Low salinity water has been reported as being capable of improving oil recovery in sandstone cores under certain conditions. The objective of this paper is the development and examination of a one-dimensional mathematical model for the study of water flooding lab experiments with special focus on the effect of low salinity type of brines for sandstone cores. The main mechanism that is built into the model is a multiple ion exchange (MIE) process, which due to the presence of clay, will have an impact on the water-oil flow functions (relative permeability curves). The chemical water-rock system (MIE process) we consider takes into account desorption and adsorption of calcium, magnesium, and sodium. More precisely, the model is formulated such that the total release of divalent cations (calcium and magnesium) from the rock surface will give rise to a change of the relative permeability functions such that more oil is mobilized. The release of cations depend on several factors like (i) connate water composition; (ii) brine composition for the flooding water; (iii) clay content/capacity. Consequently, the model demonstrates that the oil recovery also, in a nontrivial manner, is sensitive to these factors. An appropriate numerical discretization is employed to solve the resulting system of conservation laws and characteristic features of the model is explored in order to gain more insight into the role played by low salinity flooding waters, and its possible impact on oil recovery.

In this work, an innovative numerical algorithm accompanied by considerable accuracy is presented to reduce the computational cost of subsurface flow modeling. This method combines a modified multi-scale finite volume method (MMsFV) and streamline method based on the sequential approach. First, the modified multi-scale finite volume method, which includes a physical adaptation on the localization assumption, is employed to obtain a conservative velocity field with a similar cost to traditional upscaling methods. Then, the swift streamline method is utilized to solve the transport equation using the computed, conservative velocity field. The physical modification on the multi-scale framework imposes the nature of the actual flow moving from the multi-dimensional into 1-D local problems, which are constructed for calculating the boundary conditions in localization procedures. This physical modification is known as the modified variable boundary conditions (VBC) approach. The more accurate boundary conditions are generated for calculating basis and correction functions applied in multi-scale finite volume method. Here, the formulation and algorithm of the proposed and combined method, called the Modified Multi-scale Finite Volume Streamline (MMsFVSL) method, are presented for 2-D problems. Several test cases, including both incompressible single-phase and two-phase flow are investigated in which the obtained results show that the MMsFVSL method has a good accuracy with a high speed-up factor to reduce the total CPU time in the simulation process. Consequently, the MMsFVSL method offers a significantly effcient simulation algorithm capable of direct simulation for high resolution geological models.

In this paper, a statistical second-order two-scale (SSOTS) method is presented in a constructive way for predicting heat transfer performances of random porous materials with interior surface radiation. Firstly, the probability distribution model of porous materials with random distribution of a great number of cavities is described. Secondly, the SSOTS formulations for predicting effective heat conduction parameters and the temperature field are given. Then, a statistical prediction algorithm for maximum heat flux density is brought forward. Finally, some numerical results for porous materials with different random distribution models are calculated, and compared with the data by theoretical methods. The results demonstrate that the SSOTS method is valid to predict the heat transfer performances of random porous materials.

Custom designed rigid gas permeable lenses show promise for correcting the vision of subjects with significant higher order aberration beyond defocus (myopia and hyperopia) and astigmatism. Such aberrations could be coma, trefoil, spherical aberration, secondary astigmatism etc. Although, there exist several techniques for designing the central part of the front optic zone for subjects with significant higher order aberration, there does not exist a method for continuously differentiable interpolation of the corrected region and the rest of the front surface of the lens. This paper presents a method for C^1 interpolation based on the solution of the biharmonic equation with appropriate boundary conditions.

Most disease transmission models assume no immunity or permanent immunity for simplicity, however, hosts have temporary immunity for most diseases. In this note we find that the immunity duration is actually the most sensitive parameter for dynamics of disease transmission. We provide numerical schemes to sketch Hopf bifurcations (forward or backward), sensitivity surfaces, periodicity diagrams (one dimensional or two dimensional parameter space) for a disease transmission model with immunity delay. The methods introduced here can be easily modified for a specific disease transmission model. We also test how different incidence functions change dynamics via bifurcation diagrams.