Chemical reactors reaction invariants

K.V. Waller and P.M. Makila, Chemical reaction invariants and variants and their use in in reactor modeling, simulation and control,... 

Nitric acid is one of the three major acids of the modem chemical industiy and has been known as a corrosive solvent for metals since alchemical times in the thirteenth centuiy. " " It is now invariably made by the catalytic oxidation of ammonia under conditions which promote the formation of NO rather than the thermodynamically more favoured products N2 or N2O (p. 423). The NO is then further oxidized to NO2 and the gases absorbed in water to yield a concentrated aqueous solution of the acid. The vast scale of production requires the optimization of all the reaction conditions and present-day operations are based on the intricate interaction of fundamental thermodynamics, modem catalyst technology, advanced reactor design, and chemical engineering aspects of process control (see Panel). Production in the USA alone now exceeds 7 million tonnes annually, of which the greater part is used to produce nitrates for fertilizers, explosives and other purposes (see Panel). 

The reaction stage is the heart of a chemical manufacturing process. In the reactor the raw materials are brought together under conditions that promote the production of the desired product invariably, by-products and unwanted compounds (impurities) will also be formed. 

Independent composition specifications depend on the relationships among individual species and the chemical reactions taking place in the reactor, but they are invariant of the specific set of independent reactions selected. Since the set of independent reactions generated by the reduced matrix of the Gaussian elimination... 

Equation 4.3.8 is the reaction-based, differential design equation of an ideal batch reactor, written for the mth-independent reaction. As will be discussed below, to describe the operation of a reactor with multiple chemical reactions, we have to write Eq. 4.3.8 for each of the independent reactions. Note that the reaction-based design equation is invariant of the specific species used in the derivation. For an ideal batch reactor with a single chemical reaction, Eq. 4.3.8 reduces to... 

These are systems where the state variables describing the system are lumped in space (invariant in all space dimensions). The simplest chemical reaction engineering example is thp perfectly mixed continuous stirred tank reactor. These systems are described at steady state by algebraic equations while in the unsteady state they are described by initial value ordinary differential equations where time is the independent variable. 

These are systems where the state variables are varying in one or more directions of the space coordinates. The simplest chemical reaction engineering example is the plug flow reactor. These systems are described at steady state either by an ordinary differential equation (where the variation of the state variables is only in one direction of the space coordinates, i.e. one dimensional models, and the independent variable is this space direction), or partial differential equations (when the variation of the state variables is in more than one direction of the space coordinates, i.e. two dimensional models, and the independent variables are these space directions). The ordinary differential equations of the steady state of the one-dimensional distributed model can be either initial value differential equations (e.g. plug flow models) or two-point boundary value differential equations (e.g. models with superimposed axial dispersion). The equations describing the unsteady state of distributed models are invariably partial difierential equations. 

The problems of simultaneously treating spatial distributions of both temperature and concentration are currently the concern of the chemical engineer in his treatment of catalyst particles, catalyst beds, and tubular reactors. These treatments are still concerned with systems that are kineticaliy simple. The need for a unified theory of ignition has been highlighted by contemporary studies of gas-phase oxidations, many features being revealed that neither thermal theory, nor branched-chain theory for that matter, can resolve alone. A successful theoretical basis for such reactions necessarily involves the treatment of both the enorgy balance and mass balance equations. Such equations are invariably coupled and cannot be solved independently of each other. However, much information is offered by the phase-plane analj s of the syst (e.g. stability of equilibrium solutions, existence of oscillations) without the need for a formal solution of the balance equations. 

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