一种新的油水相渗数学模型建立及应用——以吐哈盆地低黏油藏为例

doi:10.7657/XJPG20240612

摘要/Abstract

摘要：

针对吐哈盆地低黏油藏油相相对渗透率初期急剧下降，高含水期后下降变缓的特点，提出了一种新的油水相渗数学模型。新模型待定参数求解简便，拟合精度较高，不仅可以描述初期急剧下降、后期下降变缓的油相相对渗透率曲线，以及弓背形水相相对渗透率曲线，还可以描述常见的“X”形油水两相相对渗透率曲线。为了应用方便，提出了新的油水相渗数学模型对应的水驱油解析法，并与Gao简化式油水相渗数学模型对比，进一步论证了油层平均含水饱和度与出口端含水饱和度的线性关系式，直接代入分流量方程中，可得到一种新的广义含水变化规律。油藏应用效果较好，可供同类油藏借鉴。

关键词: 吐哈盆地, 低黏油藏, 油相, 水相, 相对渗透率, Welge方程, 水驱油解析法, 水驱规律

Abstract:

The low-viscosity reservoirs in the Tuha basin exhibit rapid decline of oil relatively permeability in the initial development stage and slower decline in the late development stage with high water-cut. This paper presents a new mathematical model of oil/water relative permeability. The new model simplifies the determination of parameters and offers a high fitting accuracy. It can describe the oil relative permeability curve and the convex water relative permeability curve, and also the common X-shaped oil/water two-phase relative permeability curve. For convenient application, the new model was configured with a corresponding water flooding analytical method, and then compared with the Gao’s simplified model of oil/water relative permeability. In this way, the linear relationship between the average water saturation of oil layer and the water saturation at the outlet end was further validated. By directly substituting this relationship into the fractional flow equation, a new generalized water cut variation pattern was derived. The actual application of this model shows good results, making it a valuable reference for similar reservoirs.

Key words: Tuha basin, low-viscosity reservoir, oil, water, relative permeability, Welge equation, water flooding analytical method, water flooding pattern

中图分类号:

TE341

葛启兵, 刘倩, 马建红, 高文君. 一种新的油水相渗数学模型建立及应用——以吐哈盆地低黏油藏为例[J]. 新疆石油地质, 2024, 45(6): 725-734.

GE Qibing, LIU Qian, MA Jianhong, GAO Wenjun. Establishment and Application of a New Mathematical Model of Oil/Water Relative Permeability: A Case Study of Low-Viscosity Reservoirs in Tuha Basin[J]. Xinjiang Petroleum Geology, 2024, 45(6): 725-734.

图/表 12

表1

吐哈盆地稀油油藏油水两相相渗数学模型拟合结果"

岩样号	渗透率/mD	油相			水相
岩样号	渗透率/mD	n	b	相关系数	$K r w (S o r)$	m	c	相关系数
鄯10-131井4号	1.43	0.141 5	-0.118 0	0.999 99	0.250 6	1.235 3	-0.439 1	1.000 00
陵13-211井12号	38.10	0.263 3	-0.237 8	1.000 00	0.267 3	2.814 3	-0.091 6	0.999 94
温检5-1井3号	103.00	0.258 3	-0.229 9	1.000 00	0.256 9	1.577 0	0.077 2	0.997 25
温检3-1井122号	67.40	0.485 2	-0.447 4	0.999 99	0.359 9	1.996 2	-0.285 7	0.999 99
温西6-522井12号	0.87	0.165 0	-0.149 6	1.000 00	0.222 0	0.933 4	0.468 2	1.000 00
葡北20井A5-2号	46.80	0.098 0	-0.101 3	1.000 00	0.406 1	3.077 1	-3.152 2	0.991 58
果新8-45井08199号	125.00	0.100 3	-0.100 9	1.000 00	0.309 5	0.732 6	-0.444 7	0.998 56
葡4井132号	104.17	0.228 0	-0.208 4	0.999 99	0.153 4	1.306 9	2.989 5	0.998 24

