Example 16.3_2


Project by Amanda Blankenship and Juliette Guarriello


At low pressure, mass diffusivity (DAB) is a function of temperature and pressure only. Bird, Stewart, and Lightfoot give an equation for mass diffusivity of two gases at low pressure (eq 16.3_1). At high pressures the composition of the gas mixture becomes important. Little is known about the dependence of mass diffusivity on pressure, except in the unique case of self-diffusivity (interdiffusion of identical molecules), which can be calculated using the Enskog kinetic theory. This relationship is shown in Figure 16.3-1 on page 506. Experimental evidence suggests that the same relationship can be used if the critical values pc and Tc are replaced by the values of the pseudo-critical properties of the mixture.

For ease, we have coded Figure 16.3_1 into a Matlab program. The program inputs the pseudo-reduced temperate (Tr) and pressure (pr) and returns the ratio of pDAB/(pDAB)0. The Matlab code is available here.

Now we will solve Example 16.3-2.

Example 16.3-2

Estimate DAB for a mixture of 80mole percent methane and 20 mole percent ethane at 2000 psia and 104 degF. (136 atm, 313 K) The experimental value of (pDAB)0 at 293 K is 0.163 atm*cm^2/s.

> restart;

Start with equation 16.3_1 on page 505:

> eq:=p*DAB/((pcA*pcB)^(1/3)*(TcA*TcB)^(5/12)*(1/MA+1/MB)^(1/2))=a*(T/sqrt(TcA*TcB))^b;

[Maple Math]
[Maple Math]

Solve for DAB, and use unapply to turn it into a function of T and p.

> DAB:=solve(eq,DAB);

[Maple Math]
[Maple Math]

> DAB:=unapply(DAB,T,p);

[Maple Math]
[Maple Math]

Constants a and b for non-polar gas pairs are given on p 505. Problem statement gives us experimental value of (pDAB)0 at 293 K.

> a:=2.745e-4: b:=1.823: pDAB293_0:=.163*atm*cm^2/s:

Use equation 16.3-1 to find new (pDAB)0 at 313 K.

> ratio:=p*DAB(313,p)/(p*DAB(293,p));

[Maple Math]

> pDAB313_0:=ratio*pDAB293_0;

[Maple Math]

Input pressure and temperature of mixture. Input critical properties of components (from Table B-1) and composition of mixture.

> p:=136*atm: T:=313*K:

> TcCH4:= 190.7*K: pcCH4:= 45.8*atm:

> TcC2H6:= 305.4*K: pcC2H6:= 48.2*atm:

> xCH4:=0.8: xC2H6:=0.2:

Use critical properties of components to find pseudo-critical properties of mixture.

> pc:=pcCH4*xCH4+pcC2H6*xC2H6;

[Maple Math]

> Tc:=TcCH4*xCH4+TcC2H6*xC2H6;

[Maple Math]

Now find pseudo-reduced properties of mixture.

> pr:=p/pc; Tr:=T/Tc;

[Maple Math]

[Maple Math]

Using matlab program based on Figure 16.3-1 (p 506), the ratios of pDAB to (pDAB)0 is found to be 0.7315. Use this ratio to find pDAB.

> pDAB:=0.7315*pDAB313_0;

[Maple Math]

Divide by pressure to find DAB.

> DAB:=pDAB/p;

[Maple Math]

>