Three classic ultrafiltration problems solved with the Exponential Integral

Three problems from ultrafiltration process design and analysis, typically solved using numerical methods, are solved analytically with the aid of the Exponential Integral special function. The lesson for the chemical engineering student is to always consider the possibility that analytical solutions involving special functions might exist for problems previously thought to be solvable with numerical methods only. When encountering new integrals, even ones that seem intractable, students should consider the use of a symbolic integrator to check if an easily implementable analytical solution exists, even one based on unfamiliar functions.

► Analytical solution of performance equations for batch, fed-batch and continuous single-pass ultrafiltration. ► Highlighting of the use of special functions in design calculations. ► Calculation of special functions from their series definition using Excel. ► Illustration of the use of web-based mathematics resources for solving chemical engineering problems.