The total free energy of a molecule includes the classical molecular mechanical energy (which is understood as the free energy in vacuum) and the solvation energy which is caused by the change of the environment of the molecule (solute) from vacuum to solvent. The solvation energy is important to the study of the inter-molecular interactions. In this paper we develop a fast surface-based generalized Born method to compute the electrostatic solvation energy along with the energy derivatives for the solvation forces. The most time-consuming computation is the evaluation of the surface integrals over an algebraic spline molecular surface (ASMS) and the fast computation is achieved by the use of the nonequispaced fast Fourier transform (NFFT) algorithm. The main results of this paper involve (a) an efficient sampling of quadrature points over the molecular surface by using nonlinear patches, (b) fast linear time estimation of energy and inter-molecular forces, (c) error analysis, and (d) efficient implementation combining fast pairwise summation and the continuum integration using nonlinear patches.
The relative permeability is a critical property to predict field performance by reservoir numerical simulation. However, determining the relative permeability curve by experiments is time consuming and difficult for tight oil reservoirs due to the extremely low permeability. Therefore, many studies focus on the analytical solution to determine the relative permeability curve. However, no exiting solutions take the effect of boundary layer, Jamin and wettability into account. This results in overestimated results because boundary layer is even up to 60 % of the throat and throat to pore ratio reaches up to 400 in tight oil reservoirs. Therefore, an improved analytical solution is desirable to solve these two problems. In this paper, based on the collected experimental results, the Purcell's solution is modified and an improved solution considering the effect of boundary layer, Jamin and wettability is developed. Compared to the results of the relative permeability experiments, the improved solution is more accurate and reliable. Because the throat distribution of the tight oil reservoir in Daqing Field is narrower than that in Changqing Field, the productivity of the tight oil reservoir in Daqing Field is less than that in Changqing Field at first. However, the breakthrough time of the tight oil reservoir in Daqing Field is longer than that in Changqing Field. This improved solution can only be applied to tight oil reservoirs, because boundary layer and Jamin have little effect on the flow behavior in conventional reservoirs.
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