\(\frac{d[\text{NAD}^{+}]}{\text{dt}}=-\ v_{eff,FDH}+\ v_{eff,ADH}+\ {\dot{n}}_{\text{NAD}^{+},feed}-\ {\dot{n}}_{\text{NAD}^{+},transfer}+\ {\dot{n}}_{NADH,oxidation}\) (8)