Another advantage of spherical reactors is that they are the most economical shape for high pressures. As a first approximation we will assume that the fluid moves down through the reactor in plug flow. Consequently, because of the increase in cross-sectional area, Ac , as the fluid enters the sphere, the superficial velocity, , will decrease. From the Ergun equation
we know that by decreasing G, the pressure drop will be reduced significantly, resulting in higher conversions. Because the cross-sectional area of the reactor is small near the inlet and outlet, the presence of catalyst there would cause substantial pressure drop, thereby reducing the efficiency of the spherical reactor. To solve this problem, screens to hold the catalyst are placed near the reactor entrance and exit (Figures R4-1 and R4-2). Here L is the location of the screen from the center of the
reactor. We can use elementary geometry and integral calculus to derive the following expressions for cross-sectional area and catalyst weight as a function of the variables defined in Figure R4-2:
