Polyolefin process monitoring and control
Methods of controlling olefin polymerization reactor systems are provided herein. In some aspects, the methods include a) selecting n input variables, each input variable corresponding to a process condition for an olefin polymerization process; b) identifying m response variables, each response variable corresponding to a measurable polymer property; c) adjusting one of more of the n input variables in a plurality of polymerization reactions using the olefin polymerization reactor system, to provide a plurality of olefin polymers and measuring each of the m response variables as a function of the input variables for each olefin polymer; d) analyzing the change in each of the response variables as a function of the input variables to determine the coefficients; e) calculating a Response Surface Model (RSM) using general equations for each response variable determined in step d) to correlate any combination of the n input variables with one or more of m response variables; f) applying n selected input variables to the calculated Response Surface Model (RSM) to predict one or more of m target response variables, each target response variable corresponding to a measurable polymer property; and g) using the n selected input variables I s1 to I sn to operate the olefin polymerization reactor system and provide a polyolefin product.
1. A method of controlling an olefin polymerization reactor system, the method comprising:
a) selecting n input variables I 1 , I 2 , I 3 , . . . I n , each input variable corresponding to a process condition for an olefin polymerization process;
b) identifying m response variables, R 1 , R 2 , R 3 , . . . R m , each response variable corresponding to a measurable polymer property, wherein two of the m response variables are molecular weight distribution (MWD) and short chain branching (SCB);
c) adjusting one of more of the n input variables I i to I n in a plurality of polymerization reactions using the olefin polymerization reactor system, to provide a plurality of olefin polymers and measuring each of the m response variables R 1 to R m as a function of the input variables for each olefin polymer;
d) analyzing the change in each of the response variables R 1 to R m as a function of the input variables I 1 to I n to determine the coefficients C 0 and C u (for u=1 to n) according to the following general equation for each response variable R 1 to R m :
R 1-m =C 0 +Σ u=1 u=n C u ( I u )
e) calculating a Response Surface Model (RSM) using general equations for each response variable R 1 to R m (R 1-m ) determined in step d) to correlate any combination of the n input variables I 1 to I n with one or more of m response variables R 1 to R m ;
f) applying n selected input variables I s1 , I s2 , I s3 . . . I sn to the calculated Response Surface Model (RSM) to predict one or more of m target response variables, R t1 , R t2 , R t3 , . . . R tm , each target response variable corresponding to a measurable polymer property; and
g) using the n selected input variables I s1 to I sn to operate the olefin polymerization reactor system and provide a polyolefin product.
2. The method of claim 1 , wherein the general equation for each response variable R 1 to R m is
R
1
-
m
=
C
0
+
∑
u
=
1
u
=
n
C
u
(
I
u
)
+
∑
v
=
1
v
′
C
v
(
product
of
a
unique
combination
of
2
of
I
1
to
I
n
,
independently
selected
)
wherein v′ is the total number of unique combinations of any 2 of I 1 to I n , independently selected.
3. The method of claim 1 , wherein the general equation for each response variable R 1 to R m is
R
1
-
m
=
C
0
+
∑
u
=
1
u
=
n
C
u
(
I
u
)
+
∑
v
=
1
v
′
C
v
(
product
of
a
unique
combination
of
2
of
I
1
to
I
n
,
independently
selected
)
+
∑
w
=
1
w
′
C
w
(
product
of
a
unique
combination
of
3
of
I
1
to
I
n
,
independently
selected
)
wherein v′ is the total number of unique combinations of any 2 of I 1 to I n , independently selected; and w′ is the total number of unique combinations of any 3 of I 1 to I n , independently selected.
4. The method of claim 1 , wherein the general equation for each response variable R 1 to R m is
R
1
-
m
=
C
0
+
∑
u
=
1
u
=
n
C
u
(
I
u
)
+
∑
v
=
1
v
′
C
v
(
product
of
a
unique
combination
of
2
of
I
1
to
I
n
,
independently
selected
)
+
∑
w
=
1
w
′
C
w
(
product
of
a
unique
combination
of
3
of
I
1
to
I
n
,
independently
selected
)
+
∑
x
=
1
x
′
C
x
(
product
of
a
unique
combination
of
4
of
I
1
to
I
n
,
independently
selected
)
;
wherein v′ is the total number of unique combinations of any 2 of I 1 to I n , independently selected; w′ is the total number of unique combinations of any 3 of I 1 to I n , independently selected; and x′ is the total number of unique combinations of any 4 of I 1 to I n , independently selected.
