Abstract: A Hybrid Embedded Fracture (HEF) model was developed to reduce various computational costs while maintaining physical accuracy (Amir and Sun, 2016). HEF splits the computations into fine scale and coarse scale. Fine scale solves analytically for the matrix-fracture flux exchange parameter. Coarse scale solves for the properties of the entire system. In literature, fractures were assumed to be either vertical or horizontal for simplification (Warren and Root, 1963). Matrix-fracture flux exchange parameter was given few equations built on that assumption (Kazemi, 1968; Lemonnier and Bourbiaux, 2010). However, such simplified cases do not apply directly for actual random fracture shapes, directions, orientations …etc. This paper shows that the HEF fine scale analytic solution (Amir and Sun, 2016) generates the flux exchange parameter found in literature for vertical and horizontal fracture cases. For other fracture cases, the flux exchange parameter changes according to the angle, slop, direction, … etc. This conclusion rises from the analysis of both: the Discrete Fracture Network (DFN) and the HEF schemes. The behavior of both schemes is analyzed with exactly similar fracture conditions and the results are shown and discussed. Then, a generalization is illustrated for any slightly compressible single-phase fluid within fractured porous media and its results are discussed.

Abstract: To compute flows around objects with complicated motion like the intermeshing rotors, the unstructured moving grid finite volume method was developed. Computational elements are added and eliminated according to motion of rotors, to keep the computation domain around rotors which mutually reverse. Also, the geometric conservation law is satisfied in the method, using four dimensional space time unified domain for control volume. Using the method, accurate computation is carried out without interpolation of physical quantities. Applying to a flow around a sphere, computation procedure was established with introduction of concept of a hierarchical grid distinction. Then, the results of application to the flow around intermeshing rotors showed efficacy of the method. The results also showed applicability of the method to compute flows around any complicated motion.

Abstract: We extend a regularization based numerical method for a highly degenerate partial differential equation that describes biofilm growth to systems of PDEs describing biofilms with several particulate substances. The example for which we develop the method is a quorum sensing biofilm which consists of donwn- and up-regulated biomass fractions. We carry out computational studies to assess the effect of the regularization parameter, a grid refinement study and report briefly on parallel performance of our code under OpenMP on desktop workstations.

Abstract: To improve the research methods in petroleum industry, we develop a fast algorithm to simulate droplet motions in oil and water two phase flow, using phase field model to describe the phase distribution in the flow process. An efficient partial difference equation solver—Shift-Matrix method is applied here, to speed up the calculation coding in high-level language, i.e. Matlab and R. An analytical solution of order parameter is derived, to define the initial condition of phase distribution. The upwind scheme is applied in our algorithm, to make it energy decay stable, which results in the fast speed of calculation. To make it more clear and understandable, we provide the specific code for forming the coefficient matrix used in Shift-Matrix Method. Our algorithm is compared with other methods in different scales, including Front Tracking and VOSET method in macroscopic and LBM method using RK model in mesoscopic scale. In addition, we compare the result of droplet motion under gravity using our algorithm with the empirical formula common used in industry. The result proves the high efficiency and robustness of our algorithm and it’s then used to simulate the motions of multiple droplets under gravity and cross-direction forces, which is more practical in industry and can be extended to wider application.

Abstract: Centrifugal compressors are one of the most commonly used equipments powering the long distance natural gas pipeline. In this paper, a similarity conversion method of centrifugal natural gas compressors based on predictor-corrector was proposed. In other words, we used one similarity conversion to predict the key parameter and the other was used as the correction. Compared with the field test data, we found the error of the predicted outlet pressure of the compressor was controlled at about 2% and the outlet temperature fluctuated within 2℃, which could satisfy the engineering application requirements.