Mechanistic Studies of Gravity-Assisted Water Flooding in a Thick Heavy Oil Reservoir through Horizontal Injectors Using Three-Dimensional Physical Model

Laboratory experiments were conducted to investigate the mechanism(s) of water flood with horizontal injection wells. The experiment was performed using a three-dimensional (3D) physical model made by artificial sandstone of the dimension of 60 cm × 30 cm × 5 cm. The saturation profile of oil and water phases was monitored by measuring the electrical resistivity using microelectrodes. It is difficult to model a field-scale gravity-assisted water flood process in the laboratory as the gravity force is very small in the physical model. In this paper, similarity criteria, dimensional analysis, and π principle were used to design the model parameters.We found that the ratios of gravity force to production pressure differential, capillary force, and viscous force are the three most important similarity criteria. Based on dimensional analysis, both capillary and viscous forces were designed in the physical model to represent the capillary and bond number in the reservoir conditions. Hence, in physical model, rock permeability of 6 darcies was selected to reduce the capillary force and the fluid viscosity of 583 cp was selected to reduce the viscous force based on calculation. The use of horizontal injection well can improve the sweep efficiency by 17.2%, compared with the case of vertical injection well. To determine the optimal driving force, the ratio of gravity force and production pressure differential was varied from 1 : 1 to 1 : 16. The experiment has shown that the ratio of 1 : 8 yields the highest heavy oil recovery (44.04%).


Introduction
Water flood provides a main driving mechanism to recover the oil, which is simple, inexpensive secondary recovery process and is being widely used.Applications of horizontal wells in water flooding as injectors and/or producers continue to grow.The horizontal wells have been shown to improve the ultimate oil recovery over that of conventional vertical wells during a regular water flood and enhanced oil recovery (EOR).More attention has been given recently to investigate how horizontal wells contribute to ultimate oil recovery in these processes.
Hovanessian and Fayers [1] found that gravity had a pronounced effect on the saturation profile and the pressure distribution curves using horizontal injectors.Numerical simulation was carried out in the study of the hybrid system of vertical producers and horizontal injectors by Cunningham and Chaliha [2].It was found that the horizontal wells added little benefit of sweep volume in the lower unit.However, there was no study of benefits of horizontal injections in an areal pattern.Al Gharaib and Gharbi [3] used numerical method to investigate a part of the nine-spot pattern where the horizontal wells were used as injectors.Their results showed that the hydrocarbon recovery from the nine-spot pattern was related to the lateral aspect ratio.Meanwhile, the long horizontal wells did not guarantee an improved oil recovery.As to physical model used in laboratory study, Ferreira et al. [4] conducted the studies in the 2D and 3D physical models which were similar to a 5-spot well pattern in a 40-acre spacing.In their pioneering study, the oil-water mobility ratio was designed to be from 1 to 10.This oil viscosity is too low to fit the scenario existing in the heavy 2 Mathematical Problems in Engineering oil reservoir.Although Ferreira et al. [4] studied the pressure profile and the displaced oil volume, they failed to monitor the fluid saturation in their model.
Very few researchers have investigated the effect of horizontal wells on water flooding of heavy oil reservoirs.Cao et al. [5] studied the dimensionless height without perforation and the perforation length in horizontal segment, with some optimization results for five-spot and nine-spot system using numerical simulation under the conditions in heavy oil reservoirs, which was related to the type of injection system, horizontal length of horizontal wells, and the position for perforation.Based on the field test conducted in Liao-He oilfield in Liaoning province, Ding [6] concluded that the gravity-assisted lateral water flooding would tap the potential of the remaining oil with the energy supplement in the upper segment of the heavy oil reservoir.
The formation of interest in this study is called Block A, which is a part of positive rhythm thick heavy oil reservoir.There is enrichment of remaining oil between the top of the reservoir and the well after water flooding and steam huff and puff [7][8][9][10].Horizontal wells at the top of reservoir are being put forward to resolve the problems existing in Block A development process and remaining oil distribution.After placing a vertical production well at the bottom and a horizontal injection well at the top, the remaining oil can be produced with the aid of the gravity of thick oil layer.Horizontal injection well has advantages of low injection pressure and large injection volume, and especially it can improve the sweep efficiency [11,12].The gravity in thick reservoir contributes to the enhancement of vertical seepage velocity, which makes oil and water exchange sufficiently.It also enlarges the swept area of reservoir longitudinally and then improves reservoir development effect.Therefore, we can use the dual advantages of the horizontal well and the gravity to explore this part of the remaining oil and reach the purpose of improving oil recovery.
In order to clearly define the contributions of different driving mechanisms involved in this gravity-assisted water flooding process in thick heavy oil reservoir, a more practical and innovative physical simulation system is required.Similarity criteria were introduced in the mechanistic study of the physical model.Meanwhile, the paper presents the contours of the oil saturation in the three-dimensional model, which is calculated using the real-time data from the electrical resistivity monitoring system.Furthermore, an optimization of the injection parameters was performed by this new approach to physical simulation method, which is forwardlooking and innovative.

