Model Mathematics

mu_Ai = R T \ln (K_Ai q_Ai) q_Ai = q_init_Ai mu_Ao = R T \ln (K_Ao q_Ao) q_Ao = q_init_Ao mu_1 = R T \ln (K_1 q_1) \frac{d}{d t} (q_1) = v_1 mu_2 = R T \ln (K_2 q_2) \frac{d}{d t} (q_2) = v_2 mu_3 = R T \ln (K_3 q_3) \frac{d}{d t} (q_3) = v_3 mu_4 = R T \ln (K_4 q_4) \frac{d}{d t} (q_4) = v_4 v_r1 = kappa_r1 (ⅇ^{\frac{A_f_r1}{R T}} - (ⅇ^{\frac{A_r_r1}{R T}})) v_r2 = kappa_r2 (ⅇ^{\frac{A_f_r2}{R T}} - (ⅇ^{\frac{A_r_r2}{R T}})) v_r3 = kappa_r3 (ⅇ^{\frac{A_f_r3}{R T}} - (ⅇ^{\frac{A_r_r3}{R T}})) v_r4 = kappa_r4 (ⅇ^{\frac{A_f_r4}{R T}} - (ⅇ^{\frac{A_r_r4}{R T}})) v_Ai = v_r4 v_Ao = - v_r3 v_1 = v_r1 - v_r3 v_2 = v_r3 - v_r2 v_3 = v_r2 - v_r4 v_4 = v_r4 - v_r1 A_f_r1 = mu_4 A_r_r1 = mu_1 A_f_r2 = mu_2 A_r_r2 = mu_3 A_f_r3 = mu_Ao + mu_1 A_r_r3 = mu_2 A_f_r4 = mu_3 A_r_r4 = mu_Ai + mu_4

q_init_Ao = g_o V_o q_init_Ai = g_i V_i