The ammonia converter size is highly dependent upon loop pressure and conversion rate. Higher loop pressure and conversion gives a smaller reactor. You must pick a catalyst (which affects conversion rate) and a reactor type (axial or radial flow? cooling method? number of beds?) and inert content (argon) in the loop. These parameters should be determined near the beginning of your project and will affect the rest of the loop design. Have you got your loop configuration and material balance nailed down? Do you know how and where you will get rid of inerts? Do you know where you will condense the ammonia product in relation to the recycle compressor? If all you have left is the detail design of the ammonia converter, the sizing will be based on the space velocity required to meet the criteria you set above. The reactor detail design will be modeled after an existing commercial reactor and one of the last things you need to do. Spend your time on getting the operating parameters right. The actual detailed reactor design should be a hand wave or two so that it looks like commercial offerings. See the process licensor brochures and manuals for examples.
One suggested reference if you can get a loaner: Ammonia: Principles and Industrial Practice (ISBN-10: 3527295933)