Joint Process and Control Designs of a Semibatch Emulsion Polymerization Reactor

Barocalorimetric technique for monitoring pressurized copolymer reactors

“…(8)] in the beginning of the reaction, when the polymerized content is small, the entries of g are excessively large and, consequently, a limit on those terms must be imposed. In the absence of monomer 1 load and/or addition (i.e., $\hat{M}$ 10 = 0, implying that P 1 = 0 and Q 1 = 0) and of pressure measurement (i.e., y p − $\hat{p}$ = 0), the preceding barocalorimetric estimator reduces to its previously reported calorimetric counterpart 3, 4, 16…”

“…In a way that is analogous to the treatment of the previously studied calorimetric homopolymer case without pressure measurement,3, 4, 16 in what follows the same nonlinear geometric estimation approach7, 13, 17 is applied to our present barocalorimetric copolymer case. Recall the measurement eq.…”

“…From conservation and finite‐capacity arguments,3, 4 the stability of the motion x II ( t ) follows, meaning that typical density, specific heat capacity, and equilibrium parameter errors produce growing errors x̃ II ( t ), which remain acceptably bounded. These observability and stability features imply the detectability of the barocalorimetric motion [i.e., the solution of eq.…”

“…Originally, the reactor calorimetric estimation and control schemes evolved from laboratory differential estimation techniques: the idea was to draw reaction rate and conversion estimates from mass and energy balances without needing the reaction rate and heat‐transfer functions 1–4. Motivated by the need to design or redesign industrial batch and semibatch polymer reactors, to attain better compromises between safety, productivity, and quality measures,4 the subject of calorimetric estimation and control has been extensively investigated 5, 6.…”

“…Diverse nonlinear techniques have been developed and successfully tested in solution and emulsion reactors, including homo‐, co‐, and terpolymerizations. Recently, a nonlinear geometric estimation approach has provided a unifying design framework for the calorimetric homopolymer case, on the basis of definitions of nonlinear observability and stability for batch motions 3, 4, 7. It has been reported that, in a pressurized copolymer emulsion reactor, the pressure evolution is correlated with the conversion and composition evolutions, depending on the particular reactor, recipe, and kind of (starved or nonstarved) regime 8, 9.…”