Entropy generation analysis of heat and water recovery from flue gas by transport membrane condenser

Highlights

• A counter-flow transport membrane condenser (TMC) was used to recovery water and heat from flue gas.

• A lumped parameter model of the heat and mass transfer was established in the TMC.

• Structural selection and operation optimization of the TMC were conducted.

• The entropy generation analysis of TMC was conducted.

Abstract

The transport membrane condenser (TMC) has been used for heat and water recovery from coal-fired power plant flue gas. The capillary condensation of water vapor in membrane pore structure is the main gas separation mode. A lumped parameter model was established to study the heat and mass transfer in TMC. Recovered water and heat flow rates, water recovery ratio, heat recovery efficiency, and pressure drops were calculated. The temperature and humidity ratio distributions were displayed. The influences of structural parameters and operating conditions on the water and heat recovery performances were analyzed. In addition, the entropy generation model was proposed to calculate entropy variations and entropy generation components. The aim is to provide insights into TMC parameter selection and operation optimization. Moreover, the relationship between entropy generation components and TMC performances were confirmed. The results show that increasing packing fraction, or decreasing the membrane inner diameter or membrane pore size can improve the heat and water recovery performances. Besides, high water flow rates and low water temperatures have advantages in the operation. Increasing the mass/heat transfer driving force can enhance heat transfer performance, but the heat transfer entropy generation rate also increases. The maximum mass transfer entropy generation rate often corresponds to the best water recovery performance.

Introduction

In China, coal-fired power generation occupies an important place in the energy supply for a long time. The exhaust flue gas from fossil flue burning is typically at high temperature and humidity. It is estimated that in China the total amount of water vapor in the exhaust flue gas reaches as high as 1.01 billion tons per year, and the latent heat of vaporization is appropriately equivalent to 100 million tons of standard coal [1]. As seen, the flue gas is a potential source of both water and energy. Considering the water resource shortage and high energy consumption in the present situation, the water and heat recovery from flue gas is now an important pursuit for these power plants.

In recent years, water and/or heat recovery from flue gas by membrane technology have been widely studied [2]. Based on the membrane pore sizes and materials, separation mechanisms of porous membranes include molecular sieving, diffusion, surface effects, capillary condensation and so on [3]. Among them, the capillary condensation mode has attracted growing interest in vapor separation due to its high transport flux and separation efficiency. When capillary condensation occurs, the water vapor condenses within the membrane pore structure and the transport of the non-condensable gas components is prevented. According to this mechanism, the Gas Technology Institute (GTI) and its partners proposed their patented Transport Membrane Condenser (TMC) composed by nanoporous ceramic membranes. This technology is particularly beneficial for coal power plants that use high-moisture coals and/or flue gas desulfurization (FGD) [[4], [5], [6], [7]].

In addition, a few experimental studies [1,[8], [9], [10], [11]] and numerical simulations [[12], [13], [14], [15], [16]] on water and heat recovery from flue gas by TMC have been conducted. Bao et al. [8] compared the heat and water recovery performances between a nanoporous membrane tube bundle and an impermeable stainless steel tube bundle. The experimental results showed that at typical condensation heat transfer conditions the convection Nusselt numbers of the membrane tube bundle are 50–80% higher. Other researchers [1,9,11] have experimentally studied the performances of single counter-flow TMC tube under different operational conditions, including inlet flue gas flow rate and temperature, water flow rate and temperature, as well as flue gas humidity. The results indicated that the heat and water fluxes increase with the rise of inlet flue gas flow rate, water flow rate and flue gas humidity. Soleimanikutanaei et al. [[13], [14], [15], [16]] did a series of work to investigate the heat and water recovery performances of the cross-flow TMC by CFD simulation.

From the literature review, it can be seen that evaluations of TMC performance were usually based on the first law of thermodynamics with the parameters such as water flux, heat flux, heat transfer coefficient, Nusselt number. However, the water and heat transfer in TMC is a typical irreversible process, which results from the heat flow from flue gas to cooling water, and the water vapor flow from flue gas bulk to the membrane pore structure. To provide a more comprehensive evaluation, in the current work the second law of thermodynamics is employed to evaluate the performance of TMC by entropy generation analysis. In the past decades, entropy generation analysis has been widely applied in heat exchanger evaluation and design. MacClintock [17] firstly introduced the entropy generation minimization (EGM) method to assess the heat exchanger performance, which means the entropy generation rate is the subject to minimization. Bejan [18] and Hesselgreaves [19] proposed their respective definitions of entropy generation number as criteria for heat exchanger performance. For various types of heat exchangers, the EGM method was widely employed to select the optimum geometry [[20], [21], [22], [23]] and operating condition [24].

However, compared with conventional heat exchangers where only heat transfer occurs, the TMC is more complicated due to water vapor transfer and condensation. Since one of the key tasks of TMC is to provide the maximum heat and water fluxes, whether the EGM method can be applied in TMC performance optimum needs to be reconsidered. In this study, we built a physico-mathematical model to simulate the coupled heat and mass transfer in a counter-flow TMC. The water vapor diffusion in flue gas stream and vapor condensation in membrane pores are also considered. A finite difference method is employed to solve the governing equations. Furthermore, we propose an entropy generation model of TMC and compared the results with the parameters based on the first law of thermodynamics. The structural and operating optimizations are performed based on the results. Besides, the relationship between entropy generation components and heat and water recovery performance is confirmed.