Establishment and Application of a New Analytical Fractional Flow Equation

doi:10.7657/XJPG20210208

Abstract

Abstract:

On the basis of determining the new generalized water flooding characteristic curves, by using reverse reasoning methods, the water flooding characteristic curves can be inverted into the laws of water cut variation, and then combined with the Welge equation, the analytical fractional flow equation when water drives oil can be derived. The new fractional flow equation is a transcendental equation, and under certain conditions, it can be simplified to the results of typical oil-water two-phase seepage experiment. If the new analytical fractional equation is combined with the Levinlet function, the relation of oil-water permeability ratio that characterizes the two-phase seepage characteristics can be obtained. The water-flooding experimental data from 4 different types of reservoirs were used to perform fitting, the results showed that the fitting degree of the new equation was high, and the fitting effects were satisfactory. Furthermore, the laws of water cut variation corresponding to the new equation can not only describe the relationship between convex-shaped recovery degree and water cut, but also can describe the correlation between S-shaped, concave-shaped recovery degree and water cut. Taking the reservoirs in Xishanyao formation of Baka oilfield as an example, the analytical fractional flow equation of actual water displacing oil was given by using production data.

Key words: generalized water flooding characteristic curve, water cut variation law, recovery degree, water cut, fractional flow equation, seepage characteristic, oil-water permeability ratio

CLC Number:

TE341

GAO Wenjun, YIN Rui, GAO Neng, SHENG Han, GAO Zhijiang. Establishment and Application of a New Analytical Fractional Flow Equation[J]. Xinjiang Petroleum Geology, 2021, 42(2): 179-187.

