Pre-simulation activities consist of: understanding the assumptions that are used in simulating the column, acquiring the inlet stream conditions, simulate the study column using commercial simulator Design II and specify the desired separation flow rates and fix the degrees of freedom. The adopted assumptions in simulating the column are structured as follow:
1) Liquid on the tray is perfectly mixed and incompressible. Compositions of the liquid stream leaving the tray will be the same as the tray molar hold-up compositions.
2) Tray vapor hold-ups are negligible because the column operating pressures are less than 10 bars (Lee and Kamarul, 2001).
3) Vapor and liquid are in thermal equilibrium. The temperature for liquid stream leaving the tray and the vapor stream leaving the tray is the same.
4) Vapor and liquid are in the phase equilibrium.
5) Pressure is constant on each tray but varies linearly up the column from bottom pressure to the top column pressure. In another word, pressure drop for each tray is the same.
6) Coolant and steam dynamics are negligible.
7) Dynamic changes in internal energy on the trays are negligible compared with the latent heat effects. Therefore, energy balance on each tray is just algebraic.
After the assumptions that are used in simulating the column have been studied, the following task is to acquire enough information for the inlet feed stream. This information is obtained from the plant simulated data (Appendix B). The given data was sufficient enough for the inlet stream.
The study column is simulated using commercial simulator, Design II, to obtain a set of steady state results that comprises the following column parameters profile:
1) Column temperature profile. 2) Column liquid flow rate profile.
59 3) Column vapor flow rate profile.
4) Trays liquid compositions profile. 5) Trays vapor compositions profile. 6) Liquid enthalpy profile.
7) Vapor enthalpy profile.
8) Bottom stream flow rate and compositions. 9) Distillate stream flow rate and compositions. 10) Sidedraw stream flow rate and compositions. 11) Pumparound stream flow rate and compositions. 12) Reflux stream flow rate and compositions.
The Design II simulation results are used as the initial guess for the dynamic simulation of the column in Matlab. The parameter profiles that are going to be used as the initial guesses for the written dynamic simulation are the column temperature profile and the liquid compositions profile.
From the degree of freedom analysis, it is shown that there are 31 degrees of freedom. Therefore, 31 variables have to be fixed in order to achieve the desired compositions for the bottom and distillate streams.
These 31 variables are:
1) 28 tray pressure. The tray pressures vary linearly from top column to the bottom of the column. Each tray encounters 0.00095 bar pressure drop.
2) Reflux flow rate = 10 kmole/hr.
3) Pumparound flow rate = 49.6 kmole/hr. 4) Reboiler duty = 2.16 x 106 kJ/hr.
3.7.2 Algorithm Formulation
The column models that describe the column behavior are bottom column model, normal tray model, feed tray model, reflux point model, pumparound point model, sidedraw tray model, reflux tray model and pumparound tray model. These models are comprised of mass balance equations, equilibrium equations, heat balance equations, summation equations and hydraulic equations. Algorithm formulation involved solving these equations in the proper order and sequence so that the column behaviors are revealed. For this research, the dynamic simulation algorithm proposed by Lee and Kamarul (2001) are referred. However, since in this research the study column has a pumparound system incorporated at the top of the column; some modifications are made before applying the stated algorithm.
The systematic procedures in formulating this research’s dynamic simulation algorithm are elaborated as follow:
The algorithm for the bottom column to the 4th tray:
1) Initialize the following derivative variables:
i) Bottom liquid level and compositions – 9 derivative variables
ii) Each tray molar hold-up and compositions – 225 derivative variables
There are 234 derivative variables that have to be initialized since there are 234 derivative equations.
2) Calculate the bubble point from the bottom tray till the 4th tray.
The tray pressure is fixed since the pressure drop for each tray is assumed to be the same. The bottom column pressure is fixed at 0.1333 bar and each tray will encounters a 0.00095 bar pressure drop. The tray temperature and liquid compositions are guessed. The guessing values are referred from the Design II steady state simulation results. The bubble point calculation procedures which were presented in Section 3.5.2.1 are referred. The purposes of bubble point calculations are to determine the tray temperature and vapor phase compositions.
61 3) Calculate the liquid and vapor enthalpy from bottom tray till the 4th tray. Based
on the Tn, xi, n and yi, n as calculated in the previous step, liquid and vapor enthalpy for each tray are determined via Equation 3.43 to 3.44.
4) Calculate the liquid flow rate by Francis Weir equations.
From the initial bottom liquid level and tray’s molar hold-up, the following variables are determined from the bottom stage till the 4th stage:
i) Bottom flow rate by Equation 3.2.
ii) Liquid leaving each tray by Equation 3.48 – 3.50.
5) Calculate the vapor flow rate from energy balance.
Based on the calculated liquid and vapor enthalpy, the vapor flow rate leaving each tray is determined by Equation 3.46 for the reboiler stage and Equation 3.47 for other trays.
6) Evaluate the molar hold-up and components composition derivative variables.
For every time increment h = 0.005 hour, the evaluation for each derivative variable is started from the bottom stage till the 4th stage using Runge-Kutta fourth order method.
The algorithm for the 3rd tray to 1st tray, pumparound point and reflux point:
7) Start at the reflux point. Initialize the derivative variables as in Step 1. Perform bubble point calculation as in Section 3.5.2.1, calculate the liquid and vapor enthalpy for all the streams and the flow rate of the liquid stream is determined using Equation 3.11. Repeat Step 4 to 6.
8) Pumparound point. Calculation procedure as Step 7 with the distillate flow rate calculated using Equation 3.14.
10) Increase time step.
After all the derivative variables at time = t are evaluated, the calculation steps are repeated until time = tfinal.