第十二讲 基于传递速率的精馏计算模型.ppt

1、First page,传递过程 与 分离技术,全日制专业硕士研究生学位课程,面向应用的 专业基础课程,第十二讲基于传递速率的精馏计算模型,Rate Based Methods,For Multicomponent Distillation,Introduction (1),In a real column, the vapor and liquid phase are not at equilibrium because of the limited rates of transport processes. For dealing with such situations, it is th

2、e most commonly used method to introduce the stage efficiency, which represents, by definition, the extent of approaching phase equilibrium in a stage.,Introduction (2),For example, the Murphree efficiency for vapor phase is defined as,(12-2),(12-3),Introduction (3),For binary systems, the theoretic

3、al values of Murphree efficiencies are between 0 and 100%. 0.65% to 4.2% for absorption into and stripping from, of carbon dioxide, water and glycerine solutions; 4.7% to 24% for absorption of olefins into oils; and 69% to 92% for absorption of ammonia into water, humidification of air.,Introduction

4、 (4),For multicomponent systems, it is much more complicated because of the coupling effects between components. When the vapor mole-fraction driving force of component A is small compared to the other components in the mixture, the transport rate of A is controlled by the other components, with the

5、 result that EMV for A is anywhere in the range from minus infinity to plus infinity.,Introduction (5),This theoretical prediction has been confirmed by conducting experiments with the ethanol / tert-butanol / water system. The obtained values of EMV for tert-butanol ranged from -2,978% to +527%. In

6、 addition, values of EMV for ethanol and water sometimes differed from the binary system significantly.,Introduction (6),In 1979, Krishna and Standart showed the possibility of applying rigorous multi-component mass-and heat-transfer theory to calculations of simultaneous transport. The theory was f

7、urther developed by Taylor and Krishna. The availability of this theory led to the development in 1985 by Krishna Murthy and Taylor of the first general rate-based, computer-aided model for application to trayed and packed columns for distillation and other continuous, countercurrent vapor-liquid se

8、paration operations.,THEORETICAL MODEL FOR AN EQUILIBRIUM STAGE (1),Feeds entering stage j are treated as a liquid and a vapor stream with molar flow rate fi,Lj , fi,Vj and molar enthalpy HLFj , HVFj respectively.,THEORETICAL MODEL FOR AN EQUILIBRIUM STAGE (2),Also leaving from (+)or entering to (-)

9、 the liquid and/or vapor phases in the stage are heat transfer rates QjV and QjL, respectively.,THEORETICAL MODEL FOR AN EQUILIBRIUM STAGE (3),Also entering the stage from the stage above is liquid molar ftow rate Lj-1 at temperature TLj-1 and pressure Pj-1 , with molar enthalpy HLj-1 and component

10、mole fractions xi,j-1 ;,THEORETICAL MODEL FOR AN EQUILIBRIUM STAGE (4),And entering the stage from the stage below is vapor molar flow rate Vj+1 at temperature TVj+1 and pressure Pj+1 , with molar enthalpy HVj+1 and component mole fractions yi,j+1.,THEORETICAL MODEL FOR AN EQUILIBRIUM STAGE (5),And

11、entering the stage from the stage below is vapor molar flow rate Vj+1 at temperature TVj+1 and pressure Pj+1 , with molar enthalpy HVj+1 and component mole fractions yi,j+1 .,THEORETICAL MODEL FOR AN EQUILIBRIUM STAGE (6),Within the stage, mass transfer of components occurs across the phase boundary

12、 at molar rates Ni,j from the vapor phase to the liquid phase (+) or vice versa (-), and heat transfer occurs across the phase boundary at rates ej from the vapor phase to the liquid phase (+) or vice versa (-).,THEORETICAL MODEL FOR AN EQUILIBRIUM STAGE (7),Leaving the stage is liquid at temperatur

13、e Tj and pressure Pj, with molar enthalpy HLj and vapor at temperature Tj and pressure Pj with molar enthalpy HVj.,THEORETICAL MODEL FOR AN EQUILIBRIUM STAGE (8),A fraction, rLj, of the liquid exiting the stage may be withdrawn as a liquid side stream at molar flow rate Uj , leaving the molar flow r

14、ate Lj to enter the stage below or to exit the column.,THEORETICAL MODEL FOR AN EQUILIBRIUM STAGE (9),A fraction, rVj, of the vapor exiting the stage may be withdrawn as a vapor side stream at molar flow rate Wj , leaving the molar flow rate Vj to enter the stage above or to exit the column.,THEORET

15、ICAL MODEL FOR AN EQUILIBRIUM STAGE (10),If desired, entrainment, occlusion, interlink flows, a second immiscible liquid phase, and chemical reaction(s) can be added to the model.,THEORETICAL MODEL FOR AN EQUILIBRIUM STAGE (11),Recall that the equilibrium-stage model of Chapter 10 utilizes the 2C +

16、3 MESH equations for each stage: C mass balances for components C phase equilibria relations 2 summations of mole fractions 1 energy balance,THEORETICAL MODEL FOR AN EQUILIBRIUM STAGE (12),In the rate-based model, the mass and energy balances around each equilibrium stage are each replaced by separa

17、te balances for each phase around a stage, which can be a tray, a collection of trays, or a segment of a packed section. In residual form, the equations are as follows, where the residuals are on the left-hand sides and become zero when the computations are converged. When not converged, the residua

18、ls are used to determine the proximity to convergence.,THEORETICAL MODEL FOR AN EQUILIBRIUM STAGE (13),Liquid-phase component material balance:,Vapor-phase component material balance:,Liquid-phase energy balance:,Vapor-phase energy balance:,(12-4),(12-5),(12-6),(12-7),THEORETICAL MODEL FOR AN EQUILIBRIUM STAGE (14),where at the phase interface, I,Equations (12-4) and (12-5) are coupled by the component mass-transfer rates:,The equations for the mole-frac