The Sherwood number representing the mass transfer coefficient for transport from a moving fluid to a swarm of spherical particles is calculated in the range of high porosities. The mass transport problem is solved both analytically and numerically under the assumption of instantaneous adsorption upon the liquid-solid interface. The velocity components within the liquid phase are obtained either by using the analytical formulations of the sphere-in-cell model or by solving numerically the creeping flow problem in a stochastically constructed packing of spheres. It is found that the agreement between numerical and analytical data is in general reasonably good for the porosity range considered. Limitations of both the numerical and analytical approaches are identified. Numerical predictions are deteriorating rapidly for extremely high porosities (above 0.95). On the other hand, the accuracy of analytically obtained Sherwood values becomes weaker as the porosity decreases because the fundamental assumptions of the analytical model are not satisfied in this case.