表1

图1

图2

表2

图3

表3

图4

图5

图6

表4

利用本文数学模型生成数据拟合结果"

井名	（19）式													（20）式																（21）式
井名	a₀		a₁			a₂		a₃			R			a₀			a₁				a₂			a₃			R			a₀
鄯10-131井	2.912 2		-12.847 8			22.812 2		-12.808 0			1.000 0			-30.861 5			143.819 9				-221.258 6			114.558 4			0.999 6			0.286 6
陵13-211井	8.113 7		-31.928 5			45.238 2		-20.943 2			0.999 9			-112.674 6			445.125 8				-584.375 9			256.585 2			0.999 5			0.359 8
温检5-1井	6.501 1		-28.083 0			44.201 0		-22.705 0			0.999 9			-125.259 2			547.078 2				-794.639 7			385.859 7			0.999 7			0.351 9
温检3-1井	5.877 9		-27.332 7			46.353 2		-25.608 9			0.999 9			-75.056 9			354.175 7				-555.021 2			291.177 5			0.999 6			0.296 3
温西6-522井	6.186 4		-30.954 7			55.806 5		-32.827 9			0.999 9			-59.759 2			302.787 8				-509.008 1			286.610 2			0.999 8			0.253 2
葡北20井	1.868 6		-7.879 9			14.617 4		-8.116 8			0.999 9			-8.996 3			42.156 4				-63.179 5			32.365 0			0.999 5			0.296 3
果新8-45井	0.310 7		0.352 3			0.775 1		-0.585 0			1.000 0			-4.510 9			20.134 2				-28.217 8			14.236 5			0.999 9			0.302 2
葡4井	28.994 5		-132.372 4			205.217 8		-105.563 7			0.999 9			-551.164 5			2 483.367 3				-3 727.663 9			1 866.294 1			0.999 6			0.334 8
井名	（21）式				（22）式										（23）式								（24）式
井名	a₁	R			a₀				k			R			a₀			a₁		R			a₀			a₁			R
鄯10-131井	0.602 3	0.997 2			1.267 8×10^-3				-6.750 0			0.909 5			-0.076 8			-0.241 9		0.989 6			2.084 8×10^-2			11.683 8			0.926 2
陵13-211井	0.555 3	0.997 5			1.606 1×10^-3				-9.244 3			0.950 4			-0.066 9			-0.321 8		0.994 8			1.820 2×10^-3			13.395 4			0.959 4
温检5-1井	0.515 3	0.997 8			4.752 0×10^-4				-9.573 2			0.947 2			-0.099 2			-0.313 8		0.997 2			1.360 9×10^-3			15.485 9			0.957 1
温检3-1井	0.562 7	0.997 3			1.560 4×10^-4				-10.217 3			0.944 6			-0.102 8			-0.266 5		0.995 6			9.572 2×10^-4			17.403 9			0.953 3
温西6-522井	0.597 7	0.998 9			3.088 4×10^-5				-11.421 8			0.933 5			-0.105 1			-0.228 8		0.996 8			3.756 3×10^-4			20.712 6			0.942 6
葡北20井	0.757 2	0.995 1			3.714 6×10^-3				-4.815 8			0.838 0			-0.030 9			-0.152 5		0.940 9			1.683 0×10^-1			8.048 3			0.863 8
果新8-45井	0.617 1	0.999 4			5.755 9×10^-3				-4.222 5			0.877 0			-0.046 7			-0.046 7		0.993 4			1.510 2×10^-1			7.891 4			0.914 8
葡4井	0.334 8	0.996 8			1.812 9×10^-8				-32.201 1			0.977 1			-0.132 8			-0.349 1		0.990 5			6.331 2×10^-7			28.487 0			0.971 6
井名	（25）式									（26）式									（27）式
井名	a₀			k			R			a₀			k			R			a₀			k			a₁			R
鄯10-131井	0.113 4			0.773 7			0.999 0			-0.007 8			-2.557 8			0.996 5			0.181 4			0.660 5			1.427 7			0.999 3
陵13-211井	0.191 3			0.869 6			0.998 1			-0.003 3			-3.523 7			0.996 9			0.265 0			0.820 2			1.246 6			0.999 0
温检5-1井	0.166 6			0.943 3			0.997 7			-0.053 7			-1.056 7			0.997 1			0.281 1			0.870 3			1.384 5			0.998 8
温检3-1井	0.139 1			0.929 1			0.998 4			1.839 9			1.229 6			0.979 1			1.763 6			2.607 4			1.309 7			0.974 1
温西6-522井	0.070 1			0.872 2			0.998 1			-0.070 7			-0.855 7			0.997 6			0.181 7			0.812 1			1.602 2			0.999 1
葡北20井	0.141 0			0.244 0			0.997 0			-0.001 5			-4.122 3			0.972 1			0.115 6			0.530 3			1.322 3			0.995 0
果新8-45井	0.173 4			0.925 3			0.999 1			-0.269 5			-0.329 2			0.998 9			0.270 3			0.866 0			1.288 8			0.999 8
葡4井	0.129 7			0.956 2			0.996 6			0.724 9			0.438 7			0.996 6			0.311 8			0.988 7			1.458 0			0.998 5

