A biological water treatment consists basically of a reaction tank where bacteria decompose and consume the existing polluting substances. When these substances are sufficiently removed, the water has to be separated from the sludge. This sludge is mainly the bacteria, so the most part is recycled in the reaction tank. Only the excess sludge, formed by bacterial growth through consuming the unwanted compounds, is actual waste that has to be removed.
To get clean water, separated from the sludge, there are different methods. Classic sedimentation is an option, possibly with a sand filtration or dead-end ultrafiltration afterwards. With MBR (or membrane bioreactor) specifically, the separation is done with membrane technology. Roughly one could compare this to a crossflow ultrafiltration treatment. The permeate stream through the membrane will then be free of sludge.
To design an MBR, important parameters to know in advance are the suspended solid concentration and the desired flow of clean permeate water.
In case of large capacity, airlift membranes can be chosen.
PCA can help you with this technology, both in design and construction of the installation.