#### 期刊菜单

A Novel Dynamic Analysis Method of Shale Gas Reservoir
DOI: 10.12677/APF.2021.111002, PDF, HTML, XML, 下载: 194  浏览: 564  国家科技经费支持

Abstract: In order to realize commercial development, multi-stage fracturing and horizontal well technologies are often used in tight gas reservoir. At present, there are mainly two methods for tight gas reser-voir performance analysis: analytical method and numerical simulation method. The analytical method is fast, but it is only suitable for homogeneous reservoir. The numerical simulation method can accurately calculate complex geometry wells (such as fractured horizontal wells) in heteroge-neous reservoir, but it is time-consuming and laborious. In order to improve the accuracy and effi-ciency of dynamic analysis of tight gas reservoir, a semi analytical method for dynamic analysis of multiple fractured horizontal wells in tight gas reservoir, namely fast marching method (FMM) is proposed. Firstly, considering the high compressibility of gas, the diffusion equation of tight gas is established. Then, fast marching method is proposed to solve the propagation time of pressure wave, and combined with the geometric approximation method, the relationship between the re-lease volume and time is quantified. Then, the commercial numerical simulation software CMG is used to verify the accuracy and reliability of the new method. The results show that the dynamic analysis method based on fast marching method is more accurate than the conventional dynamic analysis method, and the calculation speed is increased by more than 10% compared with the commercial software. Finally, the working process of fast marching method to carry out the dynamic analysis of fractured horizontal wells in tight gas reservoirs is described. It has good application value for the dynamic analysis of tight gas reservoirs with simple structural conditions.

1. 引言

2. 数学模型

2.1. 扩散方程的建立

$\nabla \cdot \left[\frac{k\left(\stackrel{\to }{x}\right)}{\mu \left(p\right)Z\left(p\right)}p\nabla p\right]=\varphi \frac{\partial }{\partial t}\left[\frac{p}{Z\left(p\right)}\right]$ (1)

${C}_{\text{t}}\left(p\right)=\frac{1}{\rho }\frac{\text{d}\rho }{\text{d}p}=\frac{Z\left(p\right)}{p}\frac{\text{d}}{\text{d}p}\left[\frac{p}{Z\left(p\right)}\right]$ (2)

$\frac{\text{d}}{\text{d}}\left[\frac{p}{Z\left(p\right)}\right]=\frac{{C}_{\text{t}}\left(p\right)p}{Z\left(p\right)}\frac{\text{d}p}{d}$ (3)

$m\left(p\right)={\left(\frac{{\mu }_{\text{g}}Z}{p}\right)}_{i}\underset{0}{\overset{p}{\int }}\frac{p\text{d}p}{{\mu }_{\text{g}}Z}$ (4)

${t}_{\text{p}}={\left({\mu }_{\text{g}}{c}_{\text{t}}\right)}_{i}\underset{0}{\overset{t}{\int }}\frac{\text{d}t}{{\mu }_{\text{g}}{C}_{\text{t}}}$ (5)

$\nabla \cdot \left[k\left(\stackrel{\to }{x}\right)\cdot \nabla m\left(\stackrel{\to }{x},{t}_{\text{p}}\right)\right]=\varphi \cdot {\left[\mu \left(p\right){C}_{\text{t}}\left(p\right)\right]}_{i}\frac{\partial m\left(\stackrel{\to }{x},{t}_{\text{p}}\right)}{\partial {t}_{\text{p}}}$ (6)

$\varphi \cdot {\left[\mu \left(p\right){C}_{\text{t}}\left(p\right)\right]}_{i}\cdot \left(-i\omega \right)\stackrel{¯}{m}\left(\stackrel{\to }{x},\omega \right)=k\left(\stackrel{\to }{x}\right){\nabla }^{2}\stackrel{¯}{m}\left(\stackrel{\to }{x},\omega \right)+\nabla k\left(\stackrel{\to }{x}\right)\cdot \nabla \stackrel{¯}{m}\left(\stackrel{\to }{x},\omega \right)$ (7)

$\stackrel{¯}{m}\left(\stackrel{\to }{x},\omega \right)={\text{e}}^{-\sqrt{-i\omega }\cdot \tau \left(\stackrel{\to }{x}\right)}\underset{k=0}{\overset{\infty }{\sum }}\frac{{C}_{k}\left(\stackrel{\to }{x}\right)}{{\left(\sqrt{-i\omega }\right)}^{k}}$ (8)

