simulink数学模型推导.pdfVIP

METHODOLOGY FOR DERIVING THE MODEL (1) Consider a STR: Fi X V S P Let y = an extensive property (X, S, P) Fo 1. General Mass Balance 1/V d(V y)/dt = Σ r gen. –Σ r cons. + Dy – γD y …(1) i o r gen. = rate of a production reaction for a component r cons. = rate of a consumption reaction for a component 3 -1 3 3 D = F/V ( m h /m ) – dilution rate V = liquid volume (m ) 3 -1 F – volumetric flow rate inlet and outlet (m h ) γ = Fo/Fi Units for each term in eqn. (1) = (kg m-3h-1) METHODOLOGY FOR DERIVING THE MODEL (2) 2. Mass Balance for Continuous Operation Typically: Fi = Fo γ = 1 dV/ dt = 0 Thus, the general mass balance equation es: dy/dt = Σ r gen. – Σ r cons. + D (yi – yo) …(2) 3. Mass Balance for Batch Operation Here, Fi = Fo = 0 ; For constant volume: dV/ dt = 0 Here, the general mass balance equation DERIVING THE MODEL (3) INSERTING REACTION RATE EQUATIONS (A) Example: Batch operation; Monod growth k ics Luedeking-Piret type product formation model Rate Expressions: 1. Biomass rx = mX (growth) r = k X (death) d d μ= mmaxS/ (KS + S) (k ics) Balance: dX/dt = rx - rd DERIVING THE MODEL (3) INSERTING REACTION RATE EQUA