Chemical tower equipment: 【Question of the Day】2011.03.11
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This post was last edited by Benben Xuan on 2011-3-12 09:15. Design calculation method: What is the plate-by-plate calculation method for distillation columns? Why should the general board-by-board calculation method be carried out by a computer? Answer: Calculating board by board means, based on the definition of the theoretical model, performing mass balance, phase balance, and heat balance calculations for each board under given conditions. Since both the phase equilibrium constants and enthalpies are functions of pressure, temperature, and the composition of the gas and liquid phases, their calculation is very complex and beyond the capabilities of manual computation. Moreover, to satisfy the three equilibrium relationships in the entire column, repeated iterations are required; therefore, computational methods are generally needed for the calculation plate by plate
The plate-by-plate calculation method employs the trial-and-error approach to sequentially solve the equations of phase equilibrium, material balance, and heat balance. This method had its mathematical model first derived by Lewis and Mathes in 1933; after the advent of computers in the 1950s, a plate-by-plate solution approach was developed, which is suitable for cases requiring clear segmentation. It is difficult to estimate the composition of unclear and non-key components at the tower top and in the reactor, which results in large errors in each round of calculations and makes convergence difficult. Before computers were widely used, it was the main method for calculating complex multi-stage equilibrium processes, but it was highly affected by truncation error propagation and gave poor results regarding the stability of complex columns. It is rarely used in computing nowadays, but it is still employed in absorption applications.
The plate-by-plate calculation method employs the trial-and-error approach to sequentially solve the equations of phase equilibrium, material balance, and heat balance. The mathematical model of this method was first derived by Lewis-Mathes in 1933; it involves extensive computational requirements. After the advent of computers in the 1950s, a method of solving it board by board was developed, and such methods are suitable for cases requiring clear segmentation.
Plate-by-plate calculation method: By using the operating line equation and the equilibrium line equation, the composition of each plate is calculated sequentially, thereby determining the theoretical number of theoretical plates required to meet the separation requirements.
Based on the given conditions, the phase equilibrium equations and operating line equations for each theoretical tray are written, and the coordinates of the intersection point of the two operating lines are determined. By alternately using the phase equilibrium equations and operating line equations, the method for determining the compositions of the gas and liquid phases in each tray is called the tray-by-tray calculation method. The plate-by-plate calculation method is relatively cumbersome, but it yields accurate results and allows for the determination of the gas-liquid phase compositions on each plate; when the number of plates is large, a computer is used for the calculations.
The plate-by-plate calculation method involves using the gas-liquid phase equilibrium relationships of the materials together with the operating line equations to derive the equations for the stripping section and the distillation section. Then, based on these distillation equations, starting from the liquid phase composition of the overhead distillate, the liquid phase composition of each tray in the distillation section is calculated step by step. Meanwhile, X + 1 is compared with X (as determined by combining the equilibrium equation and the operating line equation) to determine the location of the feed tray； Once the position of the feed plate is determined, the iterative equations for the stripping section are used to calculate the liquid phase composition of each tray in that section, until X becomes smaller than a certain value; this value represents the number of theoretical trays required for this separation process. The board-by-board calculation method is labor-intensive, but it can be completed simply using electrical algorithms by designing a calculation model.
The plate-by-plate calculation method employs the trial-and-error approach to sequentially solve the equations of phase equilibrium, material balance, and heat balance. This method had its mathematical model first derived by Lewis and Mathes in 1933; after the advent of computers in the 1950s, a plate-by-plate solution approach was developed, which is suitable for cases requiring clear segmentation. It is difficult to estimate the composition of unclear and non-key components at the tower top and in the reactor, which results in large errors in each round of calculations and makes convergence difficult. Before computers were widely used, it was the main method for calculating complex multi-stage equilibrium processes, but it was highly affected by truncation error propagation and gave poor results regarding the stability of complex columns. It is rarely used in computing nowadays, but it is still employed in absorption applications.
The plate-by-plate calculation method involves using the gas-liquid phase equilibrium relationships of the material along with the operating line equations to derive the equations for the stripping section and the distillation section. Then, utilizing these distillation equations, starting from the liquid phase composition of the overhead distillate, the liquid phase composition of each tray in the distillation section is calculated step by step. Meanwhile, X + 1 is compared with X (as determined by combining the equilibrium equation and the operating line equation) in order to determine the location of the feed tray； Once the position of the feed plate is determined, the iterative equations for the stripping section are used to calculate the liquid phase composition of each tray in that section, until X becomes smaller than a certain value; this value represents the number of theoretical trays required for this separation process
This post was last edited by Guanghai on 2011-3-11 09:31. During distillation in a distillation column, the gas phase above a given tray has the same composition as the liquid phase on the adjacent tray below it; there is gas-liquid equilibrium at each tray. Based on this principle, the gas-liquid composition of each tray is calculated starting from the bottom of the tower, until the tray with the desired composition of the product stream is obtained. Due to the complexity of the calculations, for columns that require hundreds of trays, the computation is extensive, prone to errors, and time-consuming; computer-aided calculation is accurate, fast, simple, and easy to carry out. PS: I forgot to hide it; please edit to hide it. Sorry, LZ.
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