Steady-state molar flow rates

To develop E(B) for two CSTRs in series, we use a slightly different, but equivalent, method from that used for a single CSTR in Section 13.4.1.1. Thus, consider a small amount (moles) of tracer M, nMo = F,dt, where Ft is the total steady-state molar flow rate, added to the first vessel at time 0. The initial concentration of M is cMo = nMo/(V/2). We develop a material balance for M around each tank to determine the time-dependent outlet concentration of M from the second vessel, cM2(l). 

Dissecting the Steady-State Molar Flow Rates to Obtain the Heat of Reaction... 

Oship measured the steady-state rate of permeation of CO2 gas at 155°C through a glassy polyimide film [92], The membrane area was 7.197 cm and the thickness was 0.0025 cm. When the pressure difference across the membrane was SOcmHg, the steady-state molar flow rate was 2.055 X 10 g mol/sec. Determine the permeability in barrers where 1 barrer = 10 em (STP)/(cm sec cm of Hg). 

The mole fraction compositions yt and %, are therefore to be uniform on each side of the membrane, where the subscript i denotes components 1, 2, 3,..., k. The respective steady-state molar stream rates are denoted by F, L, and V. These may designate the total flow rate of the each stream, or may be a flux rate based on the membrane area. 

Thus the changes in the molar flow rates (kmol/h m) at steady state can be set equal to the rates of production of each component. 

The changes in the molar flow rates with distance Z at steady-state conditions are... 

Fora 1000-tonne day-1 sulturic acid plant (100% H2SO4 basis), calculate the total molar flow rate (mol s 1) of gas entering the SO2 converter (for oxidation to SO3), for steady-state operation, if the fractional conversion (/so2) in the converter is 0.98, and the feed to the converter is 9.5 mol % SO2. (1 tonne = 1000 kg.)... 

To translate this into operational form, we use the total specific mass flow rate, m, rather than molar flow rate, to show an alternative treatment to that used for a BR in Chapter 12. An advantage to this treatment is that in steady-state operation, m is constant, whereas the molar flow rate need not be. Thus, using Tref as a reference temperature... 

For the liquid-phase reaction A + B products at 20°C, suppose 40% conversion of A is desired in steady-state operation. The reaction is pseudo-first-oider with respect to A, with kA = 0.0257 hr1 at 20°C. The total volumetric flow rate is 1.8 m3 h 1, and the inlet molar flow rates of A and B are FAo and Fbo mol h 1, respectively. Determine the vessel volume required, if. for safety, it can only be filled to 75% capacity. 

Consider the steady state balances around the segment AV, as shown in Fig. 2 0 = Naf — (NAF + ANaf) + rApAV where NAF is the molar flow rate of A (kmol/h). 

This is a number that goes from zero to unity as the selectivity improves. We can use the number of moles Nj, chosen on some basis for each species such that we divide each Nj by its stoichiometric coefficient to normalize them. For a steady-state flow system the molar flow rates Fj are appropriate. 

We consider a reaction of type A——>P the CSTR (Figure 8.1) is continuously fed with a stream at an initial conversion X0. Thus, the concentration of the reactant A in the feed stream is CA0 and at the outlet of the reactor is at its final value Ctt = CA= CA0 (1 — XA), which is also equal to the concentration inside the reactor volume. If the reactor is operated at steady state, the molar flow rate of A, FA the mass balance can be written for the reactant A ... 

A condenser is then installed and run at the design temperature and pressure. The volumetric flow rates of the feed stream and the vapor and liquid product streams are measured with rotameters (see p. 46), and the MEK mole fractions in the feed and vapor effluent streams are measured with a gas chromatograph. The feed stream flow rate is set to 500 liters/s and enough time is allowed to pass for the product stream rotameter readings to reach steady levels. The feed and product gas flow rates are then converted to molar flow rates using the ideal gas equation of state, and the product liquid flow rate is converted to a molar flow rate using a tabulated MEK density and the molecular weight of MEK. Here are the results. 

