基于微观结构信息的缝洞型孔隙介质等效渗透率的有限差分计算方法

Effective permeability calculation in vuggy and fractured porous media based on the micro pore structure information by using the finite difference method

研究了一种融合微观孔隙结构信息的缝洞型孔隙介质渗透率的有限差分高效近似计算方法,它适用于已知孔隙结构储层的等效渗透率计算。首先,基于岩心CT扫描图像或电成像测井电导率图像提取储层的孔隙结构;其次,采用适当尺度的规则网格对能反映孔隙结构的图像进行剖分,用二值法对缝洞孔隙和基质区域分别进行标注与识别;接着,用不同半径的等效内接圆或椭圆近似表示实际的孔隙结构;再次,用圆形管和椭圆形管的流速解析关系近似单元剖分网格的流速;最后,采用有限差分法数值计算某个层段储层的总流量和流速,进而计算该层段的等效渗透率。这里提出的孔隙结构近似表征方法适用于任何复杂孔隙结构,对于缝洞型储层的渗透率计算具有普遍适用性。为了考察文中方法的精度和有效性,对一个具有解析解的简单模型及数个数字岩心进行了渗透率计算,初步验证了文中方法的有效性。诚然,鉴于孔隙结构的剖分对有限差分等效渗透率有较大影响,在微孔发育的低孔隙储层或缝洞发育的复杂孔隙结构储层中需要加密剖分,以较好地近似储层孔隙分布。

In this study,we perform a finite difference approximation in conjunction with microscopic pore structure information for the calculation of permeability of vuggy and fractured porous medium.This method is especially efficient for the calculation of effective permeability for reservoirs with known pore structure.Generally the procedure goes as follows:First,pore structure of reservoir is extracted based on the computer tomography(CT)images from core or the conductivity images from resistivity imaging logging technique;Second,we divide the pore structure images by grid blocks with proper scales and then apply binaryzation method for the purpose of calibration and recognition of vuggy pores and matrix area;Third,the real pore structures are represented in approximation of different equivalent inscribed circles or ellipses.Hence,the grid blocks are also divided by correspond circular and elliptic tube and the fluid velocities are approximated by the analytical relation of the tube;At last,the total flux and fluid velocity of certain level are calculated numerically by finite difference method and then used for the estimation of its effective permeability.This approximated characterization method suits for any kind of complicated pore structures and especially efficient and universally valid for the calculation of effective permeability of vuggy porous reservoirs.To verify the effectiveness of this method,we calculate the permeabilities of one simple model with analytical result and several digital rocks.It is necessary to point out that the reservoirs with low porosity(in micropore)and with complicated pore structures(in vuggy porous medium)require encrypted dissection for better approximation of distribution of pores given that the result of effective permeability from finite difference is highly influenced by the dissection method.