(311c) Recent Advances In Mean Age Theory for Quantitative Mixing Analysis

In this talk, recent advances in the mean age theory will be discussed. This theory opens a whole new paradigm for quantitatively characterizing mixing processes in chemical reactors using CFD. It is a key extension to the current residence time distribution (RTD) theory. From this theory, mean residence time and higher moments of RTD can be computed with a small fraction of CPU time required by the current unsteady tracer tracking method but with significantly better accuracy^[1]. From the solution of mean age, undesired features of a reactor, such as dead zones, short circuiting paths, etc., can easily be identified and characterized quantitatively. Such defects in reactor design can only be inferred or guessed using RTD theory.

With the solutions of mean age and the second moment of age, the degree of mixing can be computed for a steady continuous reactor^[2]. Three variances are defined. The relations of these variances explain why RTD theory can only show the closeness of a mixing process to an ideal mixer but not quantify the mixing state. These variances and the degree of mixing can be used to quantitatively compare the effects of design and operating parameters of a continuous flow stirred tank reactor (CFSTR) such as reactor aspect ratio, impeller type and locations, and inlet/outlet sizes and locations, etc.^[3] Mean age distribution can also be used to characterize the transient tracer concentration distribution in a CFSTR. The time history of tracer concentration inside the reactor can be divided into two stages, a location dependent initial stage and a location independent stationary stage. Time dependent tracer concentration equation needs to be solved for only the first stage which is about the batch blend time. The rest of the history can then be determined by the steady mean age solution. Mixing performance of a CFSTR can then be completely determined quantitatively. Mean age distribution also offers an extremely efficient method in calculating blend time in a batch stirred tank reactor. The predicted blend times are in excellent agreement with correlations in the literature^[4]. The required computing resources are orders of magnitude smaller than the current method of tracking transient tracer concentration history. This method will enable CFD to become a reliable tool for industrial reactor design and scale-up.

References

[1] Liu, M. and Tilton, J.N., 2010, "Spatial Distributions of Mean Age and Higher Moments in Steady Continuous Flows," AIChE J., 54, 2561.

[2] Liu, M., 2011, "A method for computing the degree of mixing in steady continuous flow systems," Chem. Eng. Sci., 66, 3045.

[3] Liu, M., 2011, "Prediction of Tracer Concentration and Mixing in CFSTRs with Mean Age Distribution," Ind. & Eng. Chem. Res., 50, 5838.

[4] Liu, M., 2011, "Quantitative characterization of mixing in stirred tank reactors with mean age distribution," Can. J. Chem. Eng., (available online).