Numerical Simulation of Proppant Transport in Hydraulic Fractures

  • Author / Creator
    Roostaei, Morteza
  • This research focuses on the study of mechanisms of proppant transport in reservoirs during frac-packing operation. As an attempt to improve current numerical modeling of proppant transport, a multi-module, numerical proppant, reservoir and Geomechanics simulator was developed, linked and tailored for capturing the processes and mechanisms that are believed to be of significance in frac-pack operations. Extensive laboratory experiments have shown that several factors affect the final distribution of proppants in the fracture. Most often these factors are accounted for through an empirical correlation coming from a wide range of experiments. Although it is extremely hard, or impossible, to include all of these interacting phenomena of proppant transport in a numerical model, we have investigated most of them and involved them in our numerical model. The complicating phenomena that are addressed in the literature and has been captured by our developed tool are: hindered settling velocity (terminal velocity of proppants in the injection fluid), effect of fracture walls, proppant concentration and inertia on settling (due to extra drag exerted on particles, compared to single particle motion in Stokes regime in unbounded medium), possible propped fracture porosity and also mobility change due to the presence of proppants and fracture closure or extension during proppant injection. Most of the current (published) numerical models for simulating proppant transport require an analytical hydraulic fracture model. Most of the time the fracture width, if not assumed to be constant, is calculated based on PKN, KGD, P3D or PL3D models. Even in most recent works, an adaptive re-meshing technique is employed to couple a fully 3D fracture model with a proppant transport model, yet the fracture model is fully elastic. These models neglect plastic deformations of the medium, assuming plasticity has minor effects during the operation. In addition, unlike our model, conventional simulators do not include deformation resulting from the interaction between stress and fluid flow response in a porous medium. The main objective of this research is to link a numerical hydraulic fracture model to a proppant transport model to study the fracturing response and proppant distribution and to investigate the effect of proppant injection on fracture propagation and fracture dimensions. The results have provided valuable information in the field for frac-packing operations and optimization. An investigation of different design parameters in proppant transport operation was performed. This investigation not only is useful in testing the robustness of the developed numerical tool, it provides practical recommendations and trends in a better design of the treatment operation. Moreover, the errors in the model were distinguished through this sensitivity analysis when an unexpected relationship between inputs and outputs was observed. From a numerical point of view, we have utilized different techniques to reduce the expected long computational time of the model. Local mesh refinement, dimensional splitting and sparse method of solving matrix equations were employed to optimize the running time of the model. Geomechanics and fluid mechanics equations were solved by finite difference method, while the hyperbolic proppant transport PDE were solved by WENO scheme of finite volume through the application of flux limiters. The reason of using this method is that the solution of hyperbolic PDEs may encounter smooth transition or there can be large gradients of the field variables. The numerical challenge posed in a shock situation is that high-order finite difference schemes lead to significant oscillations in the vicinity of shocks despite that such schemes result in higher accuracy in smooth regions. On the other hand, first-order methods provide monotonic solution convergences near the shocks, while giving poorer accuracy in the smooth regions. Accurate numerical simulation of such systems is a challenging task using conventional numerical methods. As of now, there is a significant uncertainty in the effect of proppant properties and fluid parameters on the final proppant distribution. Therefore, our tool will increase the understanding of the relationship between fluid and proppant properties and the final distribution of these particles, which in turn determines the conductivity of the propped fracture, leading to reduction of the mentioned uncertainty and more realistic production forecast especially for reservoirs under improved or enhanced oil recovery scheme as found in heavy oil and oil sands projects.

  • Subjects / Keywords
  • Graduation date
    Fall 2017
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.