1.1.7 Residual curve

Points: 9 No answer

Within this OPAL task you are supposed to construct a residuum curve, which is relevant for batch distillation. The respective slide from the lecture is shown below.

Be aware that the mixture compositions considered on the lecture slide differ from the ones we treat in this OPAL exercise.

Let the feed be an equimolar liquid mixture of cyclopentane (1), heptane (2) and decane (3). Equimolar means that $$x_1=x_2=x_3=0.333$$ (three digits precision).

At a total pressure $$p_{tot}=0.1MPa$$ this mixture boils at $$T=352K$$.

The vapor pressures $$p^{sat}_i$$ of the three pure compounds are tabulated below.

$$T$$ in $$K$$$$p^{sat}_1$$ in $$MPa$$$$p^{sat}_2$$ in $$MPa$$$$p^{sat}_3$$ in $$MPa$$ $$y_1$$    $$y_2$$               $$y_3$$ 
3520.244190.054890.00386
3540.257590.058660.00423   
3560.271540.062620.00463
3580.286060.066800.00506   

TASK 1:

Compute the composition of the first boiling bubble and add the computed values $$y_i$$ into the table above.

TASK 2:

While the emerging vapour is subtracted via the top, the composition if the residual liquid changes. The residuum equation quantifies this change. What is the change of the fraction of compound 2 in the residual mixture, if  $$dx_1=-0.05$$ (with three digits precision).

$$dx_2=$$ .

A change of $$dx_1=-0.05$$ means that the new $$x_1=0.283$$ (precision 3 digits) and a change of $$dx_2=0.016$$ means that the new $$x_2=0.349$$ (precision 3 digits). As a consequence $$x_3=$$ . This residual liquid mixture boils at $$T=356K$$

TASK 3:

Compute for the composition of the residuum liquid mixture the composition of the corresponding vapour phase $$y_i$$ and insert the values in the table above.

TASK 4:

Compute $$dx_2=$$ for $$dx_1=-0.05$$.

 

For the computation of the entire residual curve one would have to repeat these computations many times. The small change $$dx_1=-0.05$$ that we chose is (most probably) a bit large. If one put this computation in practice in a computer program, one would choose a much smaller step size $$dx_1$$. $$dx_1$$ should then be chosen as small as its value does no more influence the trajectory of the residual curve.