Continuous steady-state flow process

A special case of the above equation applies to a continuous steady-state flow process when all of the rate terms are independent of time and the accumulation term is zero. Thus, the differential material balance for any component i in such a process is given by... 

The word refrigeration implies the maintenance of a temperature below that of the surroundings. This requires continuous absorption of heat at a low temperature level, usually accomplished by evaporation of a liquid in a steady-state flow process. The vapor formed may be returned to its original liquid state for reevaporation in either of two ways. Most commonly, it is simply compressed and then condensed. Alternatively, it may be absorbed by a liquid of low volatility, from which it is subsequently evaporated at higher pressure. Before treating these practical refrigeration cycles, we consider the Carnot refrigerator, which provides a standard of comparison. 

The esterification by-product, water, is removed via a process column in a continuous steady-state mode of operation. The bottom product of the column, being mainly EG, flows back into the esterification reactor. The condensed top product consists mainly of water with small traces of EG. In cases where a reverse-osmosis unit is connected to the distillate flow line, the residual EG can be separated very efficiently from the water [124], The combination of a process column with reverse osmosis saves energy cost and capital investment. The total organic carbon (TOC) value of the permeate is sufficiently low to allow its discharge into a river or the sea without any environmental impact. 

Stationary state flow processes resemble equilibria in their invariance with time partial time differentials of density, concentration, or temperature will vanish, although flows continue to occur in the system, and entropy is being produced. If the property is conserved, the divergence of the corresponding flow must vanish, and hence the steady flow of a conserved quantity is constant and source-free. At equilibrium, all the steady-state flows become zero. 

In the continuous processing, a steady-state flow of luminous gas is established and maintained for the duration of operation, e.g., 1 month, without interruption. Due to the factors described above, it takes some time, e.g., 30 min, to establish a steady-state flow of luminous gas. Once a steady state is established, it can be maintained it for sufficient time to allow continuous processing. Substrates are fed into the steady-state flow of luminous gas in a cross-flow pattern. The rate of transport of substrate and the length of the path in the luminous gas phase determine the treatment time. 

This equation is identical to Equation 4.2-2 for continuous steady-state processes, except that in this case the input and output terms denote the initial and final amounts of the balanced substance rather than flow rates of the balanced substance in continuous feed and product streams. The words initial and final may be left out for brevity, as long as you don t lose sight of what input and output mean in the context of batch processes. 

A labeled flowchart of a continuous steady-state two-unit process is shown below. Each stream contains two components. A and B, in different proportions. Three streams whose flow rates and/or compositions are not known are labeled 1,2. and 3. 

For a differential balance on a continuous process (material flows in and out throughout the process) at steady-state (no process variables change with time), the accumulation term in the balance (the rate of buildup or depletion of the balanced species) equals zero. For an integral balance on a batch process (no material flows in or out during the process), the input and output terms equal zero and accumulation = initial input — final output. In both cases, the balance simplifies to... 

This qualitative explanation for the oscillatory behavior of the particle number density is supported by theory. Assume the system can be modeled as a continuous steady state stirred tank reactor (CSTR) that is, reactants enter and products leave from a perfectly mixed tank with composition equal to that of the products. The set of equations derived in the previous section applies, but a new term must be subtracted from the right-hand side in each case to account for the loss of particles from the CSTR by the flow process. Equation (10.49) for the change in aerosol surface area with time becomes... 

The ideal continuous plug flow reactor (CPFR) has no profile at any point of the tube in the steady state. The process, however, advances along the tube, and so shows a longitudinal concentration variation. The profile of a CPFR in space is identical to the profile of a DCSTR in time in case of a constant volume process this fact is of great importance for process design ( kinetic similarity ). 

For continuous (steady state) processes in flow reactors, molar fluxes and volumetric flow rates are used to calculate concentrations and molar fractions, and... 

In a batch process, a given quantity of reacttuits is plaeed in a container, and by ehemieal and/or physieal means, a eliange is made to oecur. At the end of die process, die container holds die product or products. In a continuous process, reactants are fed in an unending flow to a piece of equipment or to several pieces in series, and products are continuously removed from one or more points. A continuous process may or may not be steady state. 

In the major catalytic processes of the petroleum and chemical industries, continuous and steady state conditions are the rule where the temperature, pressure, composition, and flow rate of the feed streams do not vary significantly. Transient operations occur during the start-up of a unit, usually occupying a small fraction of the time of a cycle from start-up to shut-down for maintenance or catalyst regeneration. 

A capillary system is said to be in a steady-state equilibrium position when the capillary forces are equal to the hydrostatic pressure force (Levich 1962). The heating of the capillary walls leads to a disturbance of the equilibrium and to a displacement of the meniscus, causing the liquid-vapor interface location to change as compared to an unheated wall. This process causes pressure differences due to capillarity and the hydrostatic pressures exiting the flow, which in turn causes the meniscus to return to the initial position. In order to realize the above-mentioned process in a continuous manner it is necessary to carry out continual heat transfer from the capillary walls to the liquid. In this case the position of the interface surface is invariable and the fluid flow is stationary. From the thermodynamical point of view the process in a heated capillary is similar to a process in a heat engine, which transforms heat into mechanical energy. 

There is an interior optimum. For this particular numerical example, it occurs when 40% of the reactor volume is in the initial CSTR and 60% is in the downstream PFR. The model reaction is chemically unrealistic but illustrates behavior that can arise with real reactions. An excellent process for the bulk polymerization of styrene consists of a CSTR followed by a tubular post-reactor. The model reaction also demonstrates a phenomenon known as washout which is important in continuous cell culture. If kt is too small, a steady-state reaction cannot be sustained even with initial spiking of component B. A continuous fermentation process will have a maximum flow rate beyond which the initial inoculum of cells will be washed out of the system. At lower flow rates, the cells reproduce fast enough to achieve and hold a steady state. 

Table 11.4 lists reactors used for systems with two fluid phases. The gas-liquid case is typical, but most of these reactors can be used for liquid-liquid systems as well. Stirred tanks and packed columns are also used for three-phase systems where the third phase is a catal5hic solid. The equipment listed in Table 11.4 is also used for separation processes, but our interest is on reactions and on steady-state, continuous flow. 

The flow reactor is typically the one used in large-scale industrial processes. Reactants are continuously fed into the reactor at a constant rate, and products appear at the outlet, also at a constant rate. Such reactors are said to operate under steady state conditions, implying that both the rates of reaction and concentrations become independent of time (unless the rate of reaction oscillates around its steady state value). 

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