Modelling of chemical processes is today the foundation to almost any operation including design, control, planning, retrofitting. As varied as the use of models is its structure: models are built for a particular purpose, to meet the requirement of the application. Though there is obviously a need for dynamic models, at least in chemical engineering the most common models are steady-state models mainly used in designing and retrofitting, but also in some control and planning applications. With distillation being the most common separation unit, its models have been subject of studies for decades. The computation of steady-state distillation models is a notorious problem as it consists of a large number of equations which proliferates mainly with the number of components and number of trays. Solving such a model implies to solve this large-scale algebraic problem for a single set of roots representing the equilibrium state of the distillation. The numerical methods being used for this purpose have usually a very small convergence radius, which gave rise to a lot of research (Komatsu and Holland 1977, Holland 1981, Taylor et al. 1996, Rabeau et al. 1997, Grossmann et al. 2005). Thus whilst computing has improved tremendously, little progress has been made in solving the initialization problem. The authors' idea for approaching the initialisation problem is to use a dynamic description (Rademaker et al. 1975, Skogestad 1992) that mimics the behaviour of a distillation column close enough so as to simulate a dynamic path starting with a very simple generic initial state and integrating up to the desired operating condition. Thereafter one may switch to a steady state description of the plant and continue the computations, if so required. Earlier studies have shown that bringing two isolated phases into contact will converge monotonically to the steady-state under the condition that the heat transfer is significantly faster than the diffusional mass transfer through the phase boundary (Asbjørnsen 1973, Preisig 2004). This is taken as a starting point to suggest a sequence of physical operations which will guide the dynamic model to converge to the desired steady-state condition. Thus by switching from a steady-state simulation to a dynamic simulation one substitutes the complex initialisation problem by a simple one plus an integration over a feasible physical path. Mathematically this implies that one solves a set of Differential Algebraic Equations (DAE) instead of a large set of algebraic equations. With DAE solvers having advanced tremendously over the past decades, using a dynamic model may even be competitive to using a steady state model. The model is constructed from simple components: each tray, boiler and condenser are considered as a dynamic flash whereby each flash is contained in a fixed volume, tray volume, boiler volume and condenser volume respectively. Staking up such two-phase containments, the column becomes a tower of dynamic flash "rums". The transfer rates for mass and heat were chosen empirically so as to satisfy above-mentioned conditions. The internal streams are driven by the heat source and sink in the boiler and the condenser, respectively. The procedure representing a feasible physical path leading to the desired steady state starts with a set of isolated containments forming pairs of gas and liquid both in isolation. Those are first brought in contact with each other, pair by pair thereby fixing the respective joint volume to represent the volume of the boiler, each stage and condenser, respectively. The individual phases are initialised within the domain of operation. Since a priori the two phases are not in equilibrium, they can exchange energy (in the form of heat and volumetric work) and mass both being diffusional processes through the common phase boundary. The conductive heat stream, driven by the different temperatures of liquid and gas phase, is significantly faster than the mass diffusion, which makes the temperatures in the two phases to converge quickly. The mass exchange driven by the chemical potentials, accordingly to fundamental transfer laws, is slower. The mass stream induces also convective energy transfer as mass carries internal energy. The heat transfer in the liquid phase is assumed to be very fast (event dynamics). This makes the temperature on the boundary identical to the liquid bulk temperature. The energy associated with the phase change is thus solely associated with the liquid phase. This simplifies also the computations as otherwise one has to compute the conditions on each phase boundary, which involves solving for roots of a set of algebraic equations (dimension: number of components + 1 for each boundary). The first step is completed when the two phases in each part of the column have reached an equilibrium. Then it is time for the second step: adjusting the liquid levels. If the liquid level is too little, meaning the fluid does not reach up to the weir height on each stage, liquid is added on the top with the overflows modelled with the weir equation. In case there is too much fluid, one may have to drain some out of the boiler so as to adjust the overall hold-up. With the next step energy is drawn in form of heat from the liquid phase of the condenser driven by the difference between the temperature of the liquid phase and the temperature of a cold reservoir. This procedure excludes anything like drop or film formation. Up to this point the gas phases are not connected. Only at this point this communication of mass driven by the pressure difference is enabled. The transfer model consists of two parts, namely a resistance in the construction, the dry tray resistance, and the hydraulic pressure drop on the tray. Finally heat is supplied to the liquid phase of the boiler driven by the difference in temperature between a warm reservoir and the liquid phase excluding any bubble formation. The complete model consists for each stage of number of components mass balances for the gas phase and the liquid phase, and an energy balance for each liquid and gas phase. The approach was found to be extremely robust. Different initial conditions were tested. Some conditions lead initially to an inverted pressure profile, that is, the pressure on the top was higher than the pressure in the boiler. Adjusting the liquid levels on the trays did not have a large effect on the pressure distribution. The pressure though changed drastically as cooling and heating was enabled. In all cases, the column converted to the correct pressure profile thereby going through a complicated inversion process for the pressure as well as the temperatures converging monotonically towards the final profile during the last phase.

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