摘要
为计算复杂条件下的煤层气井井底压力及产能变化,以分形几何学为基础,通过Langmuir等温吸附公式、Fick扩散定律、拉普拉斯变换等,建立了考虑井筒储集和表皮效应的双重分形介质煤层气不稳定渗流数学模型。利用混合拉普拉斯变换有限差分方法,通过Stehfest反演公式,计算出圆形封闭地层中心一口井定产量生产时无因次井底压力,利用拉普拉斯空间下压力和产量的关系,求出定压条件下的无因次产量,分析了分形维数、分形指数、储能比、窜流系数和吸附因子对煤层气产能动态的影响。结果表明,分形维数越大,产能曲线下降趋势越明显;分形指数与分形维数对产能的影响相反;储能比越大,早期产能越大;窜流系数越小,产能下降出现的越晚;吸附因子越大,供给能力越强,产能越大。该方法计算任意时刻井底压力和产量时,对空间网格具有良好的适应性,并且不依赖其它时刻的计算结果,误差较小,适用于一些无法求取解析解的数值模拟问题,以及复杂条件下煤层气井井底压力的计算。
To highlight changes in bottom-hole pressure and deliverability of CBM wells under complicated conditions,a mathematical model for transient seepage flow in dual-fractal CBM reservoir was established on the basis of fractal geometry by using Langmuir equation,Fick＇s law and Laplace transform,and this model considers wellbore storage and skin effects. By using the Laplace transform finite difference method and Stehfest reversion formula,the dimensionless bottom-hole pressure of a well in the central part of circular enclosed formations during single-rate production was determined. Then,depending on the correlation between pressure and production rate in Laplace space,the dimensionless production rate at constant pressure was determined,and the impacts of fractal dimension,fractal index,stored energy ratio,inter-porosity flow coefficient and adsorption factor on CBM production performance were analyzed.As revealed by the study results,the higher fractal dimension is,the faster the deliverability declines. Fractal index and fractal dimension have opposite impacts on the deliverability. The higher the stored energy ratio is,the higher the initial deliverability is. The lower the inter-porosity flow coefficient is,the later the deliverability drop occurs. The higher the adsorption factor is,the stronger the supply capacity is and the higher the deliverability is. The technique can be used to calculate bottom-hole pressure and deliverability at any moment with satisfactory adaptability to spatial mesh. Independent of calculation results at other moments and with minor errors,the technique can be deployed in numerical simulation with no analytical solution and in determination of bottom-hole pressure of CBM wells under complicated conditions.
作者
王磊
WANG Lei(No.2 Oil Production Plant of PetroChina Daqing Oilfield Company Limited,Daqing,Heilongjiang 163711,China)
出处
《油气井测试》
2018年第2期7-13,共7页
Well Testing
关键词
煤层气
产能动态分析
分形介质
拉普拉斯变换
有限差分法
试井分析
CBM
production performance analysis
fractal
Laplace transform
finite difference method
well test analysis
