Model Mathematics

N_x = N_0 ⅇ^{- (ksh x)}

\frac{d}{d x} (F_DVR_v) = - (Jv + ksh F_DVR_v)

\frac{d}{d x} (F_DVR_GLU) = - (JGLU + ksh F_DVR_GLU)

\frac{d}{d x} (F_DVR_LAC) = - (JLAC + ksh F_DVR_LAC)

\frac{d}{d x} (F_AVR_v) = Jv + ksh F_DVR_v + J_ABS_V

\frac{d}{d x} (F_AVR_GLU) = JGLU + ksh F_DVR_GLU - JGLY

\frac{d}{d x} (F_AVR_LAC) = JLAC + ksh F_DVR_LAC + 2.0 JGLY

JGLU = N_x PGLU (c_DVR_GLU - c_AVR_GLU) + (1.0 - sigma_GLU) Jv \frac{c_DVR_GLU + c_AVR_GLU}{2.0}

JLAC = N_x PLAC (c_DVR_LAC - c_AVR_LAC) + (1.0 - sigma_LAC) Jv \frac{c_DVR_LAC + c_AVR_LAC}{2.0}

c_DVR_GLU = \frac{F_DVR_GLU}{F_DVR_v}

c_AVR_GLU = \frac{F_AVR_GLU}{F_AVR_v}

c_DVR_LAC = \frac{F_DVR_LAC}{F_DVR_v}

c_AVR_LAC = \frac{F_AVR_LAC}{F_AVR_v}

JGLY = N_x \frac{Vmax c_AVR_GLU}{Km + c_AVR_GLU} Vmax = \frac{ksh}{N_0 (1.0 - (ⅇ^{- (ksh L)}))} GlyFract F_DVR_G_0

J_ABS_V = kv N_x

kv = \frac{ksh}{N_0 (1.0 - (ⅇ^{- (ksh L)}))} VolFract F_DVR_V_0

Jv = 0.3 \frac{F_DVR_v}{N_0 b} N_x F_DVR_V_0 = 3.75 N_0 x_L = \frac{x}{L} F_DVR_G_0 = F_DVR_V_0 c_DVR_GLU_0