(a)

(b)

(c)

(d)

(e)

(f)

Above all, Figure 4 demonstrates that the oil production rates descend sharply in the beginning of the production period (from the start to about 500 days) to a relatively low level. This is owing to the fact that the low permeability of the reservoir decreases the flow rates of oil far from the ERW; therefore, the oil production rates slump after the oil reserves near the ERW are depleted. This also results in the considerable decrease of the slope of the cumulative oil production curves in Figure 5 at the early production stage (generally before 750 days). Moreover, although the pressure around the ERW falls below 5 MPa, as shown in Figure 3, the average reservoir pressure for all the cases (except the cases with modified initial reservoir pressure) remains at a high level (above 7 MPa). Similar to the explanation in Section 3.1, the reason for this phenomenon is that the fluids far from the ERW hardly move, and the pressure at these regions is close to the initial reservoir pressure.

In terms of the formation rock compressibility, as illustrated in Figures 4(a) and 5(a), the oil production rates and experience little change as the value of varies. The largest difference in the values of is only m³ for different . This is because as increases, although is larger according to Equation (4), the average reservoir pressure is higher (as shown in Figure 6(a)), leading to a smaller pressure drawdown () of the reservoir, which offsets the growth in in Equation (9); therefore, the oil production rates and hardly change when differs. Moreover, a positive correlation is shown between and in Figure 5(a).

Compared with the results of , in Figures 4(b) and 5(b), more obvious variations are witnessed in oil production rates and , respectively, as changes from 1/MPa to 1/MPa. The largest difference in the values of of m³ is nearly 3 times as large as that in the results of different . This is due to the reason that the decreasing trend of the average reservoir pressure remains almost the same for different (Figure 6(b)), while larger contributes to greater . Therefore, based on Equation (9), the oil production rates and rise more evidently as goes upward. Similar to the cases of , the increase in also gives rise to the increment in (Figure 5(b)).

As for the initial reservoir pressure, it is indicated in Figures 4(c) and 5(c) that remarkable changes are found in oil production rates and . The maximal difference of is m³, which even surpasses the biggest value of in the results of different and . Since the bottom hole pressure is set as the constant value of (2 MPa), different results in marked changes in the average reservoir pressure (Figure 6(c)), and thus, the pressure drawdown () of the reservoir varies considerably, causing great impacts on oil production rates and . Apart from that, is positively proportional to due to the fact that larger contributed to a larger differential pressure used for driving out the oil (Figure 5(c)).

In terms of the effect of on , Figures 4(d) and 5(d) reveal that the oil production rates and ascend moderately as the value of rises. The maximum difference in for different is m³. In contrast to the cases analyzed above, an inverse correlation between and is manifested in Figure 5(d). This is because the bottom hole pressure is set as the same as , and lower leads to faster decrease of (Figure 6(d)), which conduces to greater pressure drawdown () of the reservoir and boosts the growth in both oil production rates and according to Equation (9).

Figures 4(e) and 5(e) indicate relatively small changes in oil production rates and as the value of varies. The reason for this phenomenon is similar to that for the situation in . Even though the increases attributed to larger , gradually ascends (as shown in Figure 6(e)) and results in lower pressure drawdown () of the reservoir, which dampens the growth of oil production rates and based on Equation (9). Furthermore, as rose, an upward trend is witnessed in (Figure 5(e)).

Based on the simulation results shown in Figures 4(f) and 5(f), marked differences in oil production rates and are illustrated as the value of ascends from 2.5 mD to 7.5 mD. The largest difference in the values of is up to m³, which is second only to that in the results of different . Although did not occur in Equation (9), in accordance with Equation (2), the reservoir fluid flows faster to the ERW when is larger; besides, also drops more intensely as increases (Figure 6(f)), which contributes to greater pressure drawdown () of the reservoir. Both two factors above enhance the oil production rates and . In addition, a positive association between and is shown in Figure 5(f).

