The Mathematical Model for Particle Suspension Flow through Porous Medium

Transport of suspensions and emulsions in porous media occurs in numerous processes of environmental, chemical, petroleum and civil engineering. In this work, a mass balance particle transport equation which includes filtration has been developed. The steady-state transport equation is presented and the solution to the complete advective-dispersion equation for particulate suspension flow has been derived for the case of a constant filter coefficient. This model in-cludes transport parameters which are particle advective velocity, particle longitudinal dispersion coefficient and filter coefficient. This work recommends to be investigated by particle longitudinal dispersion calculation from experimental data, directly. Besides, the numerical model needs to be developed for general case of a transition filter coefficient.

Dynamics of bioconvection flow of micropolar nanoparticles with Cattaneo-Christov expressions

A numerical analysis is performed to analyze the bioconvective double diffusive micropolar non-Newtonian nanofluid flow caused by stationary porous disks.The consequences of the current flow problem are further extended by incorporating the Brownian and thermophoresis aspects.The energy and mass species equations are developed by utilizing the Cattaneo and Christov model of heat-mass fluxes.The flow equations are converted into an ordinary differential model by employing the appropriate variables.The numerical solution is reported by using the MATLAB builtin bvp4c method.The consequences of engineering parameters on the flow velocity,the concentration,the microorganisms,and the temperature profiles are evaluated graphically.The numerical data for fascinating physical quantities,namely,the motile density number,the local Sherwood number,and the local Nusselt number,are calculated and executed against various parametric values.The microrotation magnitude reduces for increasing magnetic parameters.The intensity of the applied magnetic field may be utilized to reduce the angular rotation which occurs in the lubrication processes,especially in the suspension of flows.On the account of industrial applications,the constituted output can be useful to enhance the energy transport efficacy and microbial fuel cells.

The Game Theoretical Approach for Multi-phase Complex Systems in Chemical Engineering

This paper explores the application of noncooperative game theory together with the concept of Nash equilibrium to the investigation of some basic problems on multi-scale structure, especially the meso-scale structure in the multi-phase complex systems in chemical engineering. The basis of this work is the energy-minimization-multi-scale （EMMS） model proposed by Li and Kwauk （1994） and Li, et al. （2013） which identifies the multi-scale structure as a result of ＇compromise-in-competition between dominant mechanisms＇ and tries to solve a multi-objective optimization problem. However, the existing methods often integrate it into a problem of single objective optimization, which does not clearly reflect the ＇compromise-in-competition＇ mechanism and causes heavy computation burden as well as uncertainty in choosing suitable weighting factors. This paper will formulate the compromise in competition mechanism in EMMS model as a noncooperative game with constraints, and will describe the desired stable system state as a generalized Nash equilibrium. Then the authors will investigate the game theoretical approach for two typical systems in chemical engineering, the gas-solid fluidiza- tion （GSF） system and turbulent flow in pipe. Two different cases for generalized Nash equilibrinm in such systems will be well defined and distinguished. The generalize Nash equilibrium will be solved accurately for the GSF system and a feasible method will be given for turbulent flow in pipe. These results coincide with the existing computational results and show the feasibility of this approach, which overcomes the disadvantages of the existing methods and provides deep insight into the mechanisms of multi-scale structure in the multi-phase complex systems in chemical engineering.

Effects of CO₂Injection on the Seismic Velocity of Sandstone Saturated with Saline Water

Geological sequestration (GS) of carbon dioxide (CO2) is considered as one of the most promising technologies to reduce the amount of anthropogenic CO2 emission in the atmosphere. To ensure success of CO2 GS, monitoring is essential on ascertaining movement, volumes and locations of injected CO2 in the sequestration reservoir. One technique is to use time-lapsed seismic survey mapping to provide spatial distribution of seismic wave velocity as an indicator of CO2 migration and volumes in a storage reservoir with time. To examine the use of time-lapsed seismic survey mapping as a monitoring tool for CO2 sequestration, this paper presents mathematical and experimental studies of the effects of supercritical CO2 injection on the seismic velocity of sandstone initially saturated with saline water. The mathematical model is based on poroelasticity theory, particularly the application of the Biot-Gassmann substitution theory in the modeling of the acoustic velocity of porous rocks containing two-phase immiscible pore fluids. The experimental study uses a high pressure and high temperature triaxial cell to clarify the seismic response of a sample of Berea sandstone to supercritical CO2 injection under deep saline aquifer conditions. Measured ultrasonic wave velocity changes during CO2 injection in the sandstone sample show the effects of pore fluid distribution in the seismic velocity of porous rocks. CO2 injection was shown to decrease the P-wave velocity with increasing CO2 saturation whereas the S-wave velocity was almost constant. The results confirm that the Biot-Gassmann theory can be used to model the changes in the acoustic P-wave velocity of sandstone containing different mixtures of supercritical CO2 and saline water provided the distribution of the two fluids in the sandstone pore space is accounted for in the calculation of the pore fluid bulk modulus. The empirical relation of Brie et al. for the bulk modulus of mixtures of two-phase immiscible fluids, in combination with the Biot-Gassmann theory, was found to satisfactorily represent the pore-fluid dependent acoustic P-wave velocity of sandstone.

Bifurcation of Nonlinear Problems Modeling Flows Through Porous Media

This paper deals with a class of nonlinear boundary value problems which appears in the study of models of flows through porous media. Existence results of asymptotic bifurcation and continua are reported both for operator equations and for boundary value problems.

Modern methods of underground hydromechanics with applications to reservoir engineering

In the report the basic principles of new approach to the study of transport processes in porous medium are represented. The ＂percolation＂ approach has arisen as an attempt to overcome the traditional phenomenological approach in the underground hydromechanics, based on the assumption of continuity of saturated porous media, which does not allow to explain and to model a number of effects arising from the fluids flow in porous media. The results obtained are very interesting not only from the scientific point of view but as the scientific basis for a number of enhanced oil recovery technologies.