Mass balances reaction process problem

The chemical engineer almost never has kinetics for the process she or he is working on. The problem of solving the batch or continuous reactor mass-balance equations with known kinetics is much simpler than the problems encountered in practice. We seldom know reaction rates in useful situations, and even if these data were available, they frequently would not be particularly useful. 

Figure 2 Reaction process mass balance problem...

The volatile (at reaction temperature) products can be grouped into liquids and gases, depending upon the state they are at ambient conditions. However, for practical reasons in all our experimental studies we used an ice bath T = 273 K) to collect the liquid products. This way we avoided possible condensation problems of the collected gases as well as variations due to seasonal room temperature fluctuations. A diagrammatic overview of the process mass balance is shown in Figure 7.6. 

You can gain some experience by making mass balances on one unit for a simple problem comprised of just three components, as illustrated in Fig. 2.5. In Secs. 2.5 and 2.6 we will take up material balance problems involving more than one system. In Fig. 2.5 the system is the box, and we assume that the process is in the steady state without reaction, so that Eq. (2.3) applies. An independent mass balance equation based on Eq. (2.3) can be written for each compound involved in the process defined by the system boundary. We will use the symbol (o with an appropriate subscript to denote the mass fraction of a component in the streams F, W, and P, respectively. Each mass balance will have the form... 

Examine Fig. E2.4. No reaction takes place, and the process is in the steady state. Values of two streams, W and F, are not known if 1 hr is taken as a basis, nor is the concentration of the benzene in F, (If you know the concentration of benzene in F, you know all the concentrations in the aqueous feed.) Three components exist in the problem, hence three mass balances can be written down (the units are kg) ... 

A special case of information structure occurs in some problems that leads to a particularly simple material balance, one that involves only two variables. For example, refer to Fig. 2.12. You note that no reaction takes place and the process presumably is in the steady state. Two components are present, hence you can write two independent mass balances ... 

The process is fed with three streams ethane, ethylene, and chlorine. The ethane and ethylene streams have the same molar flow rate, and the ratio of chlorine to ethane plus ethylene is 1.5. The ethane/ethylene stream also contains 1.5 percent acetylene and carbon dioxide. (For this problem, just use 1.5 percent carbon dioxide.) The feed streams are mixed with an ethylene recycle stream and go to the first reactor (chlorination reactor) where the ethane reacts with chlorine with a 95 percent conversion per pass. The product stream is cooled and ethyl chloride is condensed and separated. Assume that all the ethane and ethyl chloride go out in the condensate stream. The gases go to another reactor (hydrochlorination reactor) where the reaction with ethylene takes place with a 50 percent conversion per pass. The product stream is cooled to condense the ethyl chloride, and the gases (predominately ethylene and chlorine) are recycled. A purge or bleed stream takes off a fraction of the recycle stream (use 1 percent). Complete the mass balance for this process. 

In order to realize the Polyamide-6 scenario problem presented in Subsect. 5.3.2, a process description is defined using ModKit+. The elementary models for the reaction section, the separator, and the extruder, already imported into ROME, are added as submodels of the overall process. Further, a mixer is defined in order to combine feed and recycle streams corresponding mass balances are added to the elementary mixer model. After this modeling activity the model repository ROME contains all necessary models for the overall Polyamide-6 process. The model behavior is partly described by equations (for the mixer) and partly described by model implementations in the form of input files for the modeling tools Aspen Plus, gPROMS, and MOREX. 

Some of the first considerations of the problem of diffusion and reaction in porous catalysts were reported independently by Thiele [E.W. Thiele, Ind. Eng. Chem., 31, 916 (1939)] Damkohler [G. Damkohler, Der Chemie-Ingenieur, 3, 430 (1937)] and Zeldovich [Ya.B. Zeldovich, Acta Phys.-Chim. USSR, 10, 583 (1939)] although the first solution to the mathematical problem was given by Jiittner in 1909 [F. Jiittner, Z. Phys. Chem., 65, 595 (1909)]. Consider the porous catalyst in the form of a flat slab of semi-infinite dimension on the surface, and of half-thickness W as shown in Figure 7.3. The first-order, irreversible reaction A B is catalyzed within the porous matrix with an intrinsic rate (—r). We assume that the mass-transport process is in one direction though the porous structure and may be represented by a normal diffusion-type expression, that there is no net eonveetive transport eontribution, and that the medium is isotropic. For this case, a steady-state mass balance over the differential volume element dz (for unit surface area) (Figure 7.3), yields... 

