A baffled membrane module of hollow fiber fabric can supply both countercurrent contacting and flow perpendicular to well spaced hollow fibers. The countercurrent contacting increases the number of transfer units involved in a given separation, and the perpendicular flow gives mass transfer coefficients typically five times larger than those available with other modules. The performance of such modules can be accurately predicted by a simple model verified by numerical simulation and by physical experiments. This performance is routinely better than that in more conventional designs.