Figures/Tables 11

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References 24

[1]	窦宏恩, 张虎俊, 沈思博. 对水驱特征曲线的正确理解与使用[J]. 石油勘探与开发, 2019,46(3):755-761.
	DOU Hongen, ZHANG Hujun, SHEN Sibo. Correct understanding and applying of water-flooding characteristic curve[J]. Petroleum Exploration and Development, 2019,46(3):755-761.
[2]	俞启泰. 几种重要水驱特征曲线的油水渗流特征[J]. 石油学报, 1999,20(1):56-60.
	YU Qitai. Characteristics of oil-water seepage flow for several important water drive curves[J]. Acta Petrolei Sinica, 1999,20(1):56-60.
[3]	陈元千. 水驱曲线关系式的推导[J]. 石油学报, 1985,6(2):69-78.
	CHEN Yuanqian. Derivation of relationships of water drive curves[J]. Acta Petrolei Sinica, 1985,6(2):69-78.
[4]	陈元千. 一种新型水驱曲线关系式的推导及应用[J]. 石油学报, 1993,14(2):65-73.
	CHEN Yuanqian. Derivation of a new type of water displacement curve and it’s application[J]. Acta Petrolei Sinica, 1993,14(2):65-73.
[5]	陈元千. 对纳扎洛夫确定可采储量经验公式的理论推导及应用[J]. 石油勘探与开发, 1995,22(3):63-68.
	CHEN Yuanqian. Application and derivation of Nazalov’s empirical formulas[J]. Petroleum Exploration and Development, 1995,22(3):63-68.
[6]	高文君, 徐君. 常用水驱特征曲线理论研究[J]. 石油学报, 2007,28(3):89-92.
	GAO Wenjun, XU Jun. Theoretical study on common water-drive characteristic curves[J]. Acta Petrolei Sinica, 2007,28(3):89-92.
[7]	徐君, 高文君, 杨文战. 对标定可采储量的水驱特征曲线法的改进[J]. 新疆石油地质, 2007,28(6):741-744.
	XU Jun, GAO Wenjun, YANG Wenzhan. The modification of water-drive characteristic curve to calibrate recoverable reserve[J]. Xinjiang Petroleum Geology, 2007,28(6):741-744.
[8]	高文君, 彭长水, 李正科. 推导水驱特征曲线的渗流理论基础和通用方法[J]. 石油勘探与开发, 2000,27(5):56-60.
	GAO Wenjun, PENG Changshui, LI Zhengke. A derivation method and percolation theory of water-drive characteristic curves[J]. Petroleum Exploration and Development, 2000,27(5):56-60.
[9]	童宪章. 天然水驱和人工注水油藏的统计规律探讨[J]. 石油勘探与开发, 1978,5(6):40-69.
	TONG Xianzhang. On exploration of statistical regularity in naturally flooded and artificially water flooded reservoirs[J]. Petroleum Exploration and Development, 1978,5(6):40-69.
[10]	俞启泰. 水驱特征曲线研究(四)[J]. 新疆石油地质, 1997,18(3):247-258.
	YU Qitai. Study on the water displacement curves(4)[J]. Xinjiang Petroleum Geology, 1997,18(3):247-258.
[11]	张金庆. 一种简单实用的水驱特征曲线[J]. 石油勘探与开发, 1998,25(3):56-57.
	ZHANG Jinqing. A new practical water displacement curve[J]. Petroleum Exploration and Development, 1998,25(3):56-57.
[12]	俞启泰. 一种广义水驱特征曲线[J]. 石油勘探与开发, 1998,25(5):48-50.
	YU Qitai. A new generalized water drive curve[J]. Petroleum Exploration and Development, 1998,25(5):48-50.
[13]	高文君. 双对数型水驱特征曲线理论基础[J]. 新疆石油地质, 2008,29(3):338-340.
	GAO Wenjun. Theoretic basic of bilogarithmic water-drive characteristic curves[J]. Xinjiang Petroleum Geology, 2008,29(3):338-340.
[14]	油气田开发专业标准化技术委员会. 石油可采储量计算方法：SY/T 5367—2010[S]. 北京: 石油工业出版社, 2011.
	Standardization Technical Committee for Oil and Gas Field Development. The estimated methods of oil recoverable reserves：SY/T 5367—2010[S]. Beijing: Petroleum Industry Press, 2011.
[15]	高文君, 刘志远, 薛龙龙. 利用反向推理方法确定水驱特征曲线渗流方程[J]. 断块油气田, 2020,27(4):478-483.
	GAO Wenjun, LIU Zhiyuan, XUE Longlong. Determination of seepage equation of water drive characteristic curve by reverse derivation method[J]. Fault-Block Oil & Gas Field, 2020,27(4):478-483.
[16]	高文君, 徐冰涛, 王谦, 等. 利用水驱特征曲线确定活塞式驱程度指数的方法[J]. 新疆石油地质, 2000,21(4):311-314.
	GAO Wenjun, XU Bingtao, WANG Qian, et al. Using water drive curves for determination of piston displacement degree index[J]. Xinjiang Petroleum Geology, 2000,21(4):311-314.
[17]	钟德康. 多次幂指数型广义水驱特征曲线的建模和应用[J]. 石油学报, 2017,38(3):333-341.
	ZHONG Dekang. Modeling and application of generalized water flooding characteristic curve based on multi-power exponent[J]. Acta Petrolei Sinica, 2017,38(3):333-341.
[18]	高文君, 宋成元, 付春苗, 等. 经典水驱油理论对应水驱特征曲线研究[J]. 新疆石油地质, 2014,35(3):307-310.
	GAO Wenjun, SONG Chengyuan, FU Chunmiao, et al. A study of water-drive type curves corresponding to the classical theories for water displacing oil[J]. Xinjiang Petroleum Geology, 2014,35(3):307-310.
[19]	王继强, 石成方, 纪淑红, 等. 特高含水期新型水驱特征曲线[J]. 石油勘探与开发, 2017,44(6):955-960.
	WANG Jiqiang, SHI Chengfang, JI Shuhong, et al. New water drive characteristic curves at ultra-high water cut stage[J]. Petroleum Exploration and Development, 2017,44(6):955-960.
[20]	宋兆杰, 李治平, 赖枫鹏, 等. 高含水期油田水驱特征曲线关系式的理论推导[J]. 石油勘探与开发, 2013,40(2):201-207.
	SONG Zhaojie, LI Zhiping, LAI Fengpeng, et al. Derivation of water flooding characteristic curve for high water-cut oilfields[J]. Petroleum Exploration and Development, 2013,40(2):201-207.
[21]	胡伟, 杨胜来, 翟羽佳, 等. 油–水相对渗透率曲线优化校正新方法[J]. 石油学报, 2015,36(7):871-875.
	HU Wei, YANG Shenglai, ZHAI Yujia, et al. A new optimization and correction method of oil-water phase relative permeability curve[J]. Acta Petrolei Sinica, 2015,36(7):871-875.
[22]	崔传智, 徐建鹏, 王端平, 等. 特高含水阶段新型水驱特征曲线[J]. 石油学报, 2015,36(10):1 267-1 271.
	CUI Chuanzhi, XU Jianpeng, WANG Duanping, et al. A new water flooding characteristic curve at ultra-high water cut stage[J]. Acta Petrolei Sinica, 2015,36(10):1 267-1 271.
	万吉业. 水驱油田的驱替系列及其应用(Ⅰ)[J]. 石油勘探与开发, 1982,9(6):65-72.
	WAN Jiye. A series of displacement characteristic curve and its application on the prediction performance of water-flooded oil reservoirs(Ⅰ)[J]. Petroleum Exploration and Development, 1982,9(6):65-72.
[23]	王子强, 李春涛, 张代燕, 等. 吉木萨尔凹陷页岩油储集层渗流机理[J]. 新疆石油地质, 2019,40(6):695-700.
	WANG Ziqiang, LI Chuntao, ZHANG Daiyan, et al. Flow mechanism of shale oil reservoir in Jimsar sag[J]. Xinjiang Petroleum Geology, 2019,40(6):695-700.
[24]	薛江堂, 刘珍, 薛龙龙, 等. 水驱开发油藏高含水期驱替程度和波及系数变化规律[J]. 新疆石油地质, 2018,39(5):573-577.
	XUE Jiangtang, LIU Zhen, XUE Longlong, et al. Study on displacement degree and sweep efficiency variation of water-drive reservoirs at high water-cut stage[J]. Xinjiang Petroleum Geology, 2018,39(5):573-577.