This article attempts to formulate a mathematical model for a potential explanation regarding the unavoidable impact of a rigid body's peculiar shape on the seamless flow over it. The solid body completely immersed in a Newtonian fluid and respectively has a relative open circuit flow on it will typically experience various observable phenomena like flow separation, flow transition, down-wash, stalling at the higher angle of attack, stalling velocity and how cambered airfoil can typically generate lift at a zero incidence angle. This article respectively represents an understanding of the laminar flow over a rigid body's external surface with due respect to its distinctive shape and size. This working paper formulates a more realistic and simplified mathematical model for open circuit laminar flow over a body, based on the historical data of aerodynamics and theoretical mechanics. This is intended to properly estimate forces on the continuous surface of the body in a laminar flow, to properly explain, understand and predict mentioned phenomena. Most of all the mechanism of streamline formation and its deformation with due regards to flow, shape and size of the body in an open-circuit laminar are formulated mathematically to enhance better design theory which can reduce experimentation while designing a streamlined body.

Nanoparticle (NP) transport is increasingly relevant to subsurface engineering applications such as aquifer characterization, fracture electromagnetic imaging and environmental remediation. An efficient field-scale simulation framework is critical for predicting NP performance and designing subsurface applications. In this work, for the first time, a streamline-based model is presented to simulate NP transport in field-scale subsurface systems. It considers a series of behaviors exhibited by engineered nanoparticles (NPs), including time-triggered encapsulation, retention, formation damage effects and variable nanofluid viscosity. The key methods employed by the algorithm are streamline-based simulation (SLS) and an operator-splitting (OS) technique for modeling NP transport. SLS has proven to be efficient for solving transport in large and heterogeneous systems, where the pressure and velocity fields are firstly solved on underlying grids using finite-difference (FD) methods. After tracing streamlines, one-dimensional (1D) NP transport is solved independently along each streamline. The adoption of OS enhances flexibility for the entire solution procedure by allowing different numerical schemes to solve different governing equations efficiently and accurately. For the NP transport model, an explicit FD scheme is used to solve the advection term, an implicit FD scheme is used for the diffusion term and an adaptive numerical integration is used to solve the retention terms. The model is implemented in an in-house streamline-based code, which is verified against analytical solutions, a commercial FD reservoir simulator (ECLIPSE) and an academic FD colloid transport code (MNMs). For a 1D homogeneous case, the effluent breakthrough curves (BTC) produced by the in-house simulator are in good agreement with the analytical solution and MNMs, respectively. For a two-dimensional (2D) heterogeneous case, the BTC and concentration pattern of the in-house simulator all match well with the solution produced by commercial simulator. Simulations on a synthetic three-dimensional (3D) nanocapsule application engineering design case, are performed to investigate the effect of fluid and NP properties on the displacement pattern of an existing subsurface fluid.

Acid in-situ leaching (ISL) is a common approach to the recovery of uranium in the subsurface. As some toxic and harmful substances might be produced by the chemical reactions among the injected sulphuric acid, the groundwater, and the porous media during leaching processes, the pollution control of the mining plan for ISL is important. In this study, a three-dimensional reactive transport modeling (3DRTM) was applied to decide the pollution control mining plan, considering the partial penetration through wellbore in confined aquifer and complex chemical reactions between main minerals. Based on the 3DRTM, different pumping ratio and non-uniform injection schemes were compared. The results show that the preferential pollution control mining plan is non-uniform injection ratio equal 0.1. By analyzing the characteristics of water table and streamline, it is concluded that the scheme has a strong hydraulic capture effect. In this scheme, the concentration of UO22+, H+, SO42- obtained by 3DRTM is lower. The inner well injection rate is 194.09 m3/d, the outer well injection rate is 158.89 m3/d, and the pumping rate is 264.00 m3/d. A reasonable suggestion is to adopt non-uniform injection mining mode in ISL.