Eivind Johannessen

Minimizing the entropy production in heat exchange

Abstract We present a theoretical proof that the entropy production due to heat exchange in a heat exchanger is minimum when the local entropy production is constant in all parts of the system. The solution for the minimum is independent of the value of the heat transfer coefficient. The general case is compared to the minimization problem that has equipartition of forces as solution. It is found that equipartition of forces predicts the minimum from the general solution well for typical heat exchange conditions. The discrepancy between the two solutions depends largely on the temperature dependency of the heat transfer coefficient. The optimal heat exchange conditions are very well approximated in practice with a counter-current heat exchanger; since the minimum in the entropy production space probably is flat.

Nonequilibrium thermodynamics of interfaces using classical density functional theory

A vapor-liquid interface introduces resistivities for mass and heat transfer. These resistivities have recently been determined from molecular simulations, as well as theoretically using the van der Waals square gradient model. This model, however, does not allow for direct quantitative comparison to experiment or results from molecular simulations. The classical density functional theory is used here in order to determine the equilibrium profiles of vapor-liquid interfaces. Equilibrium profiles are sufficient in the framework of nonequilibrium thermodynamics for determining the interfacial resistivities. The interfacial resistivities for heat transfer, for mass transfer, and for the coupling of heat and mass transfer can all be related to only one local thermal resistivity. This is done with integral relations for the interfacial resistivities. All interfacial resistivities can be consistently described in their temperature behavior with good accuracy.

Nonlinear flux-force relations and equipartition theorems for the state of minimum entropy production

Abstract We explain that the path of minimum entropy production in a system with nonlinear flux-force relations, which do not depend explicitly on the state variables of the system, can be characterised by equipartition of driving forces and equipartition of entropy production. The explanation is based on an optimal control theory formulation of the optimisation problem. The finding helps explaining recent numerical observations on the second law optimal state of chemical reactions.

Integral relations for the interfacial heat and mass transfer resistivities and the inverted temperature gradient

The occurrence of an inverted temperature gradient in a vapor between two liquids kept at different temperatures was first predicted by Pao [Phys. Fluids 14, 306 (1971)] using kinetic theory. Using integral relations for the interfacial heat and mass transfer resistivities derived in an earlier paper, we show the general validity of a criterion for the occurrence of an inverted temperature gradient for a one-component fluid in the slow evaporation/condensation regime. This criterion was first derived by Pao and subsequently rederived in an equivalent form using nonequilibrium thermodynamics. The general validity of this criterion means that there will always be an inverted temperature gradient in the vapor between a hot and cold liquid. We present numerical solutions of the nonequilibrium van der Waals square gradient model which agree with this general result. The numerical results also show the effects of the magnitude of the evaporation/condensation flux and the excess resistivity in the interfaces. We...

Energy efficient design of membrane processes by use of entropy production minimization

Abstract To minimize entropy production means to reduce the lost work in a process, and to optimize the use of energy resources. Due to the need for re-compression, membrane units for separation of CO2 from natural gas require large amounts of electrical power. We show that this power requirement can be reduced by controlling the permeation process so that the entropy production is minimum. With the use of optimal control theory, we develop in this work a detailed and robust method to minimize the entropy production of a membrane unit for separation of CO2 from natural gas, by control of the partial and total pressures on the permeate side. Moreover, we show how the continuous optimal results can serve as ideal limits for the practical design. A three-step permeate pressure that approximates the optimum reduces both the entropy production and the compressor power, when the permeate gas is re-compressed.

Chapter 13:Entropy Production Minimization with Optimal Control Theory

This chapter discusses how to take advantage of optimal control theory to minimize the entropy production of process units, in a step-wise, practical approach. The main results from literature are discussed, e.g. the validity of the theorems of equipartition of entropy production or equipartition of forces, as approximations to the state of minimum entropy production. A common property of systems with possibilities for internal equilibration seems to be that operating paths with minimum entropy production constitute bands in state space, called highways in state space. We show how energy-efficient design can be facilitated with knowledge of these properties.