Ensemble Distribution for Immiscible Two-Phase Flow in Porous Media

We construct an ensemble distribution to describe steady immiscible two-phase flow of two incompressible fluids in a porous medium. The system is found to be ergodic. The distribution is used to compute macroscopic flow parameters. In particular, we find an expression for the overall mobility of the system from the ensemble distribution. The entropy production at the scale of the porous medium is shown to give the expected product of the average flow and its driving force, obtained from a black-box description. We test numerically some of the central theoretical results.Comment: 23 pages, 9 figure

A Monte Carlo Algorithm for Immiscible Two-Phase Flow in Porous Media

We present a Markov Chain Monte Carlo algorithm based on the Metropolis algorithm for simulation of the flow of two immiscible fluids in a porous medium under macroscopic steady-state conditions using a dynamical pore network model that tracks the motion of the fluid interfaces. The Monte Carlo algorithm is based on the configuration probability, where a configuration is defined by the positions of all fluid interfaces. We show that the configuration probability is proportional to the inverse of the flow rate. Using a two-dimensional network, advancing the interfaces using time integration the computational time scales as the linear system size to the fourth power, whereas the Monte Carlo computational time scales as the linear size to the second power. We discuss the strengths and the weaknesses of the algorithm.Comment: 22 pages, 15 figure

A Monte Carlo Algorithm for Immiscible Two-Phase Flow in Porous Media

We present a Markov Chain Monte Carlo algorithm based on the Metropolis algorithm for simulation of the flow of two immiscible fluids in a porous medium under macroscopic steady-state conditions using a dynamical pore network model that tracks the motion of the fluid interfaces. The Monte Carlo algorithm is based on the configuration probability, where a configuration is defined by the positions of all fluid interfaces. We show that the configuration probability is proportional to the inverse of the flow rate. Using a twodimensional network, advancing the interfaces using time integration, the computational time scales as the linear system size to the fourth power, whereas the Monte Carlo computational time scales as the linear size to the second power. We discuss the strengths and the weaknesses of the algorithm

Harnessing thermoelectric power from transient heat sources: Waste heat recovery from silicon production

Thermoelectric generators (TEGs) are compact and robust devices for converting heat into electrical power. In this work, we investigate the response of a bismuth-telluride based TEG to the transient environment of a silicon production plant, where there is a periodic change in the average temperature of the heat source. We establish a dynamic mathematical model that reproduces results from industrial, on site experiments, both at steady-state and under transient conditions. By simultaneously changing the design and location of the TEG, a peak power density of 1971 W=m2 can be obtained without exceeding material constraints of the TEG, with an average power density of 146 W=m2. In the transient case, the average power density generated during one silicon casting cycle is in all investigated cases found to be only 7 - 10% of the peak power density as the peak value of the power is only maintained for a couple of minutes. The fractional area is defined as the ratio of the total area of thermoelectric modules to the total system cross-sectional area of the TEG. We find that the power generated can be increased by reducing the fractional area, provided that the TEG is at a fixed position. If the TEG can be placed as close as possible to the heat source without exceeding the material constraints, the peak power density and the average power density reach maximum values as functions of the fractional area, beyond which the power begins to decline. The optimal fractional area that gives maximum power depends strongly on the cooling capacity. We find that with a higher cooling capacity, it is beneficial to design the TEG with a higher fractional area and place it as close as possible to the silicon melt. Possible venues to improve the performance of TEGs that operate under transient conditions are suggeste

Harnessing thermoelectric power from transient heat sources: Waste heat recovery from silicon production

Thermoelectric generators (TEGs) are compact and robust devices for converting heat into electrical power. In this work, we investigate the response of a bismuth-telluride based TEG to the transient environment of a silicon production plant, where there is a periodic change in the average temperature of the heat source. We establish a dynamic mathematical model that reproduces results from industrial, on site experiments, both at steady-state and under transient conditions. By simultaneously changing the design and location of the TEG, a peak power density of 1971 W=m2 can be obtained without exceeding material constraints of the TEG, with an average power density of 146 W=m2. In the transient case, the average power density generated during one silicon casting cycle is in all investigated cases found to be only 7 - 10% of the peak power density as the peak value of the power is only maintained for a couple of minutes. The fractional area is defined as the ratio of the total area of thermoelectric modules to the total system cross-sectional area of the TEG. We find that the power generated can be increased by reducing the fractional area, provided that the TEG is at a fixed position. If the TEG can be placed as close as possible to the heat source without exceeding the material constraints, the peak power density and the average power density reach maximum values as functions of the fractional area, beyond which the power begins to decline. The optimal fractional area that gives maximum power depends strongly on the cooling capacity. We find that with a higher cooling capacity, it is beneficial to design the TEG with a higher fractional area and place it as close as possible to the silicon melt. Possible venues to improve the performance of TEGs that operate under transient conditions are suggestedacceptedVersion© 2017. This is the authors’ accepted and refereed manuscript to the article. Locked until 10.2.2019 due to copyright restrictions. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0