Outlet streams number

We turn now to the issue of material balance closure. Material balances can be perfect when one of the flow rates and one of the components is unmeasured. The keen experimenter for Examples 7.1 and 7.2 measured the outlet concentration of both reactive components and consequently obtained a less-than-perfect balance. Should the measured concentrations be adjusted to achieve closure and, if so, how should the adjustment be done The general rule is that a material balance should be closed if it is reasonably possible to do so. It is necessary to know the number of inlet and outlet flow streams and the various components in these streams. The present example has one inlet stream, one outlet stream, and three components. The components are A, B, and I, where I represents all inerts. 

Gm is the molar flowrate of gas, W is the mass of solids in the bed, F is the number of moles of vapour adsorbed on unit mass of solid, and y0, y is the mole fraction of vapour in the inlet and outlet stream respectively. 

Pibouleau et al. (1988) provided a more flexible representation for the synthesis problem by replacing the single reactor unit by a cascade of CSTRs. They also introduced parameters for defining the recovery rates of intermediate components into the distillate, the split fractions of top and bottom components that are recycled toward the reactor sequence, as well as parameters for the split fractions of the reactor outlet streams. A benzene chlorination process was studied as an example problem for this synthesis approach. In this example, the number of CSTRs in the cascade was treated as a parameter that ranged from one up to a maximum of four reactors. By repeatedly solving the synthesis problem, an optimum number of CSTRs was determined. 

The number of all groups minus the recycle streams gives the number of the outlet streams. Azeotropes or solid components may change the rule. 

The reactor-outlet stream contains a dispersion of hydrocarbons in sulfuric acid. The first separation step is therefore a liquid-liquid split The sulfuric-acid phase contains some amounts of sec-butyl acid sulfate, which decomposes at higher temperature (15 °C) to produce conjuct polymers dissolved in the acid and a mixture of C4-C1( isoparaffins with low octane number (pseudoalkylate) that separates as a second liquid phase. The hydrocarbon phase contains a small amount of di-isoalkyl sulfates. These need to be removed before entering the distillation units otherwise they will decompose and release sulfuric acid. The sulfates are removed by washing with either dilute caustic or sulfuric acid. In the first case, sulfates are converted to salts that are discarded. With sulfuric acid, sulfates are converted to isoalkyl acid sulfates that can be recycled to the alkylation reactor [15, 10]. 

Figure 12.5 presents the performance of the process when the bioreactor Damkohler numbers, Dai and Da2, are varied. As expected, when the activity of either microbial population is reduced below a certain limit, the requirement of NO concentration in the gas-outlet stream can no longer be fulfilled. In order to ensure robustness with respect to uncertain rates of the bioreactions, we choose Dai = 10, Da2 = 5. From Figure 12.5 it follows that the requirements will be met even when the activity of both microbial populations is reduced to half of the design value. 

The number of unknown variables for a single unit is the sum of the unknown component amounts or flow rates for ail inlet and outlet streams, plus all unknown stream temperatures and pressures, plus the rates of energy transfer as heat and work. The equations available to determine these unknowns include material balances for each independent species, an energy balance, phase and chemical equilibrium relations, and additional specified relationships among the process variables. 

No phase changes or chemical reactions take place within the system 0 and H are independent of pressure and the mean heat capacities C and Cp of the system contents (and of the inlet and outlet streams) are independent of composition and temperature, and hence unchanging with time. Then if Tr is a reference temperature at which is defined to be zero and M is the mass (or number of moles) of the system contents,... 

The inlet and outlet stream-compositions, the number of transfer units, and the absorption or stripping factor are related by ... 

Few simulations were needed to achieve a quasi-optimal column design with 38 equilibrium stages, a column diameter of 0.9 m, a section pressure drop of 34.7 kPa and a steam flow rate of 3600 kg/h. The values obtained for the number of equilibrium stages and steam demand, together with the composition of ethanol in the outlet stream (51.52 % w/w) agree well with results presented in Kwiatkowski et al. (2006). 

