The key concept in the analysis and design of ideal chemical reactors for simple reactions is the conversion dependence of kτ. This function determines the relationship between the key variables: reaction kinetics (k), reactor size (V), process throughput ((Subscript[v, 0])) and reactant conversion ((Subscript[X, A])). Knowledge of three of them is necessary to determine the fourth one. So a graph of kτ vs. (Subscript[X, A]) for different situations (PFR vs. MFR, different (Subscript[C, A0]) values, etc.) is very informative. Here are some of them (see Table 5.1).

kTau1PFR = Log[1/(1 - xA)];
kTau1MFR = xA/(1 - xA);
Plot[{kTau1MFR, kTau1PFR}, {xA, 0, 1}, PlotRange -> {0, 10}, 
        PlotStyle -> {Dashing[{0.05}], Dashing[{}]}];

For 1st order rxns:
•kτ is independent of (Subscript[C, A0]);
•at constant kτ, (Subscript[X, A, MFR]) < (Subscript[X, A, PFR]);
•at constant (Subscript[X, A]), need larger kτ for MFR than for PFR, especially at high (Subscript[X, A]).

cA01 = 1;
cA02 = 5;
cA03 = 10;
kTau2p1 = xA/(cA01*(1 - xA));
kTau2p2 = xA/(cA02*(1 - xA));
kTau2p3 = xA/(cA03*(1 - xA));
kTau2m1 = xA/(cA01*(1 - xA)^2);
kTau2m2 = xA/(cA02*(1 - xA)^2);
kTau2m3 = xA/(cA03*(1 - xA)^2);
Plot[{kTau2p1, kTau2p2, kTau2p3, kTau2m1, kTau2m2, kTau2m3}, {xA, 0, 
          1}, PlotRange -> {0, 10}, 
        PlotStyle -> {{Thickness[0.005], 
              Dashing[{}]}, {Thickness[0.008], 
              Dashing[{}]}, {Thickness[0.011], 
              Dashing[{}]}, {Thickness[0.005], 
              Dashing[{0.04}]}, {Thickness[0.008], 
              Dashing[{0.04}]}, {Thickness[0.011], 
              Dashing[{0.04}]}}];

For 2nd order rxns:
•at constant kτ, (Subscript[X, A]) increases as (Subscript[C, A0]) increases;
•at constant (Subscript[X, A]), need larger kτ for MFR than for PFR, especially at high (Subscript[X, A]);
•at constant (Subscript[X, A]), need larger kτ for low (Subscript[C, A0]).

cA01 = 1;
cA02 = 5;
cA03 = 10;
kTau0p1 = xA*cA01;
kTau0p2 = xA*cA02;
kTau0p3 = xA*cA03;
kTau0m1 = xA*cA01;
kTau0m2 = xA*cA02;
kTau0m3 = xA*cA03;
Plot[{kTau0p1, kTau0p2, kTau0p3, kTau0m1, kTau0m2, kTau0m3}, {xA, 0, 
          1}, PlotRange -> {0, 1.5}, 
        PlotStyle -> {{Thickness[0.005], 
              Dashing[{}]}, {Thickness[0.008], 
              Dashing[{}]}, {Thickness[0.011], 
              Dashing[{}]}, {Thickness[0.005], 
              Dashing[{0.04}]}, {Thickness[0.008], 
              Dashing[{0.04}]}, {Thickness[0.011], 
              Dashing[{0.04}]}}];

For zero-order rxns:
•no effect of reactor type (concentration level, earliness of mixing);
•at constant kτ, (Subscript[X, A]) increases as (Subscript[C, A0]) decreases;
•at constant (Subscript[X, A]), need larger kτ for high (Subscript[C, A0]).