$\sqrt{\alpha \left(\stackrel{\to }{x}\right)}\cdot |\nabla \tau \left(\stackrel{\to }{x}\right)|=1$ (9)

$\alpha \left(\stackrel{\to }{x}\right)=\frac{k\left(\stackrel{\to }{x}\right)}{\varphi \cdot {\left[\mu \left(p\right){C}_{\text{t}}\left(p\right)\right]}_{i}}$ (10)

2.2. 压力波传播时间的求解

$\mathrm{max}{\left({D}_{ij}^{x}\tau ,{D}_{ij}^{+x}\tau ,0\right)}^{2}+\mathrm{max}{\left({D}_{ij}^{y}\tau ,{D}_{ij}^{+y}\tau ,0\right)}^{2}=\frac{1}{\alpha }$ (11)

(a) (b) (c) (d) (e) (f)

Figure 1. Schematic diagram of FMM calculation in Cartesian coordinate grid. (a) Marking the starting point of pressure wave propagation; (b) Marking the adjacent unknown node; (c) Marking the second step pressure wave propagation of point A; (d) Marking a point adjacent to the unknown node; (e) Marking the third step pressure wave propagation point D; (f) Marking D and H points adjacent to the unknown node

$t=\frac{{\tau }^{2}}{2}\frac{\text{d}\mathrm{ln}\tau }{\text{d}\mathrm{ln}{V}_{\text{p}}\left(\tau \right)}$ (12)

2.3. 致密气井生产动态分析

$\delta p\cong \delta \stackrel{¯}{p}=-\frac{1}{{C}_{\text{t}}}\frac{{q}_{\text{well}}\delta t}{{V}_{\text{p}}\left(t\right)}$ (13)

${q}_{\text{g}}\left({t}_{\text{p}}\right)=\frac{{T}_{\text{sc}}}{T{p}_{\text{sc}}}\cdot {\left(\frac{p}{{\mu }_{\text{g}}Z}\right)}_{i}\cdot \frac{m\left({p}_{i}\right)-m\left(p\right)}{\underset{0}{\overset{{V}_{\text{p}}\left(t\right)}{\int }}\frac{1}{k\cdot \varphi \cdot {A}^{2}}\left(1-\frac{{V}_{\text{p}}}{{V}_{\text{p}}\left({t}_{\text{p}}\right)}\right)\cdot \text{d}{V}_{\text{p}}}$ (14)

3. 模型验证

3.1. 物理模型

Figure 2. Schematic diagram of tight gas multistage fracturing horizontal well model

Table 1. Basic reservoir parameters of fractured horizontal wells in tight gas reservoirs

3.2. 模型验证

4. 生产动态分析工作流程

Figure 3. Comparison of bottom hole pressure calculated by FMM and CMG in unconventional gas wells

(a) (b) (c)

Figure 4. Calculation process of gas drainage volume of multiple fractured horizontal well in tight gas reservoir. (a) The diffusion time (106 s); (b) Drainage area of one month; (c) Drainage area of 10 years

Figure 5. Pressure prediction of multiple fractured horizontal well in tight gas reservoir under constant production rate

Figure 6. Production prediction of multiple fractured horizontal well in tight gas reservoir under constant pressure

5. 结论

1) 常规方法通过计算压力波传播速度来表征生产动态，而快速推进法是通过标记压力波传播时间来开展生产动态分析，具有准确和速度快的特点，这是快速推进法分析致密气井生产动态的核心优势。

2) 致密气藏生产动态分析新方法具有准确性和高效性。基于笛卡尔坐标网格开展压力波前缘传播时间计算，能同时考虑储层的非均质性和井的复杂结构，能较准确地模拟致密气藏的流体流动。并且新模型与数值模拟软件CMG计算结果吻合程度高，计算速度提高了11%，验证了计算模型高效性。

3) 快速推进法(FMM)具有灵活的运用形式，结合几何近似法，分别在定压条件下预测产气量和在定产条件下预测井底流压，根据产量压力动态响应进行合理配产。可快速地估算定压生产和定产生产情况下的井动态特性。快速推进法对构造条件简单的致密气藏生产动态分析，具有很好的应用价值。

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