The study concerns a bubble column bioreactor with biofilm on its walls in which a microbiological aerobic process occurs. The method of modelling and numerical simulation of this object is presented. The proposed mathematical model of the bioreactor takes into account: axial dispersion of the liquid and gas phase, a microbiological process in the liquid phase and the biofilm, mass transfer from the gas to the liquid and from the liquid to the biofilm, internal mass transfer resistance in the biofilm and biofilm detachment. It was shown that the system of differential equations is characterised by a large stiffness ratio exceeding 10¹⁵. Two algorithms for the determination of steady-states were proposed and compared. The one based on orthogonal collocation on finite elements used for solving the equations of liquid, gas phases and the biofilm is effective in contrast to the one based on the shooting method. It was shown that the biofilm presence positively influences the bioreactor properties, including the reduction of the substrate inhibiting effect by elimination of steady-state multiplicity.

该研究涉及在其壁上带有生物膜的鼓泡塔生物反应器，其中发生了微生物需氧过程。介绍了该对象的建模和数值模拟方法。拟议的生物反应器数学模型考虑到了：液相和气相的轴向分散，液相和生物膜中的微生物过程，从气体到液体以及从液体到生物膜的质量传递，内部质量传递生物膜和生物膜分离中的抗性。结果表明，微分方程组的特征是刚度比超过10 ¹⁵。提出并比较了两种确定稳态的算法。与基于射击方法的方法相比，一种基于对有限元素进行正交配置的方法更有效，该有限元素用于求解液相，气相和生物膜方程。结果表明，生物膜的存在对生物反应器的性能产生积极影响，包括通过消除稳态多重性而降低底物抑制作用。