Pressure retarded osmosis (PRO) and forward osmosis (FO) are osmotically driven membrane processes and emerging as viable methods for capturing clean energy and producing fresh water from sea water, respectively. The critical problems restricting the application of these processes are the accurate design and analysis of the membrane module or module configurations. Hence, a mathematical model is obtained to predict the performance of a spiral wound membrane module for osmotically driven membrane processes. Transport phenomena through the membrane are described by the previously proposed solution diffusion based model. In the current work, this model is coupled with the differential mass balances on the feed and permeate sides of the module. In addition, the Darcy's theory is used in the model to incorporate the pressure drop in the channels of module. The finite difference method is employed to solve coupled algebraic and ordinary differential equations. Here, we also employ a combination of two optimization techniques (Univariate and Fibonacci three point methods) with laboratory scale experimental data points to estimate the unknown parameters of the model. These estimated parameters are then used to predict the performance of FO and PRO at some other operating conditions and validate the mathematical model. Relatively lower maximum power density is observed at a lower draw side hydraulic pressure in the spiral wound module as compared to power density in a membrane test cell. The experimental results obtained by this module matched well with the model predictions. (C) 2015 Published by Elsevier B.V.