The solution to this problem requires an analysis of multiple gas-phase reactions in a differential plug-flow tubular reactor. Two different solution strategies are described here. In both cases, it is important to write mass balances in terms of molar flow rates and reactor volume. Molar densities and residence time are not appropriate for the convective mass-transfer-rate process because one cannot assume that the total volumetric flow rate is constant in the gas phase, particularly when the total number of moles is not conserved. In each reaction, 2 mol of reactants generates 1 mol of product. Furthermore, an overall mass balance suggests that the volumetric flow rate is constant only when the overall mass density does not change. This is a reasonable assumption for liquid-phase reactors but not for gas-phase problems when the total volume is not restricted. The exception is a constant-volume batch reactor. 

The following discussion represents a detailed description of the mass balance for any species in a reactive mixture. In general, there are four mass transfer rate processes that must be considered accumulation, convection, diffusion, and sources or sinks due to chemical reactions. The units of each term in the integral form of the mass transfer equation are moles of component i per time. In differential form, the units of each term are moles of component i per volnme per time. This is achieved when the mass balance is divided by the finite control volume, which shrinks to a point within the region of interest in the limit when aU dimensions of the control volume become infinitesimally small. In this development, the size of the control volume V (t) is time dependent because, at each point on the surface of this volume element, the control volnme moves with velocity surface, which could be different from the local fluid velocity of component i, V,. Since there are several choices for this control volume within the region of interest, it is appropriate to consider an arbitrary volume element with the characteristics described above. For specific problems, it is advantageous to use a control volume that matches the symmetry of the macroscopic boundaries. This is illustrated in subsequent chapters for catalysts with rectangular, cylindrical, and spherical symmetry. 

The presence of two scales enables modeling the mass transfer processes both in the extent of their completion and in time. When the data of mass transfer velocities are absent, used is only the degree of the processes completion. In this case in the USA within the framework of reviewed models are distinguished direct problems, i.e., reaction path models, and inverse problems, i.e., mass balance models. 

Boundary conditions are part of the mathematical description of a process. For the energy balance, the condition at the vessel wall is that the rate of heat transfer by conduction equals the rate of transfer to the heat transfer medium. Similarly the rate of mass transfer at the wall equals the rate of reaction on the wall if that is catalytic, or equals zero when the wall is inert and impermeable. Clearly, the temperature, composition and pressure of the inlet to the reactor are part of the problem specification. 

In practice, of course, it is rare that the catalytic reactor employed for a particular process operates isothermally. More often than not, heat is generated by exothermic reactions (or absorbed by endothermic reactions) within the reactor. Consequently, it is necessary to consider what effect non-isothermal conditions have on catalytic selectivity. The influence which the simultaneous transfer of heat and mass has on the selectivity of catalytic reactions can be assessed from a mathematical model in which diffusion and chemical reactions of each component within the porous catalyst are represented by differential equations and in which heat released or absorbed by reaction is described by a heat balance equation. The boundary conditions ascribed to the problem depend on whether interparticle heat and mass transfer are considered important. To illustrate how the model is constructed, the case of two concurrent first-order reactions is considered. As pointed out in the last section, if conditions were isothermal, selectivity would not be affected by any change in diffusivity within the catalyst pellet. However, non-isothermal conditions do affect selectivity even when both competing reactions are of the same kinetic order. The conservation equations for each component are described by... 

Mathematical modeling is the science or art of transforming any macro-scale or microscale problem to mathematical equations. Mathematical modeling of chemical and biological systems and processes is based on chemistry, biochemistry, microbiology, mass diffusion, heat transfer, chemical, biochemical and biomedical catalytic or biocatalytic reactions, as well as noncatalytic reactions, material and energy balances, etc. 

There are many instances in which solutions of known molarity are used in chemical reactions in the laboratory. Instead of starting with a known mass of reactants or with a desired mass of product, the process involves a solution of known molarity. The substances are measured out by volume, instead of being weighed on a balance. An example of such an application in stoichiometry is shown in Sample Problem C. 

The problems solved in Chapters 5 and 6 are simple problems with many numerical parameters specified. You may have wondered where those numbers came from. In a real case, of course, you will have to make design choices and discover their impact. In chemical engineering, as in real life, these choices have consequences. Thus, you must make mass and energy balances that take into account the thermodynamics of chemical reaction equilibria and vapor-liquid equilibria as well as heat transfer, mass transfer, and fluid flow. To do this properly requires lots of data, and the process simulators provide excellent databases. Chapters 2-4 discussed some of the ways in which thermodynamic properties are calculated. This chapter uses Aspen Plus exclusively. You will have to make choices of thermodynamic models and operating parameters, but this will help you learn the field of chemical engineering. When you complete this chapter, you may not be a certified expert in using Aspen Plus , but you will be capable of actually simulating a process that could make money. 

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