基于响应面法的油田深部地层变形的数值试验研究

摘要/Abstract

摘要：

在油田开发过程中,注水作业会打破原有地层的应力平衡状态,造成深部地层岩体变形甚至失稳破坏,并对油田开发效果造成影响。为了探寻影响深部地层变形失稳的主要因素,基于流固耦合理论,通过超拉丁方试验设计方法对油田注水涉及的不同因素进行了五因素三水平的实验分析,通过响应面法对实验得到的33组试验进行回归和因子分析,得到了各因子与地层变形的响应变量之间的关系。研究表明：地层注水变形过程中,注水压力对地层的应力场和变形场的影响都极大。储层的性质对于地层有效应力,初期较后期的影响更为显著;对于水平应变,初期的显著性较弱,后期逐渐提高;对于竖向沉降量,无较大影响。岩石力学性质的弹性模量对地层有效应力的影响较小,对水平应变和竖向沉降位移具有极大的显著性。

关键词: 注水开发油田, 地层变形, 超拉丁方试验, 响应面法, 影响因素

Abstract:

During the development of the oilfield, the water flooding disturbs the primary reservoir pressure, leads to the deformation of the deep formation in the oilfield and affects the extraction ratio of oil. In order to obtain the main effect parameters of the deformation, an experiment with 3 levels for 5 parameters was conducted by Hyper-Latin square experiment based on fluid-solid coupling theory. Then, the relationships among the deformation response and the different parameters were obtained after the regression and analysis by RSM method for 33 designed experiments. The results show that the injection pressure has significant influence on the effective stress and deformation. And the properties of the reservoirs affect more on the initial stage for the effective stress, however, the later period for the normal strain. The elastic modulus of the rock mechanics properties has little effect on the effective stress, and is a significant parameter for the normal strain and subsidence.

Key words: water flooding, stratum deformation, hyper-latin square experiment, response surface method, effect factor

中图分类号:

TE341

刘建军,郑永香,张伯虎等. 基于响应面法的油田深部地层变形的数值试验研究[J]. 油气藏评价与开发, 2018, 8(1): 16-23.

Jianjun Liu,Yongxiang Zheng,Bohu Zhang, et al. Numerical study on deformation of deep formation in oilfield based on response surface method[J]. Reservoir Evaluation and Development, 2018, 8(1): 16-23.

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水平	变量
水平	渗透率 k/10^-3μm²	孔隙度 φ,f	注水压力 P_w/MPa	初始地层压力 P₀/MPa	岩石弹性模量E/GPa
0（0.8）	16	0.24	12	8	6.78
1（1.0）	20	0.30	15	10	8.47
2（1.2）	24	0.36	18	12	10.16

编号	实验方案	编号	实验方案	编号	实验方案
1	0000010100	12	0101020000	23	0002000201
2	0102000001	13	0202000000	24	0202010101
3	0100020100	14	0002020201	25	0201020001
4	0001020101	15	0202010201	26	0001020000
5	0200000100	16	0000000002	27	0201000202
6	0202010001	17	0101020202	28	0100010102
7	0200020202	18	0201000200	29	0101010200
8	0000000100	19	0200010202	30	0202020102
9	0100010001	20	0001000201	31	0101000001
10	0002020102	21	0100010002	32	0101020100
11	0000010102	22	0102000002	33	0002010200

因素	回归系数	标准差	t值	P值
常数	29 617.4	68.703 29	431.091	<0.000 01
E（6.78×10⁶,1.016×10⁷）	23.373 13	21.631 16	1.080 53	0.301 14
P₀（8×10³,1.2×10⁴）	1 177.089	25.117 87	46.862 6	<0.000 01
k（16,24）	-225.960 4	21.804 82	-10.362 9	<0.000 01
φ（0.24,0.36）	160.587 8	26.526 95	6.053 76	0.000 06
P_w（1.2×10⁴,1.8×10⁴）	-1 522.954	20.764 36	-73.344 6	<0.000 01
EE	9.073 169	51.925 04	0.174 736	0.864 20
EP₀	42.280 2	32.100 86	1.317 1	0.212 40
Ek	-57.123 08	31.138 33	-1.834 49	0.091 48
Eφ	22.463 65	29.966 81	0.749 618	0.467 93
EP_w	38.165 44	29.230 59	1.305 67	0.216 14
P₀P₀	57.465 04	59.087 62	0.972 539	0.349 98
P₀k	19.076 9	35.510 81	0.537 214	0.600 94
P₀φ	-3.693 091	37.533 44	-0.098 394 7	0.923 24
P₀P_w	96.445 44	33.461 93	2.882 24	0.013 77
kk	64.991 98	55.713 54	1.166 54	0.266 06
kφ	15.744 67	35.033	0.449 424	0.661 14
kP_w	-275.649 4	26.956	-10.225 9	<0.000 01
φφ	12.922 98	45.157 43	0.286 176	0.779 62
φP_w	89.019 64	32.496 48	2.739 36	0.017 95
P_wP_w	-643.297 6	40.712 85	-15.800 8	<0.000 01

变量因子	有效应力	水平应变	竖向沉降
E（6.78×10⁶,1.016×10⁷）	不显著	-8.541	5.441 8
EP_w	不显著	-7.109 1	11.772
EP₀	不显著	不显著	-6.556 1
Ek	-1.471 5	不显著	-2.289 8
P_w（1.2×10⁴,1.8×10⁴）	-82.816	30.682	-62.691
P_wP_w	-18.371	6.725 4	-15.207
P₀（8×10³,1.2×10⁴）	61.14	不显著	48.602
P₀P_w	5.375 5	不显著	不显著
k（16,24）	-13.349	2.582 8	-9.349 3
kP_w	-12.162	不显著	-7.374 4
kk	不显著	不显著	4.432 4
φ（0.24,0.36）	8.134 9	不显著	5.800 2
φP_w	5.092 9	不显著	不显著

变量因子	有效应力	水平应变	竖向沉降
E（6.78×10⁶,1.016×10⁷）	不显著	-19.485	33.78
EE	不显著	不显著	-3.526 7
Ek	5.765 2	不显著	2.067
EP₀	-5.489 7	不显著	-22.268
EP_w	不显著	-5.122 3	31.057
Eφ	不显著	不显著	-2.885 6
k（16,24）	-30.315	-6.735 7	-16.335
kP_w	8.773 6	-6.596 6	3.700 9
P₀（8×10³,1.2×10⁴）	270.43	不显著	112.91
P₀k	-1.995	不显著	-2.845
P₀P₀	-3.009 2	不显著	不显著
P₀P_w	-2.557 5	不显著	不显著
P₀φ	2.331 1	不显著	3.833 8
P_w（1.2×10⁴,1.8×10⁴）	-447.49	35.195	-198.42
P_wP_w	12.154	-10.709	4.165 5
φ （0.24,0.36）	10.248	6.092 9	4.510 7
φ P_w	-6.481 6	4.902 2	-1.892 7