A mathematical model for anaerobic digestion in plug-flow reactors is proposed on the basis of mass balance considerations. The model consists of a system of parabolic partial differential equations for the variables representing the concentrations of the bio-components constituting the waste matrix and takes into account convective and diffusive phenomena. The plug-flow reactor is modelled as a one-dimensional domain; the waste matrix moves in the direction of the reactor axis and undergoes diffusive phenomena which reproduce the movement of the bio-components along the reactor axis due to a gradient in concentration. The velocity characterizing the convection of the waste matrix is not fixed a priori but it is considered as an additional unknown of the mathematical problem. The variation in the convective velocity allows to account the mass variation occurring along a plug-flow reactor due to the conversion of solids. The equation governing the convective velocity is derived by considering the density of the waste matrix within the reactor constant over time and the sum of the volume fractions of the bio-components constituting the waste matrix constrained to unity. The waste matrix undergoes biochemical transformations catalyzed​ by anaerobic microbial species which lead to the production of gaseous methane, the final product of the anaerobic digestion process. Biochemical processes are modelled using a simplified scheme and a differential equation is used to describe the dynamics of the produced gaseous methane. A finite difference scheme is used for the numerical integration. Model consistency is showed through numerical simulations which investigate the effect of the variation of some operating parameters on process performance. The model is then applied to a real case scenario of engineering interest. Simulations produce results in good agreement with experimental observations.

基于质量平衡考虑，提出了推流反应器中厌氧消化的数学模型。该模型由一个抛物线偏微分方程系统组成，这些变量代表构成废物基质的生物成分的浓度，并考虑了对流和扩散现象。活塞流反应器被建模为一维域；废物基质沿反应器轴方向移动并经历扩散现象，由于浓度梯度，该现象再现生物成分沿反应器轴的运动。表征废物矩阵对流的速度不是先验固定的，但它被认为是数学问题的另一个未知数。对流速度的变化允许考虑由于固体转化而沿活塞流反应器发生的质量变化。控制对流速度的方程是通过考虑反应器内废物基质密度随时间常数和构成废物基质的生物成分的体积分数之和而推导出来的。废物基质经历由厌氧微生物物种催化的生化转化，导致产生气态甲烷，这是厌氧消化过程的最终产物。使用简化方案对生化过程进行建模，并使用微分方程来描述产生的气态甲烷的动力学。数值积分使用有限差分格式。模型一致性通过数值模拟显示，该数值模拟研究了一些操作参数的变化对过程性能的影响。然后将该模型应用于工程感兴趣的真实案例场景。模拟产生的结果与实验观察结果非常一致。