5. The method of claim 1 , further comprising the steps of:
h) measuring one or more properties of the polyolefin product corresponding to m measured response variables, R m1 , R m2 , R m3 , R mm ; and
i) repeating steps a) through h) to reduce the difference between the target response variables R t1 to R tm and the measured response variables R m1 to R mm .
6. The method of claim 1 , wherein the step of d) analyzing the change in each of the response variables R 1 to R m as a function of the input variables I 1 to I n further comprises adding the following sum to the general equation:
+Σ v=1 v′ C v (product of a unique combination of 2 of I 1 to I n ,independently selected);
wherein v′ is the total number of unique combinations of any 2 of I 1 to I n , independently selected, such that the general equation for each response variable R 1 to R m is:
R
1
-
m
=
C
0
+
∑
u
=
1
u
=
n
C
u
(
I
u
)
+
∑
v
=
1
v
′
C
v
(
product
of
a
unique
combination
of
2
of
I
1
to
I
n
,
independently
selected
)
.
7. The method of claim 6 , wherein the step of d) analyzing the change in each of the response variables R 1 to R m as a function of the input variables I 1 to I n further comprises adding the following sum to the general equation:
Σ w=1 w′ C w (product of a unique combination of 3 of I 1 to I n ,independently selected);
wherein w′ is the total number of unique combinations of any 3 of I 1 to I n , independently selected, such that the general equation for each response variable R 1 to R m is:
R
1
-
m
=
C
0
+
∑
u
=
1
u
=
n
C
u
(
I
u
)
+
∑
v
=
1
v
′
C
v
(
product
of
a
unique
combination
of
2
of
I
1
to
I
n
,
independently
selected
)
+
∑
w
=
1
w
′
C
w
(
product
of
a
unique
combination
of
3
of
I
1
to
I
n
,
independently
selected
)
.
8. The method of claim 7 , wherein the step of d) analyzing the change in each of the response variables R 1 to R m as a function of the input variables I 1 to I n further comprises adding the following sum to the general equation:
Σ x=1 x′ C x (product of a unique combination of 4 of I 1 to I n ,independently selected);
wherein x′ is the total number of unique combinations of any 4 of I 1 to I n , independently selected, such that the general equation for each response variable R 1 to R m is:
R
1
-
m
=
C
0
+
∑
u
=
1
u
=
n
C
u
(
I
u
)
+
∑
v
=
1
v
′
C
v
(
product
of
a
unique
combination
of
2
of
I
1
to
I
n
,
independently
selected
)
+
∑
w
=
1
w
′
C
w
(
product
of
a
unique
combination
of
3
of
I
1
to
I
n
,
independently
selected
)
+
∑
x
=
1
x
′
C
x
(
product
of
a
unique
combination
of
4
of
I
1
to
I
n
,
independently
selected
)
.
9. The method of claim 1 , wherein the input variables I 1 to I n comprise reactor temperature, reaction time, average residence time, ethylene concentration, α-olefin comonomer concentration, hydrogen concentration, catalyst type, catalyst concentration, co-catalyst concentration, activator concentration, reactor configuration, reactor volume, or any combination thereof.
10. The method of claim 1 , wherein the input variables I 1 to I n comprise feed rates to reactor for the catalyst, the cocatalyst, the activator, ethylene, α-olefin comonomer, hydrogen, reactor solvent, or any combination thereof.
11. The method of claim 1 , wherein the olefin polymerization reactor system uses two or more catalysts and/or two or more co-catalysts in a single reactor, and the input variables I 1 to I n comprise catalyst type and catalyst concentration for each individual catalyst and/or co-catalyst type and co-catalyst concentration for each individual catalyst.