Normally, conversion increases with the time the reactants spend in the reactor. For continuous-flow systems, this time usually increases with increasing reactor volume consequently, the conversion X is a function, of reactor volume V. If is the molar flow rate of species A fed to a system operated at steady state, the molar cate at which species A is reacting within the entire system will be... 

Consider now a steady- ow reactor and conduct a species balance over the reactor. At steady state, the molar flow rate of species j at the reactor outlet is equal to the molar flow rate of species j at the reactor inlet plus the rate species j is being generated inside the reactor by the reaction, Gj,... 

Steady-state flow experiments were performed at 673 K and 1 atmosphere pressure using a gas blend of 88% Argon, 10% oxygen and 2% n-butane. Molar flow rates were set to insure turbulent flow [14]. The reactor effluent was monitored by leaking a small amount into the TAP-2 vacuum system and collecting the mass spectrum. 

When we applied the first law of thermodynamics to a reactor to relate either temperature and conversion or molar flow rates and concentration, wc arrived at Equation (8-9). Neglecting the work term we have for steady-state conditions... 

At steady state, a component mass balance on CO over an element of catalyst bed of thickness dl and a cross sectional area Aj, with a constant total molar flow rate 7-, gives... 

We first compute the energy flows in each step of the process. In this analysis the process is at steady state so that all the time derivatives are equal to zero and the mass flow rate M (actually we will use the molar flow rate iV) is constant throughout the process. 

Dynamic flash is a simple but very useful unit in dynamic simulation. Fig. 4.2 depicts the layout of a vapour-liquid separation. A multi-component feed of molar flow rate F with the composition z, is split in vapour V and liquid L, with the composition y-, and Xj, respectively. Optionally heat may be added or removed. Initially the flash operates at steady state. The problem is to study the dynamic response at various disturbances, as changes in throughput or composition. Modelling equations are presented below. 

At high-mass-transfer Peclet numbers, the steady-state mass balance for component i, with units of moles per time, is expressed in terms of its molar flow rate Fi and differential volume dV = ttR dz for a tubular reactor. If species i... 

At the differential level, molar flow rate and mass fraction are linearly related when the total mass flow rate (i.e., qpunai) is constant at steady state with one inlet... 

A gas-phase mass balance can be written for each component because all four components are volatile and exist in both phases. In each case, the control volnme contains all gas bubbles in the CSTR. The units of each term in all of the gas-phase mass balances are moles per time. At steady state, the inlet molar flow rate of component j is balanced by the outlet molar flow rate and the rate at which component j leaves the gas phase via interphase mass transfer. The inlet and outlet molar flow rates represent convective mass transfer. Interphase transport is typically dominated by diffusion, but convection can also contribute to the molar flux of component j perpendicular to the gas-liquid interface. All of the gas-phase mass balances can be written generically as... 

The approach to be followed in the determination of rates or detailed kinetics of the reaction in a liquid phase between a component of a gas and a component of the liquid is, in principle, the same as that outlined in Chapter 2 for gas-phase reactions on a solid catalyst. In general the experiments are carried out in flow reactors of the integral type. The data may be analyzed by the integral or the differential method of kinetic analysis. The continuity equations for the components, which contain the rate equations, of course depend on the type of reactor used in the experimental study. These continuity equations will be discussed in detail in the appropriate chapters, in particular Chapter 14 on multiphase flow reactors. Consider for the time being, by way of example, a tubular type of reactor with the gas and liquid in a perfectly ordered flow, called plug flow. The steady-state continuity equation for the component A of the gas, written in terms of partial pressure over a volume element dV and neglecting any variation in the total molar flow rate of the gas is as follows ... 

Suppose that a river with a molar flow rate of 10000 mol/s meets another, larger river flowing at 500000 m 3/s at room temperature. What is the mass flow rate of the river downstream of the intersection if you assume steady state ... 

A stirred flow reactor of volume Vj. = 2x10 m working under steady-state conditions and at pressure Pj. = 10 Pa and temperature Tj. = 1100 K is fed with a molar flow rate Fqa = 8.89x10 mol s l of a pure reactant A. The volume flow rate Qj. = 9.54x10" m and the concentration of a product B, Cj. = 1.61 mol m" are measured at the exit to the reactor. 

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