The Effect of Interlayer on Water Cut Rise in a Bottom Water Reservoir

A bottom water reservoir is universal in all reservoirs in the world. In the exploitation process of the bottom water reservoir, because the reservoir is in complete contact with bottom water, the natural energy supply of the bottom water reservoir is sufficient. At the same time, in the production process, the pressure drop generated by the formation is mainly concentrated near the wellbore, which leads to a short period of waterless oil production, fast water breakthrough, and fast water cut rise, which seriously affects the overall recovery factor and increases the risk of oil filed exploitation. Since the distribution of an interlayer enhances the heterogeneity of the reservoir, it has a prominent impact on the flow of oil and water in the bottom water reservoir. However, people know little about the impact of the interlayer on the bottom water reservoir. In this paper, the mathematical model of two-phase flow in the bottom water reservoir with the interlayer is proposed, and the numerical solution of the model is obtained by a finite element method. The influence of the distribution of the interlayer on the water cut rising law of the bottom water reservoir is analyzed. The results show that the bottom water is blocked by the interlayer and its own gravity and the rising height of the bottom water is limited, so that the interlayer has a significant inhibitory effect on the coning of the bottom water. The closer the interlayer is to the oil-water interface, the faster the water cut will rise; the narrower the interlayer is, the faster the bottom water ridge will advance; when the width of the interlayer is the same as that of the reservoir, the water cone will not appear; the higher the permeability of the interlayer is, the faster the upper body of the water cut will be; when the permeability of the reservoir and the interlayer is over 1000, the influence of the interlayer on the water cut rise is not obvious; the thickness of the interlayer on the water cut rise law has little effect. Finally, through the case analysis, it is proposed that the new horizontal wells should be arranged in the position where the interlayer develops. The findings of this study can help for the better understanding of control laws of the interlayer on the bottom water and providing a crucial theoretical basis for the development of the bottom water reservoir.


Introduction
An interlayer refers to the nonpermeable layer or ultralow permeable layer which is locally developed and discontinuously distributed in the reservoir. It is an important reason for the horizontal and vertical heterogeneity of the reservoir and is mainly controlled by the original sedimentation process and late diagenesis. In the development of a bottom water reservoir with the interlayer, the existence of the interlayer will lead to an unbalanced liquid production profile of horizontal wells, and the interlayer shielding section will produce more fluid and flood easily. Li deduced the water breakthrough prediction formula of the semipermeable barrier bottom water reservoir and made a theoretical discussion on the water cone shape [1]. Zhang and Sun analyzed the influence of interlayer properties on the inflow of the bottom water cone [2]. Based on the numerical simulation method, Zheng et al. analyzed the influence of interlayer permeability, interlayer size, and interlayer location on the development effect of the bottom water reservoir [3]. Zhao et al. used a numerical model to study the influence of permeability, size, and distribution of the interlayer on bottom water reservoir development [4]. It is considered that the water breakthrough time and productivity of horizontal wells do not increase monotonously with the decrease in interlayer permeability. There is an optimal interval for interlayer permeability, and there is also an optimal interval for interlayer size.
In terms of water cut of the oilfield, there are many factors affecting the increase in the water cut of oilfields, and different types of reservoirs have different water cut rise laws. Therefore, appropriate water cut variation curves shall be selected reasonably according to the physical properties of reservoirs and fluid properties to analyze and predict the change in water cut; then, different countermeasures can be taken in accordance with the objective law of reservoir development, thereby effectively controlling the water cut rise rate, extending the stable production period, and improving the development level of oilfields [5][6][7]. Wan divided five different types of displacement characteristic curves according to the relationship between recovery percent and water cut, including convex curve, convex and S-shaped transition curve, S-shaped curve, concave and S-shaped transition curve, and concave curve [8]. Li et al. divided the water cut rise characteristics of horizontal wells into four types such as well opening waterflooded type, rapid waterflooded type, stepped rise type, and climbing type [9]. Wei et al. developed a transient flow model considering the water influx/waterflood. Subsequently, the functions of the production decline-type curves for a vertical well with a water influx/waterflood are derived based on the material balance equation [10]. Liu and Cheng's research shows that the farther the barriers and interlayers from the OWC, the better the horizontal well development effect [11]. Xue et al. analyzed the water cut rise law of horizontal wells under four distribution patterns such as no interlayer, permeable interlayers, small-scope impermeable interlayers, and largescope impermeable interlayers [12]. Wang et al. established five distribution patterns of barriers and interlayers and studied the influence of them on water body migration in bottom water reservoirs [13]. The water cut rise characteristics of horizontal wells have been studied to some extent [14][15][16][17][18].
At present, the research on the influence of the interlayer on the development of the bottom water reservoir mostly adopts the numerical simulation method, but the numerical simulation also has its limitations, mainly for the need to establish a matching geological model and numerical simulation model; the accuracy of the model depends on the level of operation and proficiency, and the workload is huge. Therefore, it is of great theoretical value and practical significance to deduce the effect of the interlayer on the oil-water flow process in theory and establish a mathematical model that can accurately simulate oil-water flow in horizontal wells of the bottom water reservoir. This is also the advantage of our research, which is to better reflect the relationship between the interlayer and the change of water cut by establishing the oil-water two-phase mathematical model of the horizontal well in the bottom water reservoir with the interlayer. However, there will be some errors for specific instances. However, there will be some errors for specific instances.

