Abstract

The problem of a three-dimensional catalyst pellet with three characteristic sizes a, b, and c under conditions of intradiffusion resistance and a first-order reaction has been discussed. Using an exact solution in the Cartesian coordinate system, dependences for calculating the equivalent size and effectiveness factor of the pellet on Thiele parameter ψ have been proposed. A specific feature of the solution is the dependence of the pellet shape on the Thiele parameter. In dimensionless coordinates, at ψ → 0, the pellet surface tends to a sphere with unit radius; at ψ → ∞, it assumes the shape of a regular octahedron, the vertices of which are localized on the coordinate axes at a unit distance from the origin. In dimensional coordinates, depending on the ratio of parameters a, b, and c, the pellet can assume shapes similar to those of ellipsoids, discs, or “cigars.” At high Thiele parameter values, the effectiveness factor of nonspherical and spherical pellets is described by a single dependence equal to 3/ψ.

中文翻译：

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内扩散阻力对非球形催化剂球团化学过程的影响

摘要

具有三个特征尺寸a、b和c的三维催化剂颗粒的问题在内部扩散阻力和一级反应的条件下进行了讨论。使用笛卡尔坐标系中的精确解，已经提出了计算颗粒等效尺寸和有效性因子对蒂勒参数 ψ 的依赖关系。该解决方案的一个特定特征是丸粒形状对 Thiele 参数的依赖性。在无量纲坐标中，ψ → 0 处，颗粒表面趋向于单位半径的球体；在 ψ → ∞ 处，它呈现正八面体的形状，其顶点位于距原点单位距离的坐标轴上。在维度坐标中，取决于参数a、b和c的比率，小球可以呈现类似于椭圆体、圆盘或“雪茄”的形状。在高蒂勒参数值下，非球形和球形丸粒的有效性因子由等于 3/ψ 的单一相关性描述。