Growth and storage of PHB are described as functions of limiting substrate S (NH

Structured Model for PHB Production (PHB)

Growth and storage of PHB are described as functions of limiting substrate S (NH

), residual biomass R and product P (PHB)

concentrations concentrations.

Fig. 7. Structured kinetic model for PHB synthesis.

PHB [ Model ]

For the batch process,

μR dt r

dR

R=

=

Where rR is the rate of synthesis of R and μ is the specific rate of synthesis y μ p y of R,where

n S,2

n S,2 m,2

S,1 m,1 2

1 1 (S/K )

) μ (S/K

S K

μ S μ

μ

μ + +

= + +

=

PHB [ Model ]

For substrate

1 dS

The rate of synthesis of P(r ) is assumed to be the sum of a growth

R R/S

S r

Y r 1

dt

dS = = −

The rate of synthesis of P(r_P) is assumed to be the sum of a growth

associated term(r_P,1) and a biomass associated term(r_P,2) and is given by,

dP

Th th i t d t f th th i f P( )

P,2

P,1

r

r dt r

dP = = +

The non-growth associated term of the synthesis of P(r_P,2)

R) k P k K (

r =

( k P + k R) S)

r (K

1

P,2

− +

= +

PHB [ Program ]

M-file

PHB [ Program ]

Command window

PHB [ Nomenclature ]

C₁ Concentration kg/m₃

K Inhibition constant for (NH ) SO kg/m K₁ Inhibition constant, for (NH₄)₂SO₄ kg/m₃ K_S Saturation constantkg/m₃

n Hill coefficient –

P P d t t ti (PHB) k / P Product concentration (PHB) kg/m₃ Prot Protein concentration kg/m₃

R Residual biomass(R=X-P) kg/m₃ r Reaction rate kg/(m₃h)

r_P,red Reduced rate of synthesis of PHB –

S Limiting substrate NHg ₄₄+as (NH( ₄₄))₂₂SO₄₄ kg/mg ₃₃ X Biomass concentration kg/m₃

Y_P/R Yield coefficient kg/kg Y_R/S Yield coefficient kg/kg Y_R/S Yield coefficient kg/kg

μ Specific rate of synthesis of R (r_R/R) 1/h μ_P Specific rate of synthesis of P (r_P/P) 1/h

PHB ^{[ Result ]}

Fig. 8. Plots of R, S and P versus T during batch growth and production.g g g p