Optimization of Hollow-Fiber Design and Low-Pressure Membrane System Operation

An approach is presented for the numerical optimization of low-pressure membrane filtration processes. A multidimensional optimization of an ultrafiltration system is formulated for cost minimization and numerically solved for key optimal design and operating variables. Hollow-fiber ultrafiltration operation under steady-state conditions is assumed and optimized with respect to fiber radius, fiber length, crossflow velocity, transmembrane pressure, and system recovery. Optimizations are performed over variable raw water conditions using a sequential quadratic programming (SQP) algorithm. For typical small to moderately sized low-pressure membrane facilities (≈1 mgd), optimal fiber design and membrane system operation is predicted to be largely influenced by the characteristic dominance of capital costs over operating costs. Thus, total treatment costs tend to be optimal at values of decision variables where permeate fluxes are maximized, within the constraints prescribed by the system, and assuming a fixed membrane cost per unit area. For raw waters demonstrating apparent to significant membrane fouling, optimal membrane treatment is predicted to be achieved by using relatively narrow hollow fibers and relatively high crossflow velocities. For relatively clean raw waters demonstrating very high sustainable permeate fluxes, operating at low crossflow velocities—or perhaps even under the dead-end mode of operation—appears to provide the most cost-effective operation.