Geofluids
In this paper, firstly a two-phase seepage numerical simulation method for a bottom water reservoir with barriers and interlayers has been established, and then, the influence of the main factors of barriers and interlayers on the water cut rise law has been analyzed; finally, the feasibility countermeasures for the horizontal well layout have been proposed through an example analysis combined with the distribution of barriers and interlayers.

Numerical Reservoir Simulation
Research on a Bottom Water Reservoir As shown in Figure 1, the main research contents include the establishment of the two-phase flow mathematical model of the bottom water reservoir with the interlayer and the discrete solution by the finite element method and the comprehensive analysis of interlayer position, interlayer size, interlayer thickness, interlayer permeability, the included angle of barriers and interlayers with the x-axis, etc. on the water cut rise law.
2.1. Two-Phase Model of the Bottom Water Reservoir. Figure 2 shows the reservoir profile. Assume that the length of the reservoir is a, the width is b, the height is h, the length of the horizontal well is L, and the center coordinate of the horizontal well is (0, 0, 0). By ignoring the capillary force effect, oil-water two-phase seepage flow occurs. Then, the oil-water two-phase control equation is described as follows: Motion equation: State equation: Auxiliary equation for water saturation and oil saturation:

Geofluids
Water phase equation: where ρ w and ρ o are the water phase density and oil phase density, respectively (g/m 3 ); s w and s o are the water phase saturation and oil phase saturation, respectively; μ w and μ o are the water viscosity and oil viscosity, respectively (Pa·s); φ is the porosity; v is the velocity vector (m/s); t is the time (s); and k rw and k ro are the relative permeability of water and oil, respectively. Combine equations (1)- (5). The finite element method is used for discrete solution to them. The model reservoir and fluid parameters are shown in Table 1, and the selected relative permeability curves are shown in Figure 2. This oil well is produced in a constant pressure mode. The initial pressure is set to 12 MPa, the bottom hole flowing pressure 10 MPa, and the production time is 6 years.

Influence of the Properties of Barriers and Interlayers on
the Water Cut Rise Law. The influence of interlayers on the water cut of the bottom water reservoir has been quantitatively studied in terms of interlayer position, interlayer size, interlayer thickness, interlayer permeability, the included   Figure 2, and the basic reservoir parameters are shown in Table 1.