表4

表5

利用Gao简化数学模型生成数据拟合结果"

井名	（19）式													（20）式																（21）式
井名	a₀		a₁			a₂		a₃			R			a₀			a₁				a₂			a₃			R			a₀
鄯10-131井	5.084 0		-24.613 0			43.667 9		-24.937 4			0.999 8			-44.702 6			212.074 3				-332.485 9			174.515 1			0.999 1			0.235 2
陵13-211井	4.508 4		-17.128 3			25.118 7		-11.883 0			0.999 9			-84.959 8			337.677 2				-445.915 6			197.281 0			0.999 9			0.392 1
温检5-1井	2.805 2		-11.660 2			20.038 4		-10.931 1			0.999 9			-75.083 1			334.694 9				-495.651 9			245.874 7			1.000 0			0.357 0
温检3-1井	2.712 1		-11.866 8			21.306 2		-12.157 9			1.000 0			-43.683 2			208.422 5				-329.722 2			175.298 7			1.000 0			0.314 7
温西6-522井	6.963 2		-36.117 3			66.645 6		-40.146 3			0.999 9			-63.475 3			326.770 2				-557.951 6			318.761 8			1.000 0			0.221 3
葡北20井	1.727 6		-7.119 4			13.185 6		-7.214 6			0.999 9			-6.896 9			32.207 8				-47.439 4			24.074 4			1.000 0			0.314 7
果新8-45井	1.265 3		-4.554 1			8.892 3		-4.947 0			0.999 9			-8.697 6			39.394 0				-57.279 7			28.667 2			1.000 0			0.252 5
葡4井	12.638 8		-56.206 0			87.159 4		-44.654 3			1.000 0			-342.529 4			1 539.369 2				-2 304.580 8			1 151.522 4			1.000 0			0.367 8
井名	（21）式				（22）式										（23）式								（24）式
井名	a₁	R			a₀				k			R			a₀			a₁		R			a₀			a₁			R
鄯10-131井	0.683 5	0.989 2			1.392 3×10^-3				-6.464 8			0.820 7			-0.052 6			-0.190 0		0.941 9			2.931 6×10^-2			11.208 0			0.842 1
陵13-211井	0.512 9	0.998 9			1.325 3×10^-3				-9.599 0			0.925 8			-0.072 5			-0.343 8		0.998 2			1.061 8×10^-3			14.238 1			0.939 2
温检5-1井	0.509 3	0.996 7			3.027 7×10^-4				-10.570 3			0.908 2			-0.098 4			-0.314 9		0.993 9			4.798 3×10^-4			17.116 9			0.921 6
温检3-1井	0.534 2	0.999 1			1.273 9×10^-4				-10.482 3			0.920 3			-0.107 6			-0.278 2		0.997 4			6.337 9×10^-4			18.189 2			0.932 6
温西6-522井	0.651 5	0.995 7			1.417 2×10^-5				-12.726 1			0.876 8			-0.089 2			-0.198 3		0.981 7			1.161 3×10^-4			22.855 9			0.887 7
葡北20井	0.801 0	0.997 0			2.808 8×10^-3				-5.347 0			0.830 0			-0.021 2			-0.127 4		0.940 9			1.199 0×10^-1			8.644 6			0.854 0
果新8-45井	0.686 3	0.997 6			3.424 4×10^-3				-5.440 4			0.866 1			-0.038 2			-0.038 2		0.980 3			6.768 3×10^-2			9.119 5			0.893 1
葡4井	0.367 8	0.998 9			1.172 1×10^-6				-21.595 8			0.949 5			-0.133 0			-0.347 2		0.999 5			1.588 5×10^-8			34.282 8			0.954 7
井名	（25）式									（26）式									（27）式
井名	a₀			k			R			a₀			k			R			a₀			k			a₁			R
鄯10-131井	0.124 5			0.265 9			0.992 8			-0.010 7			-2.007 1			0.962 3			0.133 5			0.494 3			1.444 5			0.993 5
陵13-211井	0.241 6			1.002 8			0.998 8			-0.543 5			-0.222 8			0.998 9			0.338 4			0.892 6			1.253 2			0.999 7
温检5-1井	0.152 3			0.746 7			0.999 7			-0.000 6			-7.887 5			0.999 0			3.758 9			3.170 3			1.194 9			0.948 7
温检3-1井	0.146 1			0.876 5			0.999 7			-0.004 6			-3.496 0			0.999 5			0.302 7			0.949 6			1.490 5			0.999 0
温西6-522井	0.060 0			0.498 2			0.998 6			-0.003 5			-3.558 6			0.989 4			0.132 9			0.674 4			1.614 2			0.998 0
葡北20井	0.109 5			0.242 3			0.993 3			-0.000 8			-4.852 0			0.970 6			0.103 6			0.522 7			1.313 2			0.993 4
果新8-45井	0.136 5			0.568 2			0.998 1			-0.002 7			-3.598 3			0.995 5			0.188 8			0.685 4			1.301 7			0.998 7
葡4井	0.178 4			1.143 9			0.999 5			1.076 1			0.875 6			0.999 7			0.366 8			1.005 2			1.467 1			0.999 8

