Semi-Implicit Finite Volume Procedure for Compositional Subsurface Flow Simulation in Highly Anisotropic Porous Media

Subsurface multiphase flow in porous media simulation is extensively used in many disciplines. Large meshes with non-orthogonalities (e.g., corner point geometries) and full tensor highly anisotropy ratios are usually required for subsurface flow applications. Nonetheless, simulations using two-point flux approximations (TPFA) fail to accurately calculate fluxes in these types of meshes. Several simulators account for non-orthogonal meshes, but their discretization method is usually non-conservative. In this work, we propose a semi-implicit procedure for general compositional flow simulation in highly anisotropic porous media as an extension of TPFA. This procedure accounts for non-orthogonalities by adding corrections to residual in the Newton-Raphson method. Our semi-implicit formulation poses the guideline for FlowTraM (Flow and Transport Modeller ) implementation for research and industry subsurface purposes. We validated FlowTraM with a non-orthogonal variation of the Third SPE Comparative Solution Project case. Our model is used to successfully simulating a real Colombian oil field.

Numerical Simulation of Insulin Depot Formation and Absorption in Subcutaneous Tissue Modeled as a Homogeneous Anisotropic Porous Media

In this study, a numerical model of the insulin depot formation and absorption in the subcutaneous adipose tissue is developed using the commercial Computational Fluid Dynamics (CFD) software. A better understanding of these mechanisms can be helpful in the development of new devices and cannula geometries as well as predicting the concentration of insulin in the blood. The injection method considered in this simulation is by the use of an insulin pump using a rapid acting U100 insulin analogue. The depot formation is analyzed running Bolus injections ranging from 5-15 units of insulin corresponding to 50-150µl. The insulin is injected into the subcutaneous tissue in the abdominal region. The tissue is modeled as a fluid saturated porous media. An anisotropic approach to define the tissue permeability is studied by varying the value of the porosity in parallel and perpendicular direction having an impact on the viscous resistance to the flow. Following recent experimental findings this configuration results in a disk shaped insulin depot. To be able to run the simulation over longer timeframes the depot formation model has been extended implementing the process of absorption of insulin from the depot. The developed model is then used to analyze the formation of the insulin depot in the tissue when using different flow rates and cannula geometries. The numerical model is an effective option to evaluate new cannula designs prior to the manufacturing and testing of prototypes, which are rather time consuming and expensive.