A new theoretical method to calculate shale fracture conductivity based on the population balance equation
A new theoretical method to calculate shale fracture conductivity based on the population balance equation
复制标题
DOI：
10.1016/j.petrol.2015.07.019
复制
发表时间：
2015-10
影响因子：
--
通讯作者：
Junjing Zhang;D. Zhu;A. Hill
中科院分区：
文献类型：
--
作者：
Junjing Zhang;D. Zhu;A. Hill
页岩裂缝导流能力在决定页岩井的长期产量方面起着至关重要的作用。高裂缝导流能力是通过泵入更多支撑剂并最大限度地减少压裂液对导流能力的损害来实现的。目前，裂缝导流能力要么按照 ISO 13503-5 在实验室中测量，要么使用通过回归分析从大量实验室测试中得出的相关性进行计算。需要一种方便实用的工具来计算反映实际压裂设计的页岩裂缝导流能力。本文提出了一种计算页岩裂缝导流能力的新关联式，该关联式考虑了支撑剂特性、裂缝设计变量和地层力学特性。这种相关性基于规模减小的群体平衡方程。它利用群体平衡概念来预测闭合应力增加下的压碎支撑剂尺寸分布。通过将计算结果与实测数据进行比较，验证了积分微分方程的数值解。破碎粒度分布决定了砂包的渗透性。裂缝宽度是通过考虑支撑剂嵌入和支撑剂颗粒重排来单独计算的。然后计算裂缝电导率并与实验室测量的电导率进行比较。最后，通过引入新的修正项，考虑了水损害对页岩裂缝导流能力的影响。结果表明，通过正确选择选择方程和破碎方程，群体平衡方程可以合理地预测压碎支撑剂粒径的减小量。计算出的页岩裂缝导流能力可以与使用 Barnett 页岩测量的裂缝导流能力相匹配。指数表达式可用于解释 Barnett 页岩中的水害效应。
Shale fracture conductivity plays a critical role in determining the long term production of shale wells. High fracture conductivity is achieved by pumping more proppants and minimizing conductivity damage by fracturing fluid. Currently, fracture conductivity is either measured in laboratory following ISO 13503-5 or calculated using correlations derived from extensive laboratory tests by regression analysis. There is a need for a handy and practical tool to calculate shale fracture conductivity reflecting realistic fracturing designs.This paper presents a new correlation to calculate shale fracture conductivity that considers proppant properties, fracture design variables and formation mechanical properties. This correlation is based on the population balance equation for size reduction. It utilizes the population balance concept to predict the crushed proppant size distribution under increasing closure stress. Numerical solution of the integro-differential equation is validated by comparing the computed results with the measured data. The crushed grain size distribution determines the permeability of the sand pack. Fracture width is calculated separately by considering proppant embedment and proppant grain rearrangement. Fracture conductivity is then calculated and compared with laboratory measured conductivity. Finally, the effect of water damage to shale fracture conductivity is considered by bringing in a new modification term.Results show that the population balance equation can reasonably predict the crushed proppant size reduction by properly choosing the selection equation and breakage equation. The calculated shale fracture conductivity can match with the measured fracture conductivity using the Barnett Shale. An exponential expression can be used to account for the water damage effect in the Barnett Shale.