- Detection of clear speech in highly reverberant and noisy enclosures is an extremely difficult problem. Recently, spherical microphone arrays have been studied that are suitable for noise reduction and de-reverberation in three dimensions. This paper presents the development of a model for investigating speech intelligibility in noisy enclosures when recorded and processed by spherical microphones arrays. The model uses the image method, diffuse sound fields, spherical array beamforming and speech intelligibility measures, to predict the array order required to overcome noise and reverberation when detecting speech in noisy enclosures. Having such a model, one can design a spherical array that overcomes given acoustic conditions, or assess whether a given problem can be solved by a practical array configuration.