The mathematical modelling of transient systems using differential-algebraic equations

On‐line parameter estimation in a high‐pressure low‐density polyethylene tubular reactor

“…Alternatively, the simultaneous solution of the algebraic and the differential equations has been suggested (Brenan et al, 1989). Perregaard et al (1992) conducted a comparative study of the two approaches and concluded that the relative efficiency of the two approaches depends on the relative number of the differential and the algebraic equations and the number of iterations required on the average to solve the algebraic system (see also Pantelides et al, 1988;Pontor and Gaethrop, 1991).…”

Nonlinear analysis in process design

“…Other, more experimental, codes are available to solve semiexplicit systems with index = 1, including LIMEX (Deuflhard and Nowak, 1987), DASP3 (Soderlind, 1980), andDRIBLOCK (Mach, 1986). Pantelides et al (1988) show examples of higher index systems, often involving phase equilibrium. They also show that design specifications can increase the index and that different specifications can result in different indexes.…”

Rigorous dynamic modeling and simulation of wine distillations

“…(1)-(10)) corresponds to a DAE system of index two (Pantelides, Gritsis, Morrison, & Sargent, 1988). There is no generalpurpose stable algorithm to solve high index DAEs, and before any algorithm integrate the equations, a set of consistent initial conditions must be defined, hence not all differential variables may be freely chosen (Ascher & Petzold, 1998).…”