Numerical simulation of proppant transport in hydraulic fractures
Numerical simulation of proppant transport in hydraulic fractures
复制标题
DOI：
10.1016/j.petrol.2017.11.044
复制
发表时间：
2018-04
影响因子：
--
通讯作者：
M. Roostaei;A. Nouri;V. Fattahpour;D. Chan
中科院分区：
文献类型：
--
作者：
M. Roostaei;A. Nouri;V. Fattahpour;D. Chan
在油井水力压裂处理中，支撑剂颗粒在注入液中的运移是一个核心问题。在本文中，我们提出了一种创新的支撑剂在固定矩形和椭圆形槽中的输运模型。该模型对现有的支撑剂输运模型进行了改进，采用了一种非振荡的数值格式，在解域的任何地方都具有很高的精度，甚至接近陡峭的梯度。此外，还考虑了惯性、裂缝壁和支撑剂浓度对支撑剂沉降的影响，以及支撑剂浓度随支撑剂浓度的变化规律。本文介绍了控制支撑剂输运现象的数学方程，并讨论了特殊的前沿捕获数值技术、边界条件、支撑剂和泥浆质量守恒方程之间的耦合以及溶液稳定性所需的时间步进限制。我们将从支撑剂输运实验室实验中获得的已发表相关性纳入到我们的数值模型中，以更好地捕捉问题的物理性质。由于传统的有限差分离散方法在求解双曲输运偏微分方程时存在不足，采用5阶WENO格式避免支撑剂前缘的振荡和扩散。结果表明，该技术能够以最小的振荡和扩散捕获支撑剂的分布。研究人员进行了一系列敏感性分析，以探索这些假设的合法性，并为更准确地预测支撑剂和流体运移提供指导。数值结果显示了注入液粘度、支撑剂颗粒与注入液之间的密度差、支撑剂尺寸和注入液流量对支撑剂分布的影响。灵敏度分析的结果说明了选择合适的注射液粘度的重要性，因为粘度的微小变化可能对浓度分布产生明显的影响。此外，我们发现在合理范围内，支撑剂粒径和密度的变化对支撑剂浓度分布的影响不大。此外，我们还研究了由密度差异（对流）驱动的重力驱动支撑剂垂直运动的数量，并将其与支撑剂沉降的第二次重力驱动运动进行了比较。在支撑剂注入过程中，这两种公认的机制都可能发生在裂缝内部，然而，每种机制作为支撑剂注入设计参数的函数的重要性还没有得到充分的认识。
A central issue in hydraulic fracturing treatment in petroleum wells is the transport of proppant particles by the injection fluid. In this paper, we present an innovative proppant transport model in a fixed rectangular- and elliptic-shaped slots. The proposed model is an improvement to the current modeling of proppant transport by applying a non-oscillatory numerical scheme which has high accuracy everywhere in solution domain, even close to the steep gradients. In addition, inertia, fracture wall, and concentration effects on proppant settling along with slurry evolution as a function of proppant concentration has been considered.This paper introduces the mathematical equations that govern the proppant transport phenomenon and discusses special front capturing numerical techniques, boundary conditions, coupling between proppant and slurry mass conservation equations and time stepping restrictions required for the solution stability. We incorporated published correlations obtained from proppant transport laboratory experiments in our numerical model to better capture the physics of the problem. 5th- order WENO scheme was used to avoid oscillation and diffusion at the proppant front since traditional finite difference discretization was found to be insufficient in solving the hyperbolic transport partial differential equations. Results show that the technique used in this study can capture the proppant distribution with minimum oscillation and diffusion.A series of sensitivity analysis was conducted to explore the legitimacy of these assumptions and to provide guidelines that allow more accurate predictions of the proppant and fluid transfer. Numerical results are presented to show how proppant distribution is impacted by the injection fluid viscosity, density difference between proppant particles and injection fluid, proppant size, and fluid flow injection rate. Results of the sensitivity analysis illustrate the significance of choosing appropriate viscosity of the injection fluid as small changes in the viscosity may cause noticeable effects on the concentration distribution. In addition, we found that variation of proppant size and density within a reasonable range have a modest effect on proppant concentration distribution.Furthermore, we also investigated the amount of gravity driven vertical motion of proppant which is driven by density differences (convection) and compare it to a second gravity driven motion which is proppant settlement. Both of these two well recognized mechanisms can occur inside a fracture during proppant placement, however, the importance of each mechanism as a function of proppant injection design parameters is not fully understood.