1. Introduction
Chemical reactors are devices or vessels within which chemical processes are carried out for experimental or manufacturing purposes [1, 2]. The preparation of many industrially important chemicals by reversible reactions, for example, the production of hydrogen by steam reforming, is limited by reaction rates that are relatively low under conditions of favorable equilibrium [3, 4]. A number of measures have been devised for the purpose of creating more favorable equilibrium conditions, in order to increase reaction rates and hence productivity for a particular reaction [5, 6]. In the case of the production of hydrogen by steam reforming, for example, the disadvantage of the relatively low equilibrium constant at normal pressures, for the temperatures at which the reaction takes place, may be overcome by the use of increased pressure to the steam-hydrogen equilibrium, resulting in increased productivity of hydrogen [7, 8]. The presence of a catalyst in other cases, for example, in the production of sulfur trioxide from sulfur dioxide and oxygen, permits the use of a lower, more advantageous temperature by shortening the time needed to establish equilibrium consequently resulting in shorter reaction times and increased productivity.
For every equilibrium reaction in which the reverse reaction is favored by high temperatures, there is some intermediate temperature at which the forward production rate and equilibrium reconversion can be balanced to give an optimum design for the forward reaction in an isothermal reactor system [9, 10]. If temperature is controlled to vary with time, an optimum heat-up and cool-down cycle for this system exists [11, 12]. For such a cycle, heat is supplied or removed uniformly to or from the reactor contents, so that the temperature change of the reactor contents is progressively isothermal, or in other words, is substantially uniform throughout the reactor at a given time [13, 14]. This is conventionally accomplished by heating the reactor and contents uniformly, or by heating the reactor and stirring the contents thereof [15, 16]. The temperature differential or gradient consequently imposed, is in respect of time only, referred to as a time-temperature gradient. The optimum time-temperature relation for a slug of gas in a well-designed sulfur dioxide converter, for example, calls for an increase in temperature in the early stage, to maximize the reaction rate, followed by a decrease in temperature in the final stage, to take advantage of more favorable equilibrium conversions at the lower temperatures [17, 18]. When pressure has an influence on the ratio of the fugacity coefficients for the components of an equilibrium reaction, or when there is a change in the total number of moles of products as compared with the total number of moles of reactants; it can be expected that the production capacity of a reactor unit will vary with the pressure [19, 20]. The usual way of coping with the situation is to predetermine and fix the pressure of such a reaction at a practical and advantageous level and carry out the reaction according to the optimum time-temperature cycle, which can be determined by standard techniques.
The production capacities of such systems can be increases considerably and in some cases by as much as 100 percent over those capacities obtained by using the optimum time-temperature cycle, by heating the reactor and contents to reaction temperatures and above, non-uniformly, so that two or more zones of unequal temperatures are created throughout the reactor [21, 22]. The temperature differential or gradient consequently imposed is in respect of position in the reactor, as well as time, referred to as a time-position-temperature gradient. The cooler portion or portions of the reactor prevent dissociation of the product and excessive pressure build-up, while permitting a higher reaction rate in the warmer portion or portions of the reactor than would otherwise be obtainable [23, 24]. Moreover, the increased density of the gaseous components within the cooler portion or zones of the reactor permits larger charges of reactants to be made and stored within the reactor, without the accompanying disadvantage of over-pressurization [25, 26]. The over-all result is an increase in productivity of the reactor, or in other words, more pounds per hour of sought-for product [27, 28]. It is accordingly necessary to provide a means for increasing productivity of chemical reactors in equilibrium reactions wherein the forward reaction is favored by conditions of high pressure. It is further necessary to provide a means for increasing the productivity of a chemical reactor in equilibrium reactions wherein the total number of moles of product components is less than the total number of moles of reactant components. It is also necessary to provide a means for increasing the productivity of a high-pressure chemical reactor in equilibrium reactions wherein the compressibility of the products is greater than the compressibility of the reactants. It is very necessary to provide a means for increasing the productivity of a chemical reactor used for producing hydrogen by steam reforming.
The present study is focused primarily upon the heat management of thermally coupled reactors for conducting simultaneous endothermic and exothermic reactions. Computational fluid dynamics simulations are carried out to better understand how to manage thermally coupled reactors for conducting simultaneous endothermic and exothermic reactions. Thermally coupled reactors are used for conducting simultaneous endothermic and exothermic chemical reactions. The endothermic reaction may be conducted in the one or more process layers and may comprise a steam reforming reaction. The exothermic reaction may be conducted in the one or more heat exchange layers and may comprise a combustion reaction or a partial oxidation reaction. Exothermic heat may transfer from the one or more heat exchange layers to the one or more process layers. When more than one process layer and more than one heat exchange layer are used, they may be aligned in alternating sequence, or two or more process layers and two or more heat exchange layers may be positioned adjacent to each other. The present study aims to provide a fundamental understanding of the mechanisms of how to manage thermally coupled reactors for conducting simultaneous endothermic and exothermic reactions. Particular emphasis is placed upon the mechanisms involved in the heat transfer processes in thermally coupled reactors for hydrogen production by steam reforming.