PARTIAL STEADY-STATE DECOUPLING OF THE PRETT AND GARCIA HEAVY OIL FRACTIONATOR. Prett and Garcia presented in Ref. [7] a 7 x 5 transfer function model for a heavy oil fractionator column. Here we will consider the partial decoupling of this system by focusing on a 2 x 2 subsystem involving the top

Question

PARTIAL STEADY-STATE DECOUPLING OF THE PRETT AND GARCIA HEAVY OIL FRACTIONATOR.

Prett and Garcia presented in Ref. [7] a 7 x 5 transfer function model for a heavy oil fractionator column. Here we will consider the partial decoupling of this system by focusing on a 2 x 2 subsystem involving the top end point, and the intermediate reflux temperature as the two outputs, with top draw rate and the intermediate reflux duty as the two inputs. This subsystem has the following transfer function model:

[latex]G(s) = \begin{bmatrix}\frac{4.05 e^{-27s}}{50s + 1} & \frac{1.20 e^{-27s}}{45s + 1} \ \ \frac{4.06 e^{-8s}}{13s + 1} & \frac{1.19}{19s + 1} \end{bmatrix} [/latex] (22.80)

The steady-state gains are dimensionless, and the time delays and time constants are in minutes. Analyze the sensitivity of this system to model errors, and assess the feasibility of decoupling.

Accepted Answer

The steady-state gain matrix for this subsystem is:

[latex]K = \begin{bmatrix} 4.05 & 1.20 \ 4.06 & 1.19 \end{bmatrix} [/latex] (22.81)

with determinant:

[latex]|K|= -0.0525 [/latex] (22.82)

which is very close to zero, indicating that decoupling will be very difficult. The RGA for this system calculated in the usual manner, is:

[latex]\Lambda = \begin{bmatrix} -91.8 & 92.8 \ 92.8 & -91.8 \end{bmatrix} [/latex] (22.83)

Thus, because of the small value of the determinant of the gain matrix, and the inordinately large values of the RGA elements, we conclude that decoupling will be extremely difficult for this system.

Question 22.7: PARTIAL STEADY-STATE DECOUPLING OF THE PRETT AND GARCIA HEAV...

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