2f232088-b9f3-438b-9948-4cb953dea391 42 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Ligand system M 14 : m 1 : a 1 : x log x log10 : xo 1 : slope 4 : 61 sys

Ligand: One site competition

Justification . . .

The Ligand model is chosen for its non-symmetric

shape around pH [7]. It simulates real processes,

thus validates the remaining of the project.

In short: the project produces a buffered solution

of adjustable pH.

]]>

x 0.01 log 1 log 0.011 log range :

x c 1 0.01 x ≤ (x 2 ≤ (& cases :

Binding function x xo H S m M m - (110 a log x xo - (- (H *^+ / + :

ratio1 ratio2 21 mat x xo slope S pH1 - 0 ≡ x 0.75 1 solve x xo slope S pH2 - 0 ≡ x 1 1.25 solve 21 mat :

pH1 3 : pH2 11 : 21 sys

Predict pH from plant titration

x xo slope S vectorize x c * 1 20 1 5 - 2 2 mat 1 7 + 20 black 1 5 mat ratio1 pH1 o 5 black 1 5 mat ratio2 pH2 o 5 black 1 5 mat 5 1 sys

Exposé . . .

Assume that for a unary ratio of acid/base your plant response

is of equi-titration. A pH control loop will enable adjusting

the unary ratio. This proposal is only explicative by induction.

In real plant, pH control is difficult to implement and maintain.

For any desired operating pH, easy to solve/tabulate the

corresponding unary ratio. At this point, each titrant flow loop

can be regulated/controlled. Things not being so perfect, from

the operating pH, some Feed-Forward control strategy will trim

the reluctant unary ratio flow control loops. Here, the titration

is approximated from experimental pilot plant. Observe that

the model titration is not symmetric wrt unary ratio [7/1].

]]>

pH1 pH2 21 mat ratio1 ratio2 21 mat 12 mat 31121 mat 0.8149 1.1307 21 mat 12 mat

ratio1 ratio2 + 2 / 0.9728

A suggestive primitive ratio flow control loop

Binding function x S m M m - (110 a log x xo - (- (slope *^+ / + :

x Inv1 xx S x + 1 ≡ xx 1 roots :

x Inv2 xx S x - 0 ≡ xx 1 roots :

The complete solution is the real part. y f slope 10 ln * xo a log10 + (* y M - y m - / ln - slope 10 ln * / Re :

3 f 0.8149

x c 1 0.5 x ≤ (x 1.5 ≤ (& cases :

fake scale for plot s 10 :

roots aren't explicit solutions

x S x c * s x 1 - Inv1 * x c * s x Inv2 * x c * 3 1 sys

maple solution is an explicit fnct.

x S x c * s x f * x c * 2 1 sys

compens 17 f - : u 311 3.01 range : ratio u u f vectorize compens + augment : 31 line

compensation factor.
f(x) is NOT symmetric
thus f(7)≠ 1 7 f 17 f - 21 mat 0.9833 0.0167 21 mat

ratio ratio :

ratio 3 0.8316 3.01 0.8323 3.02 0.8329 3.03 0.8336 3.04 0.8342 3.05 0.8348 3.06 0.8354 3.07 0.8361 3.08 0.8367 3.09 0.8373 3.1 0.8379 112 mat

vx ratio 1 col : vy ratio 2 col : 21 line

a vx vy Intercept : b vx vy Slope : 21 line

a b 21 mat 0.7394 0.0368 21 mat :

x λ a b x * + :

x λ ratio 2 1 sys ratio x λ 2 1 sys

The 'ratio' may be approximated by a model function ... not offered in this document as it is a demo/tutor only.