Monomer concentration prediction and control in a polymerization process

1. In an ethylene monomer slurry polymerization process for forming solid high density polyethylene polymer particles in a reaction mixture of ethylene monomer, ethylene polymerization catalyst, and hydrogen in liquid solvent and controlling the physical properties of said polyethylene polymer particles utilizing at least one process measurement taken from said polymerization process, said polymerization process employing a densitometer to obtain the density of said polymerization reaction mixture containing said ethylene monomer, the improvement comprising:

(a) measuring at least one pressure and at least one temperature in said reaction mixture, calculating the average concentration of solids in said reaction mixture, measuring the density of said reaction mixture with said densitometer, measuring said ethylene monomer concentration, each of said measurements providing an analog signal output, and converting said analog signals to digital signals;

(b) providing a digital computer with a data base that includes said digital signals obtained from step (a);

(c) programming said digital computer according to a densitometer quadratic concentration model having constants and a real root for determining the ethylene monomer concentration in said reaction mixture, said densitometer quadratic concentration model comprising

(1) a reference temperature calculated according to the equation

TRX=measured temperature T minus 200

(2) a reference pressure is calculated according to the equation

PRX=measured pressure P minus 585.3

(3) a composition term using ethylene in mole % and hydrogen in mole % calculated using the equation,

AX

=

C

2

=

2

+

H

2

28.57

100

(4) reaction mixture liquid density polynomial terms a calculated using the equation,

DENLIQ 1= a 1 +a 2 TRX+a 3 AX+a 4 PRX+a 5 TRX*AX+a 6 TRX*PRX*AX+a 7 TRX 2

DENLIQ 2 =DENLIQ 1 +b 1 AX 2 +b 2 TRX*AX 2 +b 3 AX 2 PRX DENLIQ 3 =DENLIQ 2 +c 1 TRX 3

(5) a polyethylene polymer particle density term calculated using the equation,

DENPOL=d 1 +d 2 TRX

(6) a reaction mixture liquid density term calculated using the equation,

DENLIQ

=

100

*

slurrydensity

*

DENPOL

-

FSOLIDS

*

slurrydensity

*

DENPOL

100

*

DENPOL

-

FSOLIDS

*

slurrydensity

(7) a reaction mixture polyethylene polymer particle solids concentration term calculated using the equation,

QSOLIDS

=

100

*

DENPOL

*

(

slurrydensity

-

DENLIQ

⁢

⁢

3

)

⁢

Slurrydensity

*

(

DENPOL

-

DENLIQ

⁢

⁢

3

)

(8) said constants in said quadratic concentration model calculated are calculated according to the equations,

Q CONSTANTS= e 1 +e 2 TRX+e 3 PRX+e 4 TRX 2 +e 5 TRX 3

QA=f 1 +f 2 TRX+f 3 PRX

QB=g 1 +g 2 TRX+g 3 TRX*PRX

QC=Q CONSTANTS− DENLIQ

(9) said real root in said quadratic concentration model for the determination of the ethylene monomer concentration in said reaction mixture is calculated using the equations,

QA *( X 2 )+ QB*X+QC= 0

X

=

-

QB

-

(

QB

)

2

-

4

*

QA

*

QC

2

*

QA

and

(10) the concentration of ethylene monomer in said reaction mixture is calculated using the equation,

C

2

=

=

2

⁡

[

100

*

X

-

H

2

28.57

]

wherein “*” indicates a multiplication function, and the parameters a i , b i , c i , d i , e i , f i , g i are constants in each one of the equations shown above and their numerical values are

a

b

C

d

0.4633

−0.68998

−0.0000002

0.927

−0.0008884

−0.0300355

0.000307

−0.36508

0.0033084

0.0000462

−0.0036994

0.0000238

−0.0000082

E

f

g

0.4633

−0.68998

−0.36508

−0.0008884

−0.030055

−0.0036994

0.0000462

0.0033084

0.0000239

−0.0000082

−0.0000002

(d) calculating the physical properties comprising polyethylene polymer particle density, reaction mixture density, polyethylene solids concