Stochastic Simulation on Preferential Seepage Channels in Water-Flooding Reservoirs

Stochastic Simulation on Preferential Seepage Channels in Water-Flooding Reservoirs Ying Zhang Southwest Petroleum University, college of science, Chengdu, Sichuan, People s Republic of China, 610500. e-mail:1186752815@qq.com Feng Yao Jiangsu Oilfield Oil Recovery Engineering Research Institute, Yangzhou, Jiangsu Province, People s Republic of China, 225000. Dongsheng Xu Southwest Petroleum University, college of science, Chengdu, Sichuan, People s Republic of China, 610500. Biao Ma Southwest Petroleum University, college of petroleum engineering, Chengdu, Sichuan, People s Republic of China, 610500. Hengshen Yao Southwest Petroleum University, college of science, Chengdu, Sichuan, People s Republic of China, 610500. ABSTRACT In order to design a more accurate method of profile control and water shutoff, the technique that quantitatively describes the distribution of preferential seepage channels was proposed. The method being researched concerns about plugging the preferential seepage channels and adjusting oil-water mobility ratio in which way leads to water move forward. After simulating the distribution of high permeability zones and the probability distribution of the pores of different level,the preferential channels was divided into several sub-areas in its crosswise. Also, the probability distribution and volume of the divided channels at different levels should be calculated, together with the connecting distance between channels of different levels. On the basis of stochastic simulation, plugging control scheme can be designed, which determined the amount of blocking agent and optimizing strength. At the last of the paper, an example was given which proved the feasibility of the method. KEYWORDS: Preferential seepage channel, Profile control and water shutoff, Stochastic simulation, Probability distribution - 803 -

Vol. 20 [2015], Bund. 2 804 INTRODUCTION At present, most oilfield in China has developed into a stage of high-water-cut producing. At the circumstance, there always exists high permeability zones even higher permeability zones in reservoirs, namely preferential seepage channels or large pore paths. Watering in this case, the injected water will circulate along the preferential seepage channel inefficiently or even valid that reduces the swept volume, as a result, the ultimate oil displacement efficiency is poor. In order to increase the recovery efficiency of oilfield, not only oil production rate and injection intensity should be controlled, but also a more advanced technology of profile control and water shutoff should be taken. So it is necessary to study the distribution of high permeability zones and the probability distribution of pore radius in preferential seepage channels. After stochastic simulation, the volume of high permeability zones should be calculated in order to ascertain the amount and strength of blocking agent. In this paper, stochastic simulation method is used in the quantitative description and determination of high permeability zones according to the seepage mechanism of porous media. METHODS While water-flooding, the pressure gradient is different in reservoir, for instance, the pressure gradient adjacent the production well is larger, where the scouring force from water to layer is larger too, which is more likely to lead to the formation of preferential seepage channels or large pore paths. In order to make further analysis, the method to simulate preferential seepage channels could be denoted as follows. In a five-spot pattern, injection well is at point O, production well is at point W, R e is the distance between injection well and production well. Based on previous study, unit interval [0, RR ee ] could be divided into several portions, here the interval was divided into 100 divisions for further study. Figure 1 showed a division which divided the interval [0, RR ee ] into 9 portions. Figure 1: Dividing schematic plot

Vol. 20 [2015], Bund. 2 805 Each of the portion could be considered as incompressible liquid which is nonreversing. Seeing from the macro sense, every portion flowed different. So it could be decided that the 100 portions together formed the flow between injection well and production well. According to Darcy s law, flow formula of the j portion could be written as: QQ jj = KK jjaa jj PP jj aaaaaa where AA jj is wetted cross-sectional area of the j portion, mm 2 ; KK jj is permeability of the j portion, mmmm; PP jj is differential pressure on both ends of the j portion, mmmmmm; QQ jj is the flow of the j portion, mm 3 per month; LL is the length of one portion, which could be expressed as RR ee, mm; 100 μμ is viscosity, mmmmmm ss; aa is unit correction coefficient, aa = 0.3858 Considering the above formula, the permeability of the j portion could be depicted as: KK jj = aaqq jjμμμμ AA jj PP jj Based on above formula, when flow, pressure difference and seepage cross-sectional area are known, then the value of permeability could be solved. The method to calculate flow, differential pressure and seepage cross-sectional area are listed below. Flow calculation By using the linear combination of water absorption capacity in one month of i portion described as QQ 1 and liquid production capacity in one month of the i portion described as Q 2, the value of flow of the i portion could be written as: 100 ii QQ ii = QQ 1 100 + QQ 2 ii, ii = 1,2,,100 100 Differential pressure calculation Figure 2: Pressure schematic plot

Vol. 20 [2015], Bund. 2 806 As we can see from figure 2, while the injection well A and production well B worked at the same time, the pressure at one point M could be inferred, the process are revealed below. pp MM = pp ee + pp WWWW pp ee IIII rr ee rrww IIII rr ee pp ee pp WWWW rr 1 IIII rr ee rrww IIII rr ee rr 2 Where pp WWWW = pp WWWW SS pp WWWW + SS SS 2 pp ee 1 SS 2 pp WWWW = pp WWWW SS pp WWWW + (SS SS 2 ) pp ee 1 SS 2 SS = IIII rr ee RR IIII rr ee rr ww where rr 1 is the distance between point M and the injection well A; rr 2 is the distance between point M and the production well B; rr ee is the supply radius; rr ww is the wellbore radius; R is the distance between injection well and production well; pp WWWW, p WB is respectively the pressure at bottom of the injection well and the production well while the injection well and production well worked at the same time. Seepage cross-sectional area calculation y A W θ Bxy (, ) β O r x Figure 3: Cross-sectional area schematic plot As shown in figure 3, when the radius of the circle is r, the curve depicted as yy = xx αα, they intersect at point (xx, yy),solve the system of equations below, and the answer is the point (xx, yy) which we are searched for. yy = xx αα xx 2 + yy 2 = rr 2

Vol. 20 [2015], Bund. 2 807 Next, ββ could be got from ββ = tttttt 1 yy, θθ = ππ 2ββ, set reservoir thickness as h, xx 2 then we can solve the seepage cross-sectional area by the following formula: AA = rrrrh = rr ππ 2 2tttttt 1 yy xx h Now the value of flow, differential pressure, seepage cross-sectional area is known, so the permeability of the section which radius was r could be calculated. By using the method mentioned in paper The Method of Stochastic Simulation on High Permeability Zones in Water-flooding Reservoirs, the probability of pores of different level could be solved. Channel volume calculation For the sake of quantitative analysis the location of big hole and its distribution of different level, further study should be carried out on the volume of the channel of all levels, the process is revealed below: As can be seen in Figure 3, RR ee was the distance between the injection well O and the production well W, aa = 2 2 RR ee, set the radius of the circle as r and the curve as yy = aa 1 αα xx αα, they intersect at point (xx, yy),solve the equation set below: yy = aa1 αα xx αα xx 2 + yy 2 = rr 2 Then the answer (xx, yy) can be obtained. From Got tttttttt = xx rr aa αα 1, ββ = tttttt 1 xx rr aa αα 1, θθ = ππ 2 2ββ, The area of the sector AOB could be written as: SS AAOOOO = ππππrr2 The area yy = xx tttttttt and yy = aa 1 αα xx αα shaped: xx 0 SS = (μμ tttttttt aa 1 αα μμ αα ) dddd 0 2 = 1 2 xx rr 2 tttttttt aa1 αα αα + 1 xx rr αα+1 = 1 2 1 aa + 1 xx αα+1 rr aa αα 1 The area of big hole distribution within the circle which radius was r: SS rr = 2SS + SS AAAAAA = 1 2 αα + 1 xx αα+1 rr ππ2 4ππtttttt 1 aa αα 1 + 4 xx rr aa αα 1 The probability distribution of small pores, medium pores, large pores and extremely large pores at radius r was respectively pp 1 (rr), pp 2 (rr), pp 3 (rr), pp 4 (rr), divided the interval

Vol. 20 [2015], Bund. 2 808 [0, RR ee ] into 100 portions, each portion is the same length, the length is R e n the pore of the r portion which was in i level can be calculated by: where SS rr = 1 2 xx αα+1 rr αα+1 the value of xx rr can be got from nn VV ii = (SS rr SS rr 1 ) h pp ii RR ee rr nn rr=1 + ππ2 4ππtttttt 1 xxrr aa αα 1 aa αα 1 4 Application of the method yy = aa 1 αα xx αα xx 2 + yy 2 = rrrr ee nn 2,then the volume of rrrr ee nn 2 rr = 1,2,, nn 1 SS 0 = 0 At one oilfield in China there exists an injection well (number 86), it has 6 corresponding production wells; by using the method we proposed, divided each preferential seepage channels formed between the injection well and the production wells into 100 portions. Next, simulation method can be used to determining the pore level at different nodes. At last, to obtain the distribution of preferential seepage channel, connected the adjacent nodes only the same level or higher level from the injection well to the production well. The figures are provided below. Table 1 lists the volume of channel at different level between the injection well and its corresponding production well. Figure 4: extremely large pores between injection well and production well

Vol. 20 [2015], Bund. 2 809 Figure 5: large and extremely large pores between injection well and production well Figure 6: 4 level pores between injection well and production well Figure 7: extremely large pores between injection well and number 47 production well

Vol. 20 [2015], Bund. 2 810 Figure 8: large and extremely large pores between injection well and number 47 production well Well number Whole volume Table 1: Volume of 4 level pores VV 1 VV 2 VV 3 VV 4 5087 4109.29342 1761.58518 278.282724 13.3061005 2056.11942 5047 17295.571 2887.84854 4576.71666 1072.13044 8768.87536 5073 43106.6147 16210.6384 5069.59998 245.973408 21580.403 7886 25178.5445 4897.4507 7100.61984 532.040681 12648.4333 5124 15791.2486 2773.93913 4817.42104 273.959475 7925.92892 275 13862.3687 4198.9254 2586.80343 131.00254 6945.63733 Figure 9: 4 level pores between injection well and number 47 production well VV 1 refers to the volume of extremely large pores. VV 2 refers to the volume of large pores.

Vol. 20 [2015], Bund. 2 811 VV 3 refers to the volume of medium pores VV 4 refers to the volume of small pores As a consequence, we could ensure the quantity of plugging agent. After implementing it into practice, the result shows that the method is effective in enhancing oil recovery. CONCLUSIONS Firstly, by means of the formula to calculate flow, differential pressure and seepage cross-sectional area, we can obtain the permeability at any point. In addition, on the basis of quantitatively analysis the distribution and probability distribution of the pores at different level, we can calculate the volume of pores at different level, what s more, we can determine the quantity of the plugging agent according to the result. Finally, by applying the simulation method to practical, it can be concluded that the method is useful to solve the problem of preferential seepage channel exists in reservoir. ACKNOWLEDGEMENTS Here and now, I would like to extend my sincere thanks to all those who have helped me make this paper possible and better. Especially my honorable supervisors, Dongsheng Xu and Hengshen Yao. I appreciate your help so much. REFERENCES [1] Zhao hua, Meiqin Lin, Zhaoxia dong, Mingyuanli, Guiqing Zhang, Jie Yang. Study of deep profile control and oil displacement technologies with nanoscale polymer microspheres. Journal of colloid and Interface Science: Volume 424, 15 june2014, Pages67-74 [2] Ru qiao, Rui Zhang, Weiqun Zhu, Peijun Gong. Lab simulation of profile modification and enhanced oil recovery with a quaternary ammonium cationic polymer. Journal of Industrial and Engineering Chemistry. Volume 18, issue 1, 25 January 2012,Pages 111-115. [3] Ru Qiao, Weiqun Zhu. Evaluation of modified cationic starch for impeding polymer channeling and in-depth profile control after polymer flooding. Journal of Industry and Engineering Chemistry. Volume 16, issue 2, 25 March 2010, Page 278-282. [4] Yanbin Cao, Dongqing Liu, Zhongping Zhang. Steam channeling control in the steam flooding of super heavy oil reservoirs, Shengli Oilfield. Petroleum Exploration and Development. Volume 39, issue 6, December 2012, Pages 785-790. [5] Jing Wang, Huiqing Liu, Zenglin Wang, Jie Xu, Dengyu Yuan. Numerical simulation of preformed particle gel flooding for enhancing oil recovery. Journal of Petroleum Science and Engineering. Volume 112, December 2013, Pages 248-257.

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