焦石坝地区页岩Cole-Cole模型参数的快速计算方法

doi:10.13809/j.cnki.cn32-1825/te.2020.05.006

Abstract

Abstract:

Calculation of 4 parameters, ρ₀, m, τ and c, of Cole-Cole model by complex rock core resistivity data measured with multi-frequency is an important nonlinear optimization problem in rock core complex resistivity experiments. However, in Jiaoshiba Zone, a very small τ and c with big value range cause the difficulty of the convergence of optimization program. Therefore, the initial value determination and optimized iteration step have been studied. The improved program performances well on the speed of convergence, and avoids the calculation failure caused by out-range of the parameter τ. The study indicates that according to the maximum property and asymmetry property, the parameter τ can be obtained directly, and good iteration initial values of the rest 3 parameters can be obtained either. Meanwhile, by transforming the error function to be Tyler series, the optimized iteration step can be obtained and the convergence speed can be upgraded significantly.

Key words: Cole-Cole model, least square method, gradient descent algorithm, iteration initial value estimation, optimized iteration step, shale in Longmaxi Formation

CLC Number:

P315.69

LIU Zhiying,ZHANG Baiqiao,XU Wei,LUO Bing,LI Minghua,LI Wei. A fast computing method for rock electric parameters of Cole-Cole model in Jiaoshiba Zone[J].Reservoir Evaluation and Development, 2020, 10(5): 42-48.

Figures/Tables 9

Fig. 1

Table 1

Table 2

Parameters and computing results of program-1"

样号	总迭代次数	相对误差/%	初始值	计算结果
2	不收敛
18	不收敛
23	19 394	9.07	c^（0）=0.5 τ^（0）=1.0×10^-6 m^（0）=0.9 $ρ 00$ =4 000	c=0.796 784 τ=3.213 45×10^-6 m=0.999 83 ρ₀=4 003.354 93

Table 2

Fig. 2

Table 3

Processing of program-1"

样号	迭代次数	相对误差	当前迭代值
样号	迭代次数	相对误差	$ρ 0 k m k c k τ k$
23	3 000	593.4 %	4 314.495 3	0.897 643	0.698 743	1.029 5×10^-6
	8 000	164.72 %	4 394.180 4	0.958 395	0.768 959	3.019 4×10^-6
	15 000	43.61 %	4 009.352 6	0.999 875	0.719 845	3.579 9×10^-6

Table 3

Table 4

Parameters and computing results of program-2"

样号	总迭代次数	相对误差/%	初始值	计算结果
2	不收敛
18	不收敛
23	8 394	9.56	c^（0）=0.5 τ^（0）=1.0×10^-6 m^（0）=0.9 $ρ 00$ =4 000	c=0.795 344 2 τ=3.228 42×10^-6 m=0.992 713 56 ρ₀=4 002.566 89

Table 4

Table 5

Processing of program-2"

样号	迭代次数	相对误差/%	当前迭代值
样号	迭代次数	相对误差/%	$ρ 0 k m k c k τ k$
23	2 000	763.8	4 108.325 6	0.901 436	0.704 852	2.094 9×10^-6
	6 000	108.4	4 287.649 5	0.980 784	0.746 424	3.787 4×10^-6
	8 000	10.65	4 003.906 3	0.999 763	0.726 441	3.706 5×10^-6

Table 5

Table 6

Parameters and computing results of program-3"

样号	总迭代次数	相对误差/%	初始值	计算结果
2	12	7.57	c^（0）=0.8 m^（0）=1.001 $ρ 00$ =893.5	c=0.786 648 66 τ=1.074 09×10^-6 m=0.999 987 3 ρ₀=593.384 774
18	19	6.45	c^（0）=0.8 m^（0）=0.809 9 $ρ 00$ =90.3	c=0.826 65 τ= 3.580 51×10^-7 m=0.902 873 43 ρ₀=84.846 30
23	8	9.23	c^（0）=0.8 m^（0）=0.917 61 $ρ 00$ =4 457.3	c=0.798 434 τ=3.222 04×10^-6 m=0.999 830 ρ₀=4 002.943 1

Table 6

Table 7

Processing of program-3"

样号	迭代次数	相对误差/%	当前迭代值
样号	迭代次数	相对误差/%	$ρ 0 k m k c k τ k$
2	0	10.76	893.500 00	1.001 000 0	0.800 000	1.074 09×10^-6
	5	8.73	649.488 10	0.999 424 0	0.790 821
	10	7.57	593.302 60	0.999 988 0	0.786 605
18	0	7.03	90.300 00	0.809 900 0	0.800 000	3.580 51×10^-7
	8	6.51	85.348 23	0.902 727 6	0.826 130
	16	6.44	84.828 41	0.902 808 3	0.826 650
23	0	9.37	4 457.300 0	0.917 600 0	0.800 000	3.222 04×10^-6
	3	9.24	4 138.187 3	0.960 949 5	0.810 452
	6	9.23	4 002.996 7	0.999 829 7	0.798 430

Table 7

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样号	组	取心深度/m	层位	岩性描述	钻切方向	岩心规格/cm
2	龙马溪	3 566.60	9	黑色页岩	垂直层理	柱样：?24.48×36.55
18	龙马溪	3 636.60	3	黑色页岩	垂直层理	柱样：?24.48×15.93
23	龙马溪	3 558.65	浊积砂	泥质砂岩	无层理	柱样：?24.93×84.62

A fast computing method for rock electric parameters of Cole-Cole model in Jiaoshiba Zone

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References 16

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