Semianalytical Solution of the Nonlinear Dual-Porosity Flow Model with the Quadratic Pressure Gradient Term

Table 2

Theoretical offset of type curves between the linear and nonlinear models ().

			DV	RDV (%)			DV	RDV (%)
	Linear	Nonlinear			Linear	Nonlinear
10^−1	0.0445	0.0445	0	0	0.0436	0.0435	0.0001	0.23
10^1	1.9772	1.7977	0.1795	9.08	0.9454	0.7385	0.2069	21.88
10^3	4.9392	3.6310	1.3082	26.49	0.5076	0.2695	0.2381	46.91
10^5	7.0647	4.6454	2.4193	34.24	0.3588	0.1528	0.2060	57.41
10^7	8.9812	5.4067	3.5745	39.80	0.4995	0.1814	0.3181	63.68

Explanations: β = dimensionless coefficient of nonlinear term; = dimensionless time; = dimensionless wellbore storage coefficient; = dimensionless pressure; = dimensionless pressure derivative; DV = differential value; RDV = relative differential value. Quantitative analysis of the nonlinear influence is made by setting as 0.01, and the corresponding type curves (curves ②) are shown in Figure 1.