11 replies to this topic

[sgkim]

Hello Keekooceeaou,

The heat of solution being neglected, the following equation shall be met based on the energy balance.

m1*Cp1*(t-t1)+m2*Cp2*(t-t2)+.....+mi*Cpi*(t-ti)+..=0 .........(1)

where, mi, Cpi, ti are mass(or mass rate), specific heat and temperature for i-th stream respectively, and t temperature of the mixture.

(Σmi*Cpi)* t = Σ(mi*Cpi*ti).........................(2)

Therefore t = Σ(mi*Cpi*ti)/(Σmi*Cpi)..........(3)

If all specific heats are equal, then t = Σ(mi*ti)/Σ(mi)......(3a)

For dilute sulfuric acid solutions the above equations can be applied, but enthalpy-concentration-temperature diagram is required for the mixing of high-concentration sulfuric acids.

Enthalpy balance: Total enthalpy H = (Σmi*hi) = (Σmi)*h --> h =(Σmi*hi)/(Σmi) --> find t from H-C-T diagram having specific enthalpy of h at the mixture concentration.

sgkim

[Art Montemayor]

Keek:

I believe the reason you are confused with the equations that sgkim gave is because he left out the basic premise of developing the equations:

What goes in = What goes out

The above basic equation applies to mass and heat. That is why the "Golden Rule" of all Chemical Engineers should be: "When in doubt and confused, make a heat and mass balance." This old rule still works. All Sgkim has done is make a heat and mass balance. The best way to learn engineering is to develop or derive the equations yourself. That way, you never froget the relationships and you certainly understand the basic and fundamental concepts involved. Try it yourself .....


m1 + m2 = m3

Qi = mi Cpi (T2 - T1)
or,
Qi = mi (H2 - H1)

You have to rely on enthalpy values when you deal with dilute solutions because the specific heats of the dilute solutions are very close to each other and the enthalpies are more accurate.

I think I'm correct in stating the above. I'll let Sgkim elaborate on anything I've stated that is not correct or what was meant.

[siretb]

Be very careful when calculating the temperature of the mixture of sulfuric and water.
Unless both stream are weak(dilute) sulfuric, you may get large temperature raise due to the so called "heat of dilution"
You need to work with enthalpies, as stated earlier. The figure 3-40 of Perry's handbook (5th Ed) can help you undestand
If we mix 1 lb of 20% acid at 70°F I have (approx) an enthalpy of -30 Btu/lb (ref state liquid, zero at 32°F)
with 1 lb of acid at 80% I have -100 Btu/lb

As a result I have a stream that is 50% (mass balance) with enthalpy of -(100+30)/2=-65 Btu/lb, yielding a temperature of about 140°F

This calculation is approximate only. Refer to tables to get exact enthalpy-concentration-temperature relation.

[joerd]

It is very straightforward if you follow Art Montemayor's approach:

8.6 kg x 19.16 kcal/kg = 164.78 kcal enthalpy
11 kg x 61.8 kcal/kg = 679.8 kcal
Total 19.6 kg and 844.58 kcal
Enthalpy of mixed stream = 43.1 kcal/kg at 34% acid.
Find H=43.1 and C=34% on your diagram and read the temperature.

[siretb]

Please find here a graph, with detailed calculations

Data Stream 1 8.6 kilos at 72%wt at 40°C H=-100 BTU/lb, more or less left point
Stream 2 11 kilos at 4.5% at 65°C H=+100 BTU/lb

mass balance mixture is (8.6*72+11*4.5)/(8.6+11)=34%

heat balance Hmix=(-100*8.6 + 100*11)/(8.6+11)= +12.2 BTU/lb

back to the graph at the intersection of 34% and 12.2, we read about 185°F 85°C

 sulfu.bmp   56.17KB   158 downloads

[sgkim]

Hello Keekooceeaou,

The heat of solution being neglected, the following equation shall be met based on the energy balance.

m1*Cp1*(t-t1)+m2*Cp2*(t-t2)+.....+mi*Cpi*(t-ti)+..=0 .........(1)

where, mi, Cpi, ti are mass(or mass rate), specific heat and temperature for i-th stream respectively, and t temperature of the mixture.

(Σmi*Cpi)* t = Σ(mi*Cpi*ti).........................(2)

Therefore t = Σ(mi*Cpi*ti)/(Σmi*Cpi)..........(3)

If all specific heats are equal, then t = Σ(mi*ti)/Σ(mi)......(3a)

For dilute sulfuric acid solutions the above equations can be applied, but enthalpy-concentration-temperature diagram is required for the mixing of high-concentration sulfuric acids.

Enthalpy balance: Total enthalpy H = (Σmi*hi) = (Σmi)*h --> h =(Σmi*hi)/(Σmi) --> find t from H-C-T diagram having specific enthalpy of h at the mixture concentration.

sgkim

To follow with Art Montemayor's comment on my posting, I would like to add to my posting cited above:

Equation(1) holds true only if specific heats do not change with temperature and no heat of dilution is involved.
So equations (3) or (3a) are not accurate and can be applied only for rougth estimation assuming that no heat of dilution is involved and that the specific heats do not change in the temperature range concerned.

Instead, the temperature of the mixture shall be calculated from the "Enthalpy Balance" as described in the last paragraph.

Stream 1...Total Enthalpy, H1 = h1*m1, mass m1, concentration C1
Stream 2...Total Enthalpy, H2 = h2*m2, mass m2, concentration C2
....
Mixture: Total Enthalpy, H = H1+ H2+.....,
total mass, m= m1+m2+....,
concentration of the mxture, c = (m1*c1+m2c2..)/m
specific enthalpy of the mixture, h = H/m

From H-C-T diagram find t (from h and c)

Both siretb and joerd have already posted the same method.
Thanks for your comment Art Montemayor,

sgkim