Plate heat exchangers (PHEs) used in milk thermal treatments are subject to rapid fouling, while Cleaning-in-Place (CIP) produces large amounts of wastes. Up to 80% of production costs in the dairy industry have been attributed to the effects of fouling and cleaning.

In spite of decades of research, a detailed model for simulation, monitoring, control and optimisation of full heating and cleaning cycles for PHEs is still not available. Mechanistic simulation models based on differential equations typically address only fouling but not cleaning. More detailed models based on Computational Fluid Dynamics (CFD) are computationally very expensive and impractical to use for optimization, scheduling and control of complete PHEs.

Here, a dynamic 2D model of PHEs is presented that enables optimizing milk thermal treatment operations, taking into account both fouling and cleaning. The model balances predictive accuracy and computational feasibility.

It integrates: (i) various mechanisms and kinetics for fouling and cleaning; (ii) a detailed moving boundary model of deposit growth that captures its spatial distribution; (iii) a dynamic thermo-hydraulic model of mass and heat transfer in a single PHE channel; (iv) the flexible assembly of channels into a variety of PHE configurations, and (v) the flexible definition of heating-cleaning cycles.

The fouling model has been validated for two PHE configurations against experimental data, with excellent results. Alternative fouling mechanism (due to aggregate proteins or denatured proteins, and with/without deposit re-entrainment) have been explored. Results show that the fouling observed in the two arrangements is best fitted by distinct fouling models, and that the performance of the two PHE arrangements is quite different.

Dynamic cleaning models have been integrated with the deposit moving boundary model and validated. This has enabled for the first time the seamless, detailed simulation of individual and multiple heating-cleaning cycles, where each phase starts from the detailed deposit distribution at the end of the previous phase. The models detail enables the introduction of sophisticated condition-based logic in the operation of each phase and overall cycle. Using such condition-based logic it is shown that cleaning time could potentially be reduced by ∼50%. Finally, it is shown that the heating/cleaning cycle can be optimized for maximum productivity, balancing fouling and cleaning trade-offs. This is demonstrated for one of the PHE arrangements.

牛奶热处理中使用的板式换热器（PHE）容易结垢，而就地清洗（CIP）则产生大量废物。乳制品行业高达80％的生产成本归因于结垢和清洁的影响。

尽管进行了数十年的研究，但仍无法获得用于模拟，监控，控制和优化PHE完整加热和清洁周期的详细模型。基于微分方程的机械仿真模型通常仅解决结垢问题，而不解决清洁问题。基于计算流体动力学（CFD）的更详细的模型在计算上非常昂贵，并且对于完整PHE的优化，调度和控制而言，不切实际。

在此，提出了动态PHE的2D模型，该模型能够在考虑结垢和清洁的同时优化牛奶热处理操作。该模型平衡了预测准确性和计算可行性。

它整合了：（i）结垢和清洁的各种机制和动力学；（ii）反映其空间分布的详细的存款增长动边界模型；（iii）在单个PHE通道中进行传质和传热的动态热工水力模型；（iv）将通道灵活地组装成各种PHE配置，以及（v）灵活定义加热清洁周期。

结垢模型已针对实验数据针对两种PHE配置进行了验证，并获得了出色的结果。已经探索了替代的结垢机制（由于聚集蛋白或变性蛋白，以及有/没有沉淀物的重新夹带）。结果表明，在两种布置中观察到的污垢最适合于不同的污垢模型，并且两种PHE布置的性能差异很大。

动态清洁模型已与沉积物移动边界模型集成并得到验证。这首次实现了对单个和多个加热清洁循环的无缝，详细的模拟，其中每个阶段都从上一阶段结束时的详细沉积物分布开始。这些模型的详细信息可在每个阶段和整个周期的操作中引入基于条件的复杂逻辑。使用这种基于条件的逻辑表明，清洁时间可能会减少约50％。最后，表明可以优化加热/清洁周期以获得最大生产率，平衡结垢和清洁折衷。PHE安排之一证明了这一点。