The Monitoring of Movable Fluid Saturation by Measuring the Electrical Resistivity
Electrical conduction is assumed not to be present within the rock grains or in fluids other than water.The relationship between water saturation and resistivity is depicted by Archie Equation ( 1), which is typically valid for shale-free clean formation.Hence, the evaluation of water saturation becomes possible when we measure the resistance change along the core sample during a water flood.
The greater the concentration of formation water in the rock is, the smaller the resistance between the inlet and outlet faces of the rock will be [13][14][15].Therefore, the reservoir electrical property can be used to evaluate the change of water saturation.When the porosity and water salinity are constant, the resistivity index "" is only dependent on oil and water saturation, which is where   is the resistivity of rock sample with a certain saturation and oil, gas, and water; 0 is the resistivity of rock sample with 100% water saturation; is the saturation of formation water in the rock; is saturation exponent.
The change of oil and water saturation was monitored by measuring the electrical resistance in a real-time manner.As shown in Figure 1, the saturation monitoring system is made up of microelectrode, transmission cable, digital output board, and A/D conversion interface board and computer.The electrical properties in the core flow physical model can be measured from the different points simultaneously in a real-time manner.In the displacement-type experiment in 3D physical model, the data acquisition system monitors the change of resistivity in different points and layers, and the data can be used to determine the distribution of oil and water saturation and water front.
In order to accurately determine the changes of water saturation, we have established the relationship between resistance value and water saturation in a 1D core flood model [16].We injected different ratios of oil and water (4 : 1, 3 : 2, 4 : 3, 1 : 1, 3 : 4, 2 : 3, 1 : 2, and 1 : 5) into the 1D model and then measured the resistance value under different water saturation.We then obtained the relationship of resistance and water saturation, as shown in Figure 2.
Using the established correlation, we can further calculate the oil saturation in the sample by measuring the resistance and obtain the oil saturation of the model in different locations and different time points during the core flood.

Three-Dimensional Physical Model and Simulation Experiments
3.1.Model Parameter Selection from Similarity Criteria.Based on two-phase mathematical model considering gravity and capillary force, we derived the gravity similarity criterion for a water flood from the top of the reservoir using horizontal wells, with the aid of dimensional analysis method and Buckingham  theorem, as shown in Table 1 [17,18].As depicted in Table 1, three  terms represent the contribution of four forces (gravity force, driving force, capillary force, and viscous force) in the reservoir which  influence the distribution of oil and water phases.From similarity criterion sensitivity analysis, we found that  1 and  2 have the larger impact on the development of oil field using the horizontal injection well at the top of thick oil layer.They are the main factors controlling the oil and water distribution longitudinally.Based on the similarity criterion of  1 ,  2 , and  3 as described above, we have designed and selected the size of the experimental model, the rock permeability, the injection rate, and the viscosity of crude oil.Table 2 shows the relationship between rock intrinsic permeability and capillary pressure  50 ( 50 represents the capillary pressure when mercury injection saturation is 50% on the intrusive mercury injection curve) from the routine core analysis.As expected, with the increase of the sample permeability, the capillary force  50 is reduced.Therefore, we can select a sample with reasonable capillary force by inferring from the rock permeability.We have summarized all the critical parameters involved in the  experimental design based on the similarity criterion of  1 ,  2 , and  3 , as shown in Table 3.

The Effects of Horizontal Well on the Sweep Efficiency.
As suggested by similarity criteria, we have constructed two different physical models: horizontal injection well, vertical production well, and vertical injection well, vertical production wells (the length of horizontal well was 30 cm and the vertical well was perforated at 3 cm from top to bottom), as shown in Figures 3 and 4, respectively.The electrodes were arranged uniformly on the model.We performed water flooding experiment in these two different physical models using constant injection rate of 0.1 mL/min.The resistance data was acquired in each electrode to monitor the distribution of water saturation and water flooding sweep efficiency.
The oil recovery factor, areal sweep efficiency, and remaining oil saturation in two different injection-production well patterns are summarized in Table 4.The relationship between water cut, cumulative oil recovery, and the cumulative water injection volume is shown in Figure 5.
The experiments results indicate that the oil recovery factor using horizontal injection well is better than that of vertical injection well.The remaining oil saturation after water flood using horizontal injector is 45.08%, which is less than that of vertical injection well, which is 49.61%.The areal sweep efficiency of horizontal well is 17.2% larger than vertical

Figure 1 :
Figure 1: (a) The diagram of core flow setup and data acquisition system.(b) The actual saturation measurement system and physical simulation model.

Table 1 :Figure 2 :
Figure 2: The correlation of resistance and water saturation.

Figure 3 :
Figure 3: Illustration of horizontal well pattern and physical model design.

Figure 4 :Figure 5 :
Figure 4: Illustration of vertical injection well pattern and physical model design.

Table 2 :
Permeability and capillary force of the core.

Table 3 :
The comparison of parameters for reservoir property and physical model.

Table 4 :
Comparison of the average recovery factor, the areal sweep efficiency, and the remaining oil saturation in two different injectionproduction well configurations.