Reactor volume ideal gases

Suppose a homogeneous, gas-phase reaction occurs in a constant-volume batch reactor. Assume ideal gas behavior and suppose pure A is charged to the reactor. 

Solution The obvious way to solve this problem is to choose a pressure, calculate Oq using the ideal gas law, and then conduct a batch reaction at constant T and P. Equation (7.38) gives the reaction rate. Any reasonable values for n and kfCm. be used. Since there is a change in the number of moles upon reaction, a variable-volume reactor is needed. A straightforward but messy approach uses the methodology of Section 2.6 and solves component balances in terms of the number of moles, Na, Nb, and Nc-... 

The sulfur dioxide enters the reactor with an initial concentration of 10% by volume, the remainder being air. At the exit of the first bed, the temperature is 620°C. Assume ideal gas behavior, the reactor operates at 1 bar and R = 8.3145 kJ-Kr -lonoD1. Assume air to be 21% 02 and 79% N2. Thermodynamic data at standard conditions at 298.15 K are given in Table 6.186. 

The reactor is to be designed to operate at 1 atm. Deviations from ideal gas behavior may be neglected. Note that while the volume changes associated with changes in mole numbers are negligible, you may wish to consider the effect of thermal expansion. 

The volumetric flow rate of propane at the reactor inlet is given by the product of the molal flow rate, the molal volume of the gas at standard conditions, and the pressure and temperature correction factors implied by the ideal gas law. 

The Sieverts-type apparatus consists of a calibrated volume determined physically, a reactor whose temperature is controlled by the temperature control system and the cooling system, a vacuum system, a pressure monitoring system, valves, and source of hydrogen and argon delivery. The quantity of desorbed hydrogen (number of molls) is calculated using ideal gas flow ... 

Assuming ideal gas behaviour, calculate the reactor volume needed for a 90% conversion of A if the process is conducted (i) isothermally at 1000 K and (ii) adiabatically with an inlet temperature of HOOK. 

We try to make calculations come out in round numbers so in many problems the feed concentrations are 2 moles/bter, conversions are 90%, reactor volumes 100 liters, and feed temperatures 300 or 400 K. We further assume that all heats of reaction and heat capacities are independent of temperature, pressure, and composition. We sometimes even assume the ideal gas constant R=2 cal/mole K, just because it makes it easier to remember than 1.98... . ... 

These units for diA and CA will eventually lead to the units m3 for the volume of the reactor when we come to use equation 1.35. When we substitute for 0iA in equation 1.35, however, to integrate, we must express CA in terms of aA, where the reactant A is CjHt. To do this we first note that CA-yAC where yA is the mole fraction and C is the molar density of the gas mixture (kmol/m3). Assuming ideal gas behaviour, C is the same for any gas mixture, being dependent only on pressure and temperature in accordance with the ideal gas laws. Thus 1 kmol of gas occupies 22.41m3 at 1 bar (= 1.013 x 105 N/m2) and 273 K. Therefore at 1.4 bar = 1.4 x 10s N/m3 and 1173 K it will occupy ... 

Consider the following gaseous reaction aA + bB — cC + dD. Pressure and concentration are related, and for a constant volume reactor with changing number of moles during reaction, the total pressure (n) changes with time, t. For an ideal gas, with any reactant A or B, the partial pressure is expressed as ... 

The progress of the reaction is monitored by the drop in the pressure of the system. With the standard apparatus having the reactor open to the reservoir, a 0.1 mole of gas uptake corresponds to approximately an 8 psig pressure drop. To detect smaller quantities of gas uptake, the reactor can be isolated from the reservoir so the gauge reads only the pressure of the gas in the reactor bottle. With a half full 500 mL reactor bottle a 0.1 mole gas uptake corresponds to about a 150 psig pressure drop. Approximate pressure drops for other volumes and quantities of gas consumed are easily calculated using the ideal gas law. 

Reaction Engineering with Idealized Models Liquid / slurry phase- complete mixing Gas phase- complete mixing or plug flow No heal transfer limitations Reactor volume for different degrees of mixing and for different values of malts transfer coctTicient Heat transfer area for different values of overall heal transfer coeflicients... 

The volume of an ideal gas in a reactor at any time can be related to the initial conditions by the following equation ... 

Consider the following mixture that is coming out of a methanol reactor CO, 100 kmol/h H2, 200 kmol/h methanol, 100 kmol/h. The gas is at 100 atm and 300°C. Compute the specific volume using (1) ideal gas law (2) Redlich-Kwong equation of state and (3) Redlich-Kwong-Soave equation of state. The acentric factors for the RK-Soave method are CO, 0.049 H2, -0.22 methanol, 0.559. Where did you get the other data you needed How do the three answers compare Is the gas ideal or not Comment. 

For gas-phase variable-volume batch reactors, like the one shown schematically in Figure 6.2, F/f(T) varies during the operation. Assuming ideal gas behavior, the... 

The design equation for gaseous variable-volume batch reactors was derived under two assumptions (i) AU the species are gaseous, and (ii) the mixture behaves as an ideal gas. In some operations, one or more of the species (especially heavier products generated by the reaction) may be saturated vapor. In this case, any additional amount generated will be in a condensed phase (liquid). While the ideal gas relation provides a reasonable approximation for the volume of species in the vapor phase, it cannot be applied for dieir volume in the liquid phase. Below, we modify the design equations for a variable-volume batch reactor with saturated vapors. 

To determine a, we plot xt dZ/dt) versus ln(l - Z) and obtain a from the slope. In this case, we have data of P f), so we have to derive a relation between P t) and Z(t). Selecting the initial state as the reference state and using Eq. 2.7.6. for an ideal gas in a constant-volume reactor... 

Hydropyrolysis Process. Two hydropyrolysis reactors were used in this study. The Sunnyside and Asphalt Ridge bitumen were processed in a reactor consisting of a coiled stainless steel tube 3/16" i.d. x 236" long. This reactor has been previously described by Ramakrishnan (1). The TS-IIC oil was processed in a reactor originally developed for short residence time coal liquefaction. This reactor also consists of coiled stainless steel tubes 3/16" i.d. The length of this tube system can be varied from 20 to 120 feet, and has been previously described by Wood, et al. (10). The length of the reactor for runs reported in this paper was 100 feet. Average residence times were calculated from the volumetric flow rates and the reactor volume at process conditions. The reaction mixture, which is predominantly H, was assumed for purposes of this calculation to behave as an ideal gas. The reactors were pre-sulfided with H S to inhibit catalytic reactions from wall surfaces. 

If w e consider the constant-volume reactor with incompressible fluid (a = 0,Cv = Cp), Equation 6.16 reduces to Equation 6.15 as it should because Equation 6.15 is valid for any reactor operation with an incompressible fluid. We also notice that, in the constant-pressure case, the same energy balance applies for any fluid mixture (ideal gas, incompressible fluid, etc.), and that this balance is the same as the balance for an incompressible fluid in a constant-volume reactor. Although the same final balances are obtained for these two cases, the physical situations they describe are completely different. 

Hence, 0a = 1, by definition. In summary, aU partial pressures in the rate law should be written as a product of total pressure and mole fraction. Then, mole fractions can be expressed in terms of the conversion of CO. Alternatively, the ideal gas law can be used to express partial pressures p, as QRT, and the conversion dependence of molar density C, is tabulated by Fogler (1999, p. 96) for variable-volume gas-phase flow reactors. It should be emphasized that y, ptotai and CiRT generate the same function of conversion when the s parameter in Fogler s expressions is written as... 

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