CENG0025 Process Systems Modelling and Design – 1 – CENG0025 Process Systems Modelling and Design (F. Galvanin) Coursework 2 To be submitted via Moodle by Wednesday 24 March 2021 1. Problem Description You are asked to develop, analyse and implement in gPROMS a dynamic distillation tray model and a column section model with linear tray hydraulics. In particular, you are asked to provide an investigation using gPROMS into how the product purities at the top and at the bottom of the column section may respond to changes in the liquid input to the top tray (e.g. reflux ratio) and the vapour input to the bottom tray (e.g. heat input), respectively. Your report (max 8 pages long) should be word processed and should contain the following sections: 1. Summary of main findings (strictly max. 100 words) [5] 2. Mathematical model equations for a single tray [10] 3. Mathematical model equations for a column with Ntray trays [10] 4. Degrees of freedom (DoF) analysis for a single tray [10] 5. Extension of the degrees of freedom (DoF) analysis to a column with Ntray trays [10] 6. Definition of suitable initial conditions for the column model [5] 7. Dynamic simulation results (using gPROMS) [20] 8. Discussion of the main findings, particularly related to any modelling assumptions made. Comment on the stability of the system. [20] The gPROMS code should be submitted separately (see Moodle instructions). Emphasis will be placed on the presentation of the model and the findings, as well as on the readability of the gPROMS code, therefore: 9. Marks will be allocated to the gPROMS code [5] 10. Marks will be awarded for the report structure and presentation [5] 5. Process Description Figure 1 shows a sketch of a distillation column. The feed typically enters close to the middle of the column. Vapour flows from stage to stage up the column while liquid flows from stage to stage down the column. The vapour from the top tray is condensed to liquid in the overhead condenser and a portion of that liquid is returned as reflux. The rest of the condensed vapour is withdrawn as overhead product containing mainly light component. A portion of the liquid at the bottom of the column is withdrawn as bottom product, containing mainly heavy component, whilst the rest is vaporised in the reboiler and returned to the column. (Note: you are only to model the column section; not the condenser and reboiler). The liquid from one tray goes over a weir and cascades down to the next tray through a downcomer. As the liquid moves across a tray, it comes into contact with the vapour from the tray below. Generally, as the vapour from the tray below comes into contact with the liquid, turbulent mixing is promoted. Assuming that the mixing is perfect, allows one to model the stage as a lumped parameter system as shown in Figure 2. CENG0025 Process Systems Modelling and Design – 2 – Figure 1 Tray distillation column. Figure 2 Scheme of the tray . 2.1 Key modelling assumptions 1. Multicomponent mixture with constant volatility, αi, relative to the key component. We assume that the equilibrium can be described by CompN j jj ii i x x y 1 CompNi …1 (1) 2. Real mixtures (i.e. modified Raoult’s law holds); we assume that the heat of mixing is zero. 3. Thermodynamic equilibrium (Murphree efficiency = 1). CENG0025 Process Systems Modelling and Design – 3 – 4. Perfect mixing on each tray, i.e. mole fractions on the tray are equal to the mole fractions leaving the tray. 5. The vapour holdup can be neglected. 6. Linear tray hydraulics (i.e. the liquid flow from the tray is proportional to the liquid holdup). 7. No dynamics in the downcomer, no weeping, and no entrainment. 8. Equimolar overflow. The molar vapour flow rate from one stage is equal to the molar vapour flow rate of the stage below, (i.e. Vin = Vout). 9. The properties of the mixture are independent of temperature (no energy balance needs to be considered). 3. Things to do Develop a distillation tray model and construct a column-section model given the assumptions listed above. The column section should be implemented as a composite model and include an array of (Ntray) tray models. The feed stage location is at Nfeed, i.e. the model should be applicable to any number of trays with any feed location. 