表5

图7

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岩样号	地下黏度/（mPa·s）		束缚水饱和度	残余油饱和度	水驱前缘含水饱和度	水驱前缘含水率	水驱前缘后平均含水饱和度
岩样号	原油	水	束缚水饱和度	残余油饱和度	水驱前缘含水饱和度	水驱前缘含水率	水驱前缘后平均含水饱和度
鄯10-131井4号	0.387 9	0.342 6	0.394 4	0.376 6	0.540 4	0.677 5	0.609 8
陵13-211井12号	0.263 6	0.367 8	0.305 0	0.200 0	0.719 7	0.912 7	0.759 4
温检5-1井3号	0.350 0	0.395 0	0.360 0	0.280 0	0.632 4	0.861 1	0.676 3
温检3-1井122号	0.500 0	0.395 0	0.330 4	0.329 7	0.585 0	0.865 2	0.624 7
温西6-522井12号	0.691 0	0.390 5	0.440 0	0.376 6	0.513 4	0.604 8	0.561 3
葡北20井A5-2号	0.350 0	0.395 0	0.341 0	0.224 0	0.555 2	0.784 6	0.613 9
果新8-45井08199号	0.233 0	0.333 8	0.323 0	0.220 0	0.405 8	0.351 9	0.558 4
葡4井132号	0.270 0	0.351 0	0.381 3	0.318 4	0.651 1	0.938 8	0.667 4