12. The method of claim 1 , wherein the olefin polymerization reactor system is a single loop dual catalyst configuration.
13. The method of claim 1 , wherein the reactor system comprises two or more reactors in series.
14. The method of claim 1 , wherein the olefin polymerization reactor system is a dual loop dual configuration, and each reactor comprising its own set of input variables I 1(Reactor 1) to I n(Reactor 1) , and I 1(Reactor 2) to I n(Reactor 2) .
15. The method of claim 9 , wherein the catalyst type is selected from a Ziegler-Natta catalyst, a metallocene catalyst, a Phillips catalyst, or a constrained geometry catalyst.
16. The method of claim 1 , wherein the molecular weight distribution (MWD) data (response variable) is [1] measured or [2] generated using the Bernoullian model.
17. The method of claim 1 , wherein the short chain branching (SCB) data (response variable) is [1] measured or [2] generated using the Mayo-Lewis equation.
18. The method of claim 1 , wherein the polyolefin product is a copolymer.
19. A method of controlling an olefin polymerization reactor system, the method comprising:
a) selecting one or more of m target response variables, R t2 , R t2 , R t3 , . . . R tm , each target response variable corresponding to a measurable polymer property;
b) calculating n selected input variables I s1 , I s2 , I s3 . . . I sn using the calculated Response Surface Model (RSM) of claim 1 , to achieve the one or more of m target response variables, R t1 , R t2 , R t3 , . . . R tm ;
c) using the n selected input variables I s1 to I s1 to operate the olefin polymerization reactor system and provide a polyolefin product;
d) measuring one or more properties of the polyolefin product corresponding to m measured response variables, R m1 , R m2 , R m3 , . . . R mm ; and
e) repeating steps a) through d) to reduce the difference between the target response variables R t1 to R tm and the measured response variables R m1 to R mm .
20. The method of claim 19 , wherein the input variables I 1 to I n comprise reactor temperature, reaction time, average residence time, ethylene concentration, a-olefin comonomer concentration, hydrogen concentration, catalyst type, catalyst concentration, co-catalyst concentration, activator concentration, reactor configuration, reactor volume, catalyst feed rate, co-catalyst feed rate, activator feed rate, ethylene feed rate, α-olefin comonomer feed rate, hydrogen feed rate, reactor solvent feed rate, or any combination thereof.
21. The method of claim 19 , wherein the olefin polymerization reactor system is a single loop dual catalyst configuration using two or more catalysts and/or two or more co-catalysts, and the input variables I 1 to I n comprise catalyst type and catalyst concentration for each individual catalyst and/or co-catalyst type and co-catalyst concentration for each individual catalyst.
22. The method of claim 19 , wherein the olefin polymerization reactor system is a dual loop dual configuration, and each reactor comprising its own set of input variables I 1(Reactor 1) to I n(Reactor 1) and I 1(Reactor 2) to I n(Reactor 2) .
23. The method of claim 20 , wherein the catalyst type is selected from a Ziegler-Natta catalyst, a metallocene catalyst, a Phillips catalyst, or a constrained geometry catalyst.
24. The method of claim 19 , wherein the one or more targeted resin properties comprise molecular weight distribution (MWD), short chain branching (SCB), density, PSP2, M w , M n , PDI, viscosity at desired shear rates (frequencies), HMLI, I 10 , MI, Magnitude Slick Stick, F ratio Magnitude of slip stick, Young's Modulus, Yield Stress, Yield Strain, Natural Draw ratio, Strain Hardening Modulus, ESCR, FNCT, PENT, or NPT.
25. The method of claim 24 , wherein the olefin polymerization reactor system produces more than one component of the olefin polymer, and the one or more targeted resin properties comprise M w , M n , PDI, density, and fraction for each component of the polymer.
26. The method of claim 24 , wherein the viscosity at desired shear rates (frequencies) comprise Eta(0.01), Eta(0.126), Eta(1.585), Eta(19.953), or Eta(251.189).
27. The method of claim 19 , wherein the polyolefin product is a copolymer.