1. Develop and solve the model of a single equilibrium tray: apply assumption 5 and define the partition coefficients (Ki) and relative volatilities (αi) using a modified Raoult’s law (see Section 4 for further details). Activity coefficients (required for the description of fugacity in the liquid phase), fugacity coefficients (required for the description of fugacity in the vapour phase) and vapour pressure vapP for each component should be computed from Multiflash using the foreign object interface (FOI). Consider linear tray hydraulics and constant molar overflow for the vapour (assumptions 6 and 8, respectively). Test that the single tray model works before moving to step 2 (use the column inlets in Section 4 as feeds to the tray). 2. Develop a column section model that contains an array of equilibrium tray models and the equations that link them together. Define a 1-d array for the total molar holdup on each stage, Mj, and 2-d arrays for the liquid and vapour mole fractions, xij and yij, and relate them to the corresponding variables in each tray model instance (these variables can then be used to plot column profiles). 3. Define a Process to simulate the column section using the data that are given in section 4. The operation of the column is described below: Define suitable initial values for the total holdup of component i in the tray (Mi) at t = 0 (justify your choice and/or related assumptions); The column is to be operated at steady state initially for 5 minutes, at which point a +15% step change in the reflux ratio is introduced, i.e. the liquid flow rate into the column section, Lin,1, is increased by 15%. The operation is then to continue until a new steady state has been reached (you decide how long this should be). The column should then be brought back to the original steady state (with the initial reflux flow rate) and operated for another 5 minutes before a step change in the heat input to the column section (i.e. in Vin,Ntray) of +15% of the steady state value is introduced. The operation is then to continue until a new steady state has been reached (you decide how long this should be). 4. Create graphs for your report of: The mole fraction of light component leaving the column section as vapour at the top. The mole fraction of the heavy component leaving the column section as liquid at the bottom. For each of the above, both step changes should be included in the same plot as the responses, i.e. Lin,1 and Vin,Ntray. CENG0025 Process Systems Modelling and Design – 4 – Column profiles of the light key vapour mole fraction on each tray: one for the original steady state and one for the steady state after each step change. The sensitivity of the molar fractions of the vapour at the top of the column to pressure P and temperature T. 4. Data 1. The column is ternary, i.e. Ncomp = 3. The components to be separated are benzene (B), toluene (T) and ethylbenzene (EB). The distillation column is meant to be operated at P = 300 kPa. 2. The column section consists of Ntray = 37 stages numbered from the top (i.e. top tray is Stage 1 and the bottom tray is Stage Ntray). 3. The feed tray is tray 17 counted from the top, i.e. NFeed = 17. 4. The constant relative volatility of component i with respect to component j is evaluated at T = 115 °C from j i ij K K (2) where the Ki for each component in the mixture is evaluated from the modified Raoult’s law for the description of vapour-liquid equilibrium: P P x y K i i vap i i i i . (3) In Eq. (3) vap iP , i i are, respectively, the vapour pressure, the activity coefficient and the fugacity coefficient of the i-th species in the mixture. 5. The molar feed flow rate to stage 17 is FNFeed = 1 mol/min, and the feed flow rates to all other stages are 0. 6. The composition of the feed is given by zNFeed = [B, T, EB] = [0.1, 0.1, 0.8]. (As the mole fractions must always add up to 1, the feed mole fractions to all the other trays can be set the same. Since the flow rates will be zero, there is no stream coming in). 7. The molar flow rate of vapour from the reboiler into the column section, Vin,NTray, is 3 mol/min and the mole fraction of the light component (benzene) is 0.05, i.e. yin,NTray = [B, T, EB] = [0.05, 0.05, 0.90]. 8. The molar flow rate of liquid into the column section, Lin,1 , is 4 mol/min and the mole fraction of the light component is 0.45, i.e. xin,1 = [B, T, EB] = [0.45, 0.40, 0.15]. 9. All trays in the column are identical, with linear tray hydraulics characterised by: L0 = 4 mol/min, LM 0 = 0.5 mol and τ = 0.15 min.
