General modeling and optimization with molecular weight distributions (MWDs) are essential to determine optimal designs and operations for polymerization processes. Orthogonal collocation methods in two dimensions can capture the dynamic feature of MWD in time and the distributive feature in chain length. However, there are still computational challenges for complex reactions using this method. This study proposes a general framework based on the collocation methods. For different mathematical operations caused by different types of polymeric reactions, we propose corresponding model reformulation methods with specific coefficient matrices, including moment operations caused by chain propagation and disproportionate termination, moment operation without closure caused by scission, and convolution operation caused by coupling termination. The chain-length dependent rate can also be handled well through this general framework. Case studies show the effectiveness, accuracy, and generality of our approach.

分子量分布（MWD）的常规建模和优化对于确定聚合工艺的最佳设计和操作至关重要。二维正交配置方法可以及时捕获随钻测井的动态特征和链长的分布特征。但是，使用此方法进行复杂反应仍然存在计算挑战。本研究提出了一种基于搭配方法的通用框架。对于由不同类型的聚合反应引起的不同数学运算，我们提出了具有特定系数矩阵的相应模型重构方法，包括链增长和不成比例的终止所引起的力矩操作，断裂引起的无闭合的矩操作以及偶联终止所引起的卷积操作。链长依赖性速率也可以通过此通用框架很好地处理。案例研究表明了我们方法的有效性，准确性和通用性。