State-space model for transient behavior of transport membrane condenser

Highlights

• A state-space model in a transport membrane condenser is developed and verified experimentally.

• The transient relationships between input parameters, output parameters, and performances are analyzed.

• The perturbation of the flue gas flow rate has a larger effect on the performances than that of the inlet flue gas humidity ratio.

• There is a hysteresis time in the response of the outlet water temperature with an increase in the inlet water temperature step.

Abstract

In this paper, a state-space model of a transport membrane condenser (TMC) based on a lumped heat and mass transfer model is developed and verified experimentally. The simulated results are in well agreement with the experimental data. Based on the state-space model, the transient relationships between the input parameters (inlet flue gas temperature and humidity ratio, inlet water temperature, flue gas and water flow rates), output parameters (outlet flue gas temperature and humidity ratio, outlet water temperature) and performance parameters (heat and water recovery fluxes, recovery efficiency) of the TMC are obtained and analyzed. It can be found that the perturbation of the flue gas flow rate has a larger effect on the heat and water recovery performances compared to that of the inlet flue gas humidity ratio. The performance parameters change by less than 1% with the inlet flue gas temperature step increasing from 50°C to 53°C. The inlet water parameters have significant effects on the performances. With the inlet water temperature step increasing from 15°C to 16°C, there is a hysteresis time in the response of the outlet water temperature. The comparative analysis based on the state-space model with a simply and rapid solution process can be used to determine the major input variables affecting the performances. The results are useful for the dynamic control of the TMC to obtain required stable performances.

Introduction

In recent years, with the economic development of China, the coal-fired power generation plays an increasingly important role in energy supply. For the current energy structure of China, the thermal power generation will still be in the dominant state for a long time in the future [1]. The consumptions of water and coal are huge in the process of the thermal power generation. The thermal power plants consumed about 900 billion tons of water and 1.79 billion tons of coal in 2015, which respectively account for about 15% and 50% of the total consumptions of water and coal in China [2]. There are a lot of heat and water in the flue gas produced by coal combustion [3]. Therefore the heat and water recovery in the flue gas can alleviate the current situations of water shortage and high energy demand.

With the maturity of the membrane separation technology, the heat and water recovery from flue gas utilizing the membrane separation technology has been widely studied [4]. Considering the differences of the membrane material and structure, the separation mechanism of the porous membrane mainly contain molecular sieving, diffusion, surface effect, capillary condensation and so on [5]. Among them, the capillary condensation mode is more suitable for vapor separation because of its higher mass transfer flux and separation efficiency. The Gas Technology Institute (GTI) and its partners have proposed a transport membrane condenser (TMC) composed by the nanoporous ceramic membranes in which vapor condensation within the membrane pores effectively prevents the transports of non-condensable gases. This technology is more advantageous for coal-fired power plants using high-moisture coals or flue gas desulfurization [6].

Recently, many researchers have carried out a series of experimental studies [7], [8], [9], [10] and numerical simulations [10], [11], [12], [13], [14], [15] on the heat and water recovery from flue gas by the TMC. Bao et al. [7] compared the heat and water recovery performances of a nanoporous membrane tube bundle and an impermeable stainless steel tube bundle with the same characteristic size through experimental studies. The results showed that the Nusselt numbers of the membrane tube bundle are 50-80% higher than those of the impermeable stainless steel tube bundle at the typical condensation heat transfer conditions. Chen et al. [8] experimentally studied the heat and water recovery performances of a 20 nm pore-size porous ceramic membrane. The results showed that the heat and water recovery efficiencies can reach as large as 90% in appropriate conditions. Wang et al. [9] carried out an experimental study on the heat and water recovery from gaseous streams by the TMC composed of tubular ceramic membranes. About 20-60% water recovery and 33-85% heat recovery could be achieved when using cold water as the coolant. Zhao et al. [10] experimentally studied the effects of the operational parameters on the heat and water recovery performances of a tubular ceramic membrane condenser. Yue et al. [11] investigated the heat and mass transfer performances of a monochannel tubular membrane and a multichannel ceramic tubular membrane. The multichannel membrane had much larger mass and heat transfer resistances. Lin et al. [12] disclosed the heat and mass transfer characteristics of a condensing combustion flue gas in a cross-flow transport membrane tube bundle by analyzing the variations of the temperatures, mass fractions, enthalpies, and skin fractions. Soleimanikutanaei et al. [13] simulated the heat and water recovery performances of the multi-stage shell and tube TMC under high temperature and high pressure conditions. An optimized configuration for the TMC heat exchanger unit was proposed. Subsequently, based on the combined condensation model of capillary condensation and condensation on solid wall, the influences of different structural and operating conditions on the overall performances of a membrane heat exchanger were simulated and analyzed [14], [15].

However, it is noteworthy that present investigations of the TMC are typically based on the steady state. Further, the models developed are a set of partial differential equations which are complex to solve requiring a large number of iterations. Therefore a simpler dynamic model is necessary for desicribe the heat and mass transfer inside the TMC. It should be noted that the state-space modeling method has been applied to other objects like heat exchanger, chiller, air-conditioned room and ect. [16], [17], [18]. Yao et al. [16] considered the water-to-air heat exchanger as a multi-input-and-multi-output system, and the dynamic model was developed with the energy and mass balance equations based on which the state-space model for transient behavior of the heat exchanger was derived. Subsequently, the dynamic thermal behavior of the indoor air [17] and the transient response model for the vapor compression refrigeration system [18] were developed by the means of linear approximation. Further, the influences of disturbances and initial conditions on the performance parameters were discussed. Similarly, the state-sapce modeling method can be used to the TMC modeling. In order to clearly describe the transient relationships between the inlet parameters, outlet parameters, and performance parameters of the TMC, the state-space model is developed. It can describe the transient relationships between the input, output and performance parameters in matrix forms, which are beneficial for simplifying and accelerating the solution process. An experiment is conducted to validate the model. Based on the state-space model, the transient relationships between the input parameters (inlet flue gas temperature and humidity ratio, inlet water temperature, flue gas and water flow rates), output parameters (outlet flue gas temperature and humidity ratio, outlet water temperature) and performance parameters (heat and water recovery fluxes, recovery efficiency) of the TMC are obtained and analyzed. The results are useful for the dynamic control of the TMC to obtain required stable performances.