Number of independent equality constraints Material balances (streams 1 and 2) Energy balance Composition of inlet and outlet streams the same Total no. d.f. 

Figure 5.18 illustrates the principle of SMB processes. The mobile phase passes the fixed bed columns in one direction. Counter-current flow of both phases is achieved by switching the columns periodically upstream in the opposite direction of the liquid flow. Of course, in a real plant the columns are not shifted but all ports are moved in the direction of the liquid flow by means of valves. The counter-current character of the process becomes more obvious when the relative movement of the packed beds to the inlet and outlet streams during several switching intervals is observed. After a number of switching or shifting intervals equal to the number of columns in the system, one so-called cycle is completed and the initial positions for all external streams are re-established. 

There are an equal number of inlet and outlet streams, and each one has a term of this form, so there will be some degree of cancellation of this term among the four streams. 

In 2.4 we presented differential forms of the thermodynamic stuff equations for overall mass, energy, and entropy flows through open systems. Usually, such systems, together with their inlet and outlet streams, will be mixtures of any number of components. Individual components can contribute in different ways to mass, energy, and entropy flows, so here we generalize the stuff equations to show explicitly the contributions from individual components these generalized forms contain partial molar properties introduced in 3.4. 

Problem 9.6 A mixture of O2/CO2 (stream 1) expands in turbine (see Figure Q-4b The outlet (stream 2) is mixed with a stream of pure oxygen and the new stream (number 4) passes through a heat exchanger and exits as stream 5. The efficiency of the turbine is 80%. There are no heat losses and pressure drops in pipes and in the heat exchanger can be ignored. 

The Equilibrium reactor is a vessel which models equilibrium reactions. The outlet streams of the reactor are in a state of chemical and physical equilibrium. The reaction set which you attach to the Equilibrium reactor can contain an unlimited number of equilibrium reactions, which are simultaneously or sequentially solved. Neither the components nor the mixing process need be ideal, since HYSYS can compute the chemical activity of each component in the mixture based on mixture and pure component fugacities. 

If the change in volume due to reaction can be neglected, the operation of a stirred-flow reactor can be described in terms of the concentration cp of the limiting reactant I in the inlet stream, the concentration ci of that reactant in the outlet stream and the volumetric flow rate F which must then be the same for inlet and outlet streams. Indeed a simple material balance gives for the number of moles of reactant / per unit time ... 

In application of the cost balance equation (Eq. (10)), there is usually more than one inlet outlet streams for some components. In this case the number of unknown costing parameters is higher than the number of cost balance equations for that component. Auxiliary thermoeconomic equations (according to P and F rules) are developed to solve this problem [8]. Auxiliary equations for the hybrid plant under consideration in this paper are listed in Table 3. 

An SMB imit consists of a number of chromatographic columns, separated by ports through which inlet and outlet streams can be fed or collected. The counter-current solid movement is simulated by periodically shifting the feed and withdrawal points of the imit in the same direction as the mobile phase flow (see Eig. 20, bottom). Four external streams are present the racemic feed mixture the desorbent, i.e. the eluent or the mixture of eluents constituting the mobile phase the extract stream enriched in the enantiomer A and the raffinate stream enriched in the enantiomer B. These streams divide the imit into four sections section 1 between the desorbent inlet and the extract port, section 2 between the latter and the feed inlet, section 3 between this and the raffinate outlet, and section 4 between the raffinate port and the desorbent inlet. 

Next, the mnimum number of simple separation units must be determined. Although there are single units that produce multiple output streams (such as a petroleum refining pipe still with many side draws), most units accept a single inlet stream and produce two oudet streams. For such simple separators, we need at least (iV-1) units, where N is the number of outlet streams (products, by-products, and waste). There are two types of questions to answer concerning these units in the separation section (1) What types of units should be used and (2) How should the units be sequenced ... 

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