(761d) Prediction-Correction Method for Optimization of Nonlinear SMB Separations

Simulated moving bed (SMB) chromatography is a
powerful continuous separation technique that is being used for more and more
applications in the food, petrochemical, and pharmaceutical industries. In
practice the SMB operation is difficult to optimize, especially in cases where
the adsorbing components of a mixture have nonlinear isotherms. Due to the
complex dynamics SMB operators commonly use heuristic approaches and manual
tuning to find operating conditions that satisfy high purity constraints with
some safety margins. These operating conditions may be conservative and achieve
suboptimal productivity or desorbent consumption.

We propose the prediction-correction method which
uses model-based optimization, SMB experimentation, and parameter estimation to
optimize the SMB operation in a systematic manner. The prediction-correction
(PC) algorithm (Figure 1) is designed to improve the process development stage
of SMB operation by rapidly finding the optimal operating conditions that
achieve design objectives. We use an iterative scheme where the optimal
operating conditions are predicted by solving a model-based optimization
problem and these are implemented in the SMB. Then the model parameters are
refined by fitting our model to the SMB experimental results. The refined
parameter set is used to again predict the optimal operating conditions and
these are successively implemented until the termination criteria are
satisfied. Thus, the PC method reduces the task of SMB process development into
solving a sequence of computational problems.

We show that the PC method was successfully used to
optimize the separations of linear and nonlinear isotherm systems. For the
linear isotherm system we used uridine and guanosine, and for the nonlinear
system we used cyclopentanone and cyclohexanone. For both systems the PC method
was successfully used to find optimal operating conditions where greater than
96% purity is achieved in each product stream while maximizing productivity. The
SMB experiments can be terminated before reaching the
cyclic steady state, and the operating conditions can be
updated online. In Figure 2 we show an example from the linear system results
of how the optimal operating conditions are achieved, and the PC algorithm converges
in only three iterations.

The PC algorithm can also be used to identify a
sufficient adsorption isotherm model for SMB optimization. We show in a case
study with cycloketones that a single-component Langmuir isotherm was
updated
to a competitive Langmuir isotherm, which led to better
fitting.  This isotherm model update allows
the
PC algorithm to find the optimal operating point
quickly
with
greatly increased productivity, while it may result in suboptimal
productivity without the isotherm update.

Figure
1. Prediction-correction algorithm

Figure
2. SMB experimental concentration data and simulated concentration profiles
using our model. The product purities are improved by implementing optimal
operating conditions, u_i once the model parameters are refined
by fitting the previous experimental data set in each iteration k.