This Demonstration simulates a multicomponent distillation column in steadystate. In order to describe the vaporliquid equilibrium (VLE) relationships and to compute the vapor and liquid phase enthalpies, the SoaveRedlichKwong equation of state (SRK EOS) is used (Soave, 1972 and Nasri and Binous, 2007). Rigorous modeling is performed by solving both mass and energy balance equations. All steadystate results are found to agree perfectly with those obtained using HYSYS 3.2, a major process simulator by Aspen Technology, Inc. Consider a multicomponent mixture to be fed to a distillation column containing 27 theoretical stages, a total condenser, and a partial reboiler and operating at a pressure of 16.212 bar. It is assumed that (1) the pressure is constant on all trays; (2) the vapor and liquid leaving each tray are in equilibrium (i.e., tray efficiency is 100%); and (3) the column is adiabatic. A treatment where variable pressure is considered is given by Choe and Luyben (1987). The column feed, a saturated liquid, is composed of 2.5% ethane, 35% propane, 60% butane, and 2.5% pentane at 347.8 K. Feed flow rate is set equal to 300 kmol/hr. The feed is entered at the stage. You can choose the reflux ratio and reboiler heat duty. By default, they are set to 3.073 and kJ/hr, respectively. Composition profiles in the column are given for ethane, propane, butane, and pentane in red, green, cyan, and blue, respectively. You can also see the temperature profile in Kelvin (blue curve), the equilibrium constants (for ethane, propane, butane, and pentane, given in red, green, cyan, and blue, respectively), and liquid and vapor flow rates in kmol/hr (liquid and vapor flow rates are the green and red curves, respectively). The vapor and liquid molar flow rates are not constant in both the stripping and rectifying sections of the column. This justifies rigorously calculating both mass and energy balances and not assuming the usual constant molar overflow hypothesis (CMO). The distillate bubblepoint temperature is equal to 301.21 K (for the default values of the reflux ratio and reboiler heat duty), which allows the use of cold water utility in the condenser and justifies a posteriori the use of a column pressure of 16.212 bar. The condenser heat duty is determined to be equal to kJ/hr (for the default values of the reflux ratio and reboiler heat duty). The bottom and distillate rate are 268.17 kmol/hr and 31.83 kmol/hr, respectively (for the default values of the reflux ratio and reboiler heat duty).
The Mathematica builtin command used to solve the system of nonlinear algebraic equations is FindRoot. We have solved a system of 297 nonlinear algebraic equations in less than 1.8 seconds using an Intel® Core™ 2 DUO CPU T8300 at 2.4 GHz with 3 GB of memory. G. Soave, "Equilibrium Constants from a Modified RedlichKwong Equation of State," Chemical Engineering Science, 27(6), 1972 pp. 1197–1203. Z. Nasri and H. Binous, "Applications of the SoaveRedlichKwong Equation of State Using Mathematica," Journal of Chemical Engineering of Japan, 40(6), 2007 pp. 534–538. Y. S. Choe and W. L. Luyben, "Rigorous Dynamic Models of Distillation Columns," Industrial and Engineering Chemistry Research, 26(10), 1987 pp. 2158–2161. Z. Nasri and H. Binous, "Rigorous Distillation Dynamics Simulations Using a Computer Algebra," Computer Applications in Engineering Education, 20(2), 2012 pp. 193–202.
