The simulation of bubble columns is a computationally expensive task because of the complexity of the hydrodynamics. A novel bubble-column simulation approach attempts to increase the computational efficiency by accounting for the flow regions around individual bubbles with an algebraic flow model. To improve the accuracy and reduce the number of parameters of the flow model, the linear combination of the creeping and potential flow analytical solutions is considered as a first approximation, which is found to accurately model large portions of the flow field within the considered operating range (Re <= 270). The residual consists of significant nonlinear features, e.g., bubble wake, for which two statistically based strategies, i.e., Design and Analysis of Computer Experiments (DACE) and regression with empirical models, are evaluated. Both resulted in good fits, with the DACE strategy making fewer assumptions about the data, however, requiring more parameters. The combination of analytical and empirical models is therefore recommended for use as an accurate algebraic approximation of the flow field.