Please confirm that you are discussing the PHYSICAL SIZE of the shift converter when you use the term “design”. Everyone responding is alluding to a Process Design, but you have stated that you already know the amount of catalyst required (whether calculated correctly or not) and you want to know the size (diameter and height) of the shift converter vessel. Be aware that there are two types of design: Process and Mechanical. Please confirm that you are asking for the Mechanical design.
Am I correct? There are no engineering “equations” to find diameter and height of the required vessel. There are a lot of equations for designing the mechanical strength and fabrication of the same vessel. To do the complete mechanical design, you need an experienced mechanical engineer to do the required, total ASME mechanical design. Our membership, to my knowledge, has little or no experience in doing this. If you know the catalyst quantity, you can obtain its bulk density. My experience is that you should use an acceptable superficial velocity to estimate the minimum vessel diameter. The superficial velocity is usually an experience factor and one that gives a reasonable pressure drop without catalyst bed attrition or movement. Knowing the bulk density, you obtain the height of the vessel.