3.3. Quantification of the Effect of Reservoir Properties on Cumulative Oil Production

The curves of for different properties are demonstrated in Figure 7, where each value on the -axis is the ratio of the value of the reservoir property in each case to the corresponding value in the ERW Base Case, and each value on the -axis is the of each case to that of the ERW Base Case. According to Figure 7, a 50% increase in contributes to a 63% increment in compared with the ERW Base Case, which is the largest growth among all the cases. A moderate rise of about 40% in can also be witnessed when the values of and are 0.5 times larger than that in the ERW Base Case. By contrast, the growth in (roughly 20%) is not obvious as rises from 1/MPa to 1/MPa. On the contrary, a slight downward trend in is found when goes upward from 1 MPa to 3 MPa. It is also worth mentioning that the absolute permeability has no influence on due to the reason that this property has no correlation with Equation (8).

In general, is in a direct ratio with , , , and but is in inverse proportion with . This can be elucidated by Equation (8): increases with larger and less , while the increments in , , and lead to the increase in , which results in more oil output as well.

The degree of sensitivity ( represents 10 for , or for ) are defined to quantify the impacts of various reservoir properties on ( represents 10 for or for ), which is computed by where is the change in , is the initial value of , is the maximum value of , and is the minimum value of . is the change in the value of the reservoir property ( stands for one of the reservoir properties in Table 1), is the initial value of , is the maximum value of , and is the minimum value of . Equation (10) is applicable under the condition that varies monotonically with .

Based on the simulation results, the degree of sensitivity for each reservoir property calculated by Equations (10)–(12) is demonstrated in Figure 8.

As illustrated in Figure 8, it is noteworthy that has the largest effect on both and , and the and of are 1.164 and 1.251, respectively. The impacts of and are significant on , and the values of and roughly equal 0.77, but their effects are not evident on . Moreover, although the absolute permeability has no influence on , it has an obvious effect on (0.587) owing to the fact that affects the flow rate of oil, as explained by Equation (2); therefore, has an indirect impact on .

and for different low-permeability reservoir properties are regularized to percentages and illustrated in Figure 9. Sorting these properties based on their influence on from high to low, the results are , , , , , and ; arranging these properties in terms of their impacts on from large to small, the results are , , , , , and .

4. Conclusion

ERW techniques are increasingly popular in reservoir exploration and exploitation. This work pivoted on the low-permeability reservoirs and established an ERW Base Case and a HW Case by numerical modeling techniques. The low permeability of the reservoir leads to a drastic decrease in the slope of cumulative oil production curves, and the pressure drawdown happens near the ERW and HW, while the oil reserves and pressure are close to the initial conditions of the reservoir. Furthermore, the comparison is made between the oil production and pressure distribution of the ERW Base Case and that of the HW Case. Although the curves of the cumulative oil production of the two models are similar, marked differences are found in the pressure distribution between the two models. The pressure is lower at the center of the ERW but is higher at two sides of the ERW in the ERW Base Case, whereas in the HW Case, the pressure witnessed a uniform distribution along the HW.

For the purpose of better recognizing the effect of low-permeability reservoir properties on oil production, 66 ERW cases were designed to analyze and quantify the influence of low-permeability reservoir properties on the oil output of ERWs. The results demonstrate that the oil production rates drop significantly at the early production stage, which slows down the increase of the cumulative oil production and the decrease of the average reservoir pressure. Apart from that, it is also identified that the cumulative oil production after the production period of 10 years () and the total cumulative oil production that can be driven out by natural energy () are directly proportional to the initial reservoir pressure, formation fluid compressibility, formation porosity, and formation rock compressibility and are most sensitive to the initial reservoir pressure. On the contrary, larger reservoir saturation pressure leads to lower . Besides, is in a positive ratio with an absolute permeability, while is not affected by this property.

Appendix

Model Validation

To validate the reliability of the established models, the model of Lyu et al. [23] pivoting on the development of the low-permeability reservoir is chosen for comparison due to its shape and scale similar to this work. Therefore, two numerical models with different well lengths and well distances are built under the same conditions to verify the reliability of the simulation in this paper. Figure 10 (Figures 10(a) and 10(c) for Lyu et al. [23] and Figures 10(b) and 10(d) for this work) demonstrates that the pressure distributions of this work are very similar to the corresponding results of Lyu et al. [23]. Thus, it is validated that the simulation in this research is reliable.

(a)

(b)

(c)

(d)

Data Availability

The key data is available in the paper.

Conflicts of Interest

The author declares that there are no conflicts of interest.

Acknowledgments

I gratefully thank the financial and computing power support of the Tianjin Branch of CNOOC Ltd.

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Copyright © 2023 Yanlai Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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