Influence of the Position of Barriers and Interlayers.
The center coordinates of barriers and interlayers are set to (0, 0, -10), (0, 0, -15), and (0, 0, -20). Other reservoir parameters and fluid parameters are listed in Table 1. Figure 3 shows the influence of different positions of barriers and interlayers on the water cut rise law. As can be seen in Figure 3, different positions of barriers and interlayers have no influence on the water-free oil production period; in addition, the closer the barriers and interlayers are to the OWC, the faster the water cut rises. Figure 4 shows the water cone diagrams of different positions of barriers and interlayers at t = 1000 d. The closer the barriers and interlayers to the OWC, the higher the bottom water cresting rate and the earlier the saturated water in the barriers and interlayers.   Table 1. Figure 5 shows the influence of different positions of barriers and interlayers on the water cut rise law. As can be seen in Figure 5, the smaller the width of the barriers and interlayers, the higher the water cut rise rate.
As can be seen in Figure 6, the smaller the width of the barriers and interlayers, the higher the bottom water cresting rate. When the width of the barriers and interlayers is equal to that of the reservoir, water cones no longer appear.

Influence of the Permeability of Barriers and
Interlayers. Figure 7 shows the influence of different permeability of barriers and interlayers on the water cut rise law. The higher the permeability of barriers and interlayers, the higher the water cut rise rate.
When the ratio of the permeability of barriers and interlayers to the reservoir permeability is more than 1000, the influence of the permeability of barriers and interlayers on the water cut is not remarkable. As can be seen in Figure 8, the higher the permeability of barriers and interlayers, the more serious the bottom water coning. When the ratio of the permeability of barriers and interlayers to the reservoir permeability is more than 1000, the water cone shape change is not obvious. Figure 9 shows the influence of different thicknesses of barriers and interlayers on the water cut. As can be seen in the figure, the influence of the thickness of barriers and interlayers on the water cut is small. Barriers and interlayers have a certain inhibitory effect on water cut rise, but they cannot completely seal off the entire reservoir, so the influence of their thickness is small. As can be seen in Figure 10, the variation of the water cone shape at different thicknesses of barriers and interlayers is small. Figure 11 shows the influence of different well positions on the water cut curves. As can be seen in the figure, the longer the relative distance between the well and the barriers and interlayers, the lower the water cut and the longer the water-free oil production period. As can be seen in Figure 12, as the relative distance between the well and the barriers and interlayers increases, the phenomenon of bottom water coning is more and more unobvious and even water cones disappear.

Example Analysis
The B sand body is a typical meandering river sedimentary sand body formed from splicing and superimposition of multistage channel sands and has a thickness of 10~30 m. The sand body was put into production in 2004, where there are 13 development wells. Bottom water is developed in the high part of the structure of the B sand body, and edge water is developed in the low part of the structure. The natural energy is sufficient, and the reservoir thickness is large. According to the classification statistics of the water cut rise patterns of the single wells in the B sand body, the water cut rise law of the single wells involves 4 violent waterflooded wells, 7 rapid waterflooded wells, and 2 stepped rise type wells ( Table 2). The water cut rise types of the single wells are dominated by the rapid waterflooded type, followed by the violent waterflooded type and stepped rise type, without the climbing type ( Figure 13). Figure 14 shows the effective thickness contour map of oil layers in the B sand body. Production of the production wells of the B sand body is mainly related to the distribution of barriers and interlayers in the sand body. The thickness of the interlayers in the B sand body is 0.5~8.0 m. Their genetic type is mainly the widely distributed flood plain sedimentary mudstones. The development conditions of the interlayers are complex. Due to the repeated cutting action of multistage channels, most of the flood plain mudstones have poor continuity. In general, stable interlayers remain in the middle and east of the B sand body and are mostly developed in the middle and upper parts of the reservoirs. The interlayers in the H10 well area in the central part are generally thin and have poor blocking ability. The interlayers in the H4 well area in the east are thick and have an average