Predictive model for density and melt index of polymer leaving loop reactor

1. A method comprising:

selecting operating conditions in a double loop slurry reactor to produce a polymer of a pre-determined density and a pre-determined melt flow index prior to polymerization of the polymer, by:

selecting n input variables that are linked to operating conditions;

defining a constrained neural network model of the general form:

ƒ 1 =1/(1+exp(−( a 11 *X 1 +a 12 *X 2 +a 13 *X 3 + . . . +b 1 )))

ƒ 2 =1/(1+exp(−( a 21 *X 1 +a 22 *X 2 +a 23 *X 3 + . . . +b 2 )))

ƒ 3 =1/(1+exp(−( a 31 *X 1 +a 32 *X 2 +a 33 *X 3 + . . . +b 3 )))

. . .

Res= 1/(1+exp(−( a (n+1)1 *ƒ 1 +a (n+1)2 *ƒ 2 +a (n+1)3 *ƒ 3 + . . . +b (n+1) )))

wherein the X i 's are n normalised input variables, the a ij 's and b i 's are numerical coefficients, the f i 's are intermediate functions, and Res is a resulting scaled polymer property estimate;

separately for the specified density and the specified melt flow index, adjusting numerical coefficients in the constrained neural network model to minimise error on Res under constraints, such constraints being imposed by equalities or inequalities on X i 's, a ij 's, b i 's, f i 's, Res, any partial derivative X i 's of any order, any partial derivative a ij 's of any order, any partial derivative b i 's of any order, any partial derivative f i 's of any order, any partial derivative Res of any order, or combinations thereof, wherein the partial derivatives measure variations of results derived from the constrained neural network model when only one of the input variables is changed by an infinitesimal step;

predicting a density and a melt flow index resulting from the operating conditions using the constrained neural network model;

inferring values for any combination of two input variables X i and X j , knowing the other (n−2) input variables, the specified density, and the specified melt flow index;

calculating an average amount of the polymer product in each reactor in order to use the constrained neural network model to infer estimates of a density and a melt flow index of the polymer product leaving each reactor of the double loop slurry reactor resulting from the operating conditions;

wherein the polymer product in each reactor includes polymer product that is synthesized within that reactor, or a combination of the polymer product that is synthesized within that reactor and polymer product that is admitted into that reactor from an upstream reactor;

wherein the input variables are determined before polymerisation is started to simultaneously obtain the pre-determined density and the pre-determined melt flow index for the polymer.

2. The method of claim 1 , wherein the polymer is a homopolymer comprising ethylene, or wherein the polymer is a copolymer comprising ethylene and 1-hexene.

3. The method of claim 1 , wherein the input variables comprise polymerisation temperature, ethylene concentration, amount of hydrogen, and amount of 1-hexene in a feed.

4. The method of claim 3 , wherein the input variables further comprise pressure in the double loop slurry reactor, catalyst concentration, activating agent concentration, reaction additive concentration, catalyst characterising parameters, production rate, solids concentration, and solids residence time.

5. The method of claim 1 , wherein the inferred values of the two input variables X i and X j are an amount of hydrogen and an amount of 1-hexene.

6. The method of claim 1 , wherein the catalyst system is based on a bridged bistetrahydroindenyl catalyst component.

7. The method of claim 1 , further comprising using the constrained neural network model to determine corrections to be applied to the operating conditions when the polymer product is off specifications.

8. The method of claim 7 , wherein the corrections are manually applied to an amount of hydrogen and 1-hexene.

9. The method of claim 8 , wherein the amount of hydrogen and 1-hexene are corrected to modify the density and the melt flow index.

10. The method of claim 7 , further comprising preparing a table of the corrections to be manually applied to the operating conditions in order to return the polymer product to target specifications.

11. The method of claim 10 , wherein the corrections are expressed in the table as grams of hydrogen per ton of ethylene/kilograms of 1-hexene per ton of ethylene.

12. The method of claim 1 , further comprising observing a temporal evolution of each input variable in response to a step modification of a single input variable of the constrained neural network model to determine dynamical response.

13. The method of claim 12 , wherein variation of an input variable that has a permanent effect has an integrating response that is approximated by a second-order linear dynamic response.

14. The method of claim 13 , wherein the input variable that has the permanent effect is a catalyst poison.

15. The method of claim 1 , wherein the density and the melt flow index are predicted in real time.

16. The method of claim 1 , wherein the average of the amount of polymer product in each reactor of the double loop slurry reactor is calculated at each moment in the past.

17. The method of claim 1 , wherein the selected operating conditions are manually set up prior to polymerization of the polymer.

18. The method of claim 17 , further comprising manually applying corrections to the operating conditions when the polymer product is off specifications.

19. The method of claim 18 , further comprising preparing a table of the corrections to be manually applied to the operating conditions in order to return the polymer product to predetermined specifications.