Chemical reactors equilibrium model

Modelling plasma chemical systems is a complex task, because these system are far from thennodynamical equilibrium. A complete model includes the external electric circuit, the various physical volume and surface reactions, the space charges and the internal electric fields, the electron kinetics, the homogeneous chemical reactions in the plasma volume as well as the heterogeneous reactions at the walls or electrodes. These reactions are initiated primarily by the electrons. In most cases, plasma chemical reactors work with a flowing gas so that the flow conditions, laminar or turbulent, must be taken into account. As discussed before, the electron gas is not in thennodynamic equilibrium... 

At the first level of detail, it is not necessary to know the internal parameters for all the units, since what is desired is just the overall performance. For example, in a heat exchanger design, it suffices to know the heat duty, the total area, and the temperatures of the output streams the details such as the percentage baffle cut, tube layout, or baffle spacing can be specified later when the details of the proposed plant are better defined. It is important to realize the level of detail modeled by a commercial computer program. For example, a chemical reactor could be modeled as an equilibrium reactor, in which the input stream is brought to a new temperature and pressure and the... 

In many reacting flows, the reactants are introduced into the reactor with an integral scale L that is significantly different from the turbulence integral scale Lu. For example, in a CSTR, Lu is determined primarily by the actions of the impeller. However, is fixed by the feed tube diameter and feed flow rate. Thus, near the feed point the scalar energy spectrum will not be in equilibrium with the velocity spectrum. A relaxation period of duration on the order of xu is required before equilibrium is attained. In a reacting flow, because the relaxation period is relatively long, most of the fast chemical reactions can occur before the equilibrium model, (4.93), is applicable. 

If the behaviour of complex chemical (in our case catalytic) reactions is known, it will be clear in what way these reactions can be carried out under optimal conditions. The results of studying kinetic models must be used as a basis for the mathematical modelling of chemical reactors to perform processes with probable non trivial kinetic behaviour. It is real systems that can appear to show such behaviour first far from equilibrium, second nonlinear, and third multi dimensional. One can hardly believe that their associated difficulties will be overcome completely, but it is necessary to approach an effective theory accounting for several important problems and first of all provide fundamentals to interpret the dependence between the type of observed kinetic relationships and the mechanism structure. 

A chemical plant includes tens to hundreds of process units, such as chemical reactors, heat exchangers, distillation columns, absorption towers, etc. For each unit, material and energy balances are used to relate input and output streams. Rate equations and equilibrium relations help describe the conversion of species, mass, and energy in the units. Collectively, these equations provide the equality constraints for the plant model. 

Measurement of the enthalpies and entropies of adsorption and their variation as the pore space is filled is important to establish chemical models of the interactions and to enable chemical engineers to model and optimise catalytic reactors and large-scale separations. For physisorption of gases and vapours, the most widely available approach is to measure the equilibrium uptake as a function of adsorbate pressure and at a series of constant temperatures, giving a series of isotherms. This then permits the dependence of the equilibrium pressure with temperature to be derived for any value of the uptake, or fractional coverage, 0. The differential heat of adsorption (the heat at a particular coverage, 0 ) can then be calculated using the linearised form of the Clausius lapeyron equation ... 

For instructions on the use of the equilibrium constant and Gibbs reactor models in the process simulators, see the CD-ROM that accompanies this book ASPEN Chemkd Reactors Equilibrium Reactors REQUIL or RGIBBS and HYSYS —> Chemical Reactors... 

Nelson (24) studied theoretically the general case of countercurrent equilibrium stage separation with chemical reaction and applied his technique to describe distillation reactors. His model relied on the assumption of each stage being a perfectly mixed reactor and also an equilibrium stage. 

Quasi-kinetic models deal with processes that are controlled by mass transfer rates rather than by chemical reaction rates. These models assume nearly instantaneous attainment of equilibrium within the region of interest, so changes in the species distribution are controlled by the rate of transfer of substances into or out of that region. These models are constrained by continuity equations making them similar to the chemical reactors models in Chapter 4. 

Figure 15.2 shows the flow sheet of the FP-FC system. The fuel forthe system is an aqueous solution of methanol at the molar ratio of methanol to water of 1 2 for the standard case. The fuel is evaporated in the vaporizer (VAP) at 150°C. In the reformer, the vaporized methanol and water react at 250 °C to form a hydrogen-rich gas, which contains also some CO2 and CO. The steam reformer is modeled as a Gibbs reactor assuming chemical equilibrium between the species at the outlet of the reactor. At the reforming temperature of 250 °C, the equilibrium conversion of methanol is almost 100%. The selectivity of methanol to CO2 is about 97% and to CO about 3%. In the mixer (MIX), the hydrogen-rich gas from the reformer is mixed with a small quantity of air, which is needed for the oxidation of CO present in the product gas from the reformer. The selective CO oxidation takes place in the COS reactor at 150 °C. The COS reactor is modeled as a stoichiometric reactor where 50% of the supplied O2 from the air is used for complete oxidation of CO and the remaining 50% of O2 reacts with H2. 

For proper design and simulation of HDT reactors, kinetic and reactor modeling are aspects that need to be deeply studied however, this is not a trivial task due to the numerous physical and chemical processes that occur simultaneously in the reactor phase equilibrium, mass transfer of reactants and products between the gas-liquid-solid phases, diffusion inside the catalyst particle, a complex reaction network, and catalyst deactivation. Ideally, the contribution of all these events must be coupled into a robust reactor performance model. The level of sophistication of the model is generally defined based upon the pursued objectives and prediction capability [4]. 

In this chapter, the dynamics of ideally stirred tank reactors will be analyzed. First, the assumptions, required to limit model complexity, will be discussed. Next, various types of reaction will be considered such as simple first-order reactions, equilibrium reactions, parallel reactions, etc. Subsequently, the analysis will be expanded to include non-isothermal reactors. Numerical examples of chemical reactors are given and the non-linear model descriptions are compared with the linearized model descriptions. 

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