Method for controlling a rectification column
The present invention relates to a method of controlling a concentration of a first component of a rectification column for separating a binary mixture of the first component with a second component on the basis of temperature measurements, wherein a control path defined by temperature sensors (T 3 , T 2 , T 6 ) arranged in the longitudinal direction of the column is linearized with the aid of an estimated temperature profile, wherein a real temperature profile T*(h), determined by means of the temperature sensors, is approximated by a function T(h) in dependence on a column height h, wherein the column id divided into two sections along the column height h and the function T(h) is defined section by section on the basis, in each case, of a logistical function.
1. A method of controlling a concentration of at least one first component in a rectification column for separation of a binary mixture of the first component with a second component based on temperature measurements, the method comprising:
(a) linearizing a control zone defined by temperature sensors arranged in the longitudinal direction of the rectification column with the aid of an estimate of a temperature profile, and
(b) approximating a real temperature progression T*(h) determined by means of the temperature sensors by a function T(h) as a function of a column height h, wherein:
(i) the column is divided into two sections over the column height h, and
(ii) the function T(h) is defined in sections on the basis of one logistic function in each section.
2. The method of claim 1 , in which the logistic functions are formed on the basis of a logistic function of the following form:
f
(
x
)
=
e
x
1
+
e
x
.
3. The method of claim 1 , wherein:
T
(
h
)
=
{
T
ab
(
h
)
,
h
<
h
feed
T
v
(
h
)
,
h
≥
h
feed
where T ab (h) and T v (h) are defined on the basis of one logistic function each and h feed defines the column height at which a solution consisting of 40% by volume to 60% by volume of the first component and 40% by volume to 60% by volume of the second component is fed to the column.
4. The method of claim 3 , in which:
T
v
(
h
)
=
T
0
,
v
+
v
v
·
e
(
h
-
h
0
,
v
)
k
v
1
+
e
(
h
-
h
0
,
v
)
k
v
T
ab
(
h
)
=
T
0
,
ab
+
v
ab
·
e
(
h
-
h
0
,
ab
)
k
ab
1
+
e
(
h
-
h
0
,
ab
)
k
ab
where T is normalized to boiling temperatures T_1 and T_2 of the corresponding first and second components, with 0%=T_1 and 100%=T_2 and h is normalized to an absolute column height H and T(h)=T v (h) for h ϵ [x %, 100%] in a rectifying section v, T(h)=T ab (h) for h ϵ [0%, x %] in a stripping section ab of the column height h with 0<x<100, and where T 0,v and T 0,ab are respective support vectors for the temperature, v v and v ab are a respective range for the temperature, k v and k ab are a respective shrinkage in the direction of the column height h, and h 0,v and h 0,ab are a respective support vector of the height h.
5. The method of claim 4 , wherein x is 24.
6. The method of claim 4 , in which the respective shrinkage k v or k ab in the direction of the respective height is ascertained from a comparison of a slope of the logistic function f(x) at its inflection point and the measured temperature progression T*(h) at its inflection point, wherein the inflection point of T*(h) is calculated from an average of respective slopes at a respective inflection point of temperature progressions ascertained from disturbance tests.
7. The method of claim 6 , in which h 0,v and h 0,ab are each determined by a parameter estimate.
8. The method of claim 7 , in which the Gauss-Newton method is employed for estimation.
9. The method of claim 4 , in which a value range of T v (h) is between the boiling point of the first component and the feed temperature (T 5 ) and hence T 0,v (h)=0 and v v =T feed and a value range of T ab (h) is between the feed temperature (T 5 ) and the boiling point of the second component and hence T 0,ab (h)=T feed and v ab =1−T feed , where 1 corresponds to the boiling point of the second component.
10. The method of claim 4 , in which a value range of T v (h) is between the boiling point of the first component and the feed temperature (T 5 ) and hence T 0,v (h)=0 and v v =T feed .
11. The method of claim 3 , in which:
T
v
(
h
)
=
T
0
,
v
+
v
v
·
e
(
h
-
h
0
,
v
)
k
v
1
+
e
(
h
-
h
0
,
v
)
k
v
T
ab
(
h
)
=
T
0
,
ab
+
v
ab
·
e
(
h
-
h
0
,
ab
)
k
ab
1
+
e
(
h
-
h
0
,
ab
)
k
ab
where T is normalized to boiling temperatures T_1 and T_2 of the corresponding first and second components, with 0%=T_1 and 100%=T_2 and h is normalized to an absolute column height H and T(h)=T v (h) for h ϵ [x %, 100%] in a rectifying section v, T(h)=T ab (h) for h ϵ [0%, x %] in a stripping section ab of the column height h with 0<x<100, and where T 0,v and T 0,ab are respective support vectors for the temperature, v v and v ab are a respective range for the temperature, k v and k ab are a respective shrinkage in the direction of the column height h, and h 0,v and h 0,ab are a respective support vector of the height h, and
in which a transition of the logistic functions is determined by a temperature (T 5 ) at a feed to the column.
12. The method of claim 11 , in which a value range of T v (h) is between the boiling point of the first component and the feed temperature (T 5 ) and hence T 0,v (h)=0 and v v =T feed .
13. The method of claim 11 , in which a value range of T ab (h) is between the feed temperature (T 5 ) and the boiling point of the second component and hence T 0,ab (h)=T feed and v ab =1−T feed , where 1 corresponds to the boiling point of the second component.
14. The method of claim 1 , in which a transition of the logistic functions is determined by a temperature (T 5 ) at a feed to the column.
15. The method as claimed of claim 1 , in which the first component comprises 1,2-dichlorobenzene (ODB) and the second component comprises COCl 2 (phosgene).
16. A system comprising a rectification column that executes the method of claim 1 .