ECH 4224L Unit Operations Lab I Thin Film Evaporator. Introduction. Objective

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1 Introduction In this experiment, you will use thin-film evaporator (TFE) to separate a mixture of water and ethylene glycol (EG). In a TFE a mixture of two fluids runs down a heated inner wall of a cylindrical vessel as a thin liquid film. The vessel is heated to the boiling temperature of the more volatile component of the mixture (in this case, water). This component is then evaporated and leaves the vessel as the top flow. The vapor is transferred to a cooler where it is condensed. The less volatile component leaves the system as the bottom flow and is cooled using a heat exchanger. The rate of evaporation is enhanced by creating thin films with large surface-to-volume ratio. In order to ensure the thin film flow, a wiper is continuously rotating inside the vessel (see Figure 1). To further enhance performance of the TFE, the pressure inside its chamber is reduced, which in turn reduces boiling temperature of the mixture. The system in the Unit Operations Lab uses a steam injector to reduce pressure in the TFE chamber. The injector contains a converging-diverging pipe. Reduction in the Figure 1. Schematics of the thin film pipe diameter leads to an increase of the steam velocity evaporator (Dow Chemical). which (according to the Bernoulli law) creates a low pressure zone. Objective The main objective of this experiment is a systematic investigation of effects of various parameters on the efficiency of the separation. Control parameters in this experiment are the feed flow rate F and the pressure in the TFE chamber. Effect of these parameters on the compositions and flow rates of the top and bottom streams should be investigated both theoretically and experimentally. 1-1

2 Theory The following theory assumes that the TFE is operated at a steady-state. In practice it may take a long time for the system to reach a steady-state. Therefore, it will be necessary to monitor the flow rates and concentrations of the top and bottom products as a function of time (see Operating Instructions). The thin film flow is schematically shown in Fig. 2. Due to evaporation of the more volatile component, the liquid flow rate decreases as liquid flows down the wall. Dependence of the flow rate on the position can be obtained from the mass balance and phase equilibrium conditions. F = molar flow rate of feed L = molar flow rate of the bottom product V = molar flow rate of the top product q(z) = molar flow rate of the liquid at a given position z x F = molar fraction of water in the feed x B = molar fraction of water in the bottom product y = molar fraction of water in the vapor Figure 2. Schematics of the thin film flow down the vessel wall. Film thickness decreases downstream due to evaporation. 1-2

3 Introduce the system of coordinates with z-axis pointing downwards (see Fig. 3). Introduce also the following notation: q(z) = molar flow rate of the liquid at a given z. x(z) = molar fraction of water in the liquid at a given z y(z) = molar fraction of water in the vapor at a given z Figure 3. A differential element of the thin film flow. Consider a differential element between z and z+dz. Due to evaporation, liquid flow rate q(z) is not constant and we can write q(z + dz) = q(z) + dq(z), dq(z) < 0 (1) Molar rate of evaporation of water out of this differentia element is (total amount of evaporated fluid) (water fraction in vapor) = dq(z) y(z) (2) This should be equal to rate of loss of water from the liquid phase = d[q(z) x(z)] (3) Equating right-hand sides of equations (2) and (3), we obtain: y dq = x dq + q dx (4) Rearranging the terms, we obtain: dq q = dx (5) Now, integrate from the feed inlet (z = 0) to the bottom outlet (z = H): 1-3

4 ln [ q(h) x(h) q(0) ] = dx Since q(0) = F, q(h) = L, x(0) = xf, and x(h) = xb, we obtain the Rayleigh equation 1 : x(0) (6) x B ln [ L F ] = dx (7) x F This equation provides a relationship between the flow rate L and composition xb of the bottoms product. In order to perform integration in the right-hand-side of this equation, it is necessary to obtain the relationship between y and x. To this end, we assume a local vapor-liquid equilibrium (VLE) in each differential element dz (see Figure 3). According to the Gibbs phase rule, a two-phase equilibrium of a two-component mixture has two degrees of freedom. In the TFE, one of the degrees of freedom pressure P is fixed inside the evaporator chamber, while other degrees of freedom (such as the fluid compositions and temperature) change as the liquid flows down the wall. A typical phase equilibrium diagram for a twocomponent mixture is shown in Fig. 4. The temperature Figure 4. Phase equilibrium of the mixture increases as the concentration of the more diagram for a two-component volatile component decreases. Therefore, the mixture at a constant pressure temperature at the bottom of the TFE should be higher than at the top. The VLE diagrams can be obtained, e.g., using Raoult's law and the Antoine equation. The VLE data then allows one to obtain the relationship between the fluid and vapor compositions, y = y eq (x, P), (8) that can be used in Eq. (7). Since Eq. (7) has two unknowns (L and xb), it must be supplemented by another relationship in order to develop a predictive model for the TFE performance. To this end, one can use the energy balance, 1 Originally, the Raleigh equation was developed for batch distillation, in which the fluid composition changes in time. In our application of the Rayleigh equation to the TFE, we assume a steady state process and the Rayleigh equation describes the composition change in space. 1-4

5 FH F + Q = LH L + VH V (9) Here, Hk is the molar enthalpy of stream k (k = F, L, or V) and Q is the rate of heat transfer from the heating fluid (steam) to the fluid inside the evaporator. The dominant contribution to Q is the latent heat of condensation. Therefore, Q, can be estimated assuming that the heating fluid leaving the system is a saturated liquid. We can solve Eqs. (7)-(9) numerically using VBA/Excel or python to predict flow rates and compositions of the products. These predictions should be compared with the experimental measurements. The flow rates of the top and bottom products can be determined experimentally using the sight glasses attached to the product tanks. The stream compositions can be determined by measuring the refractive index (RI) of corresponding samples (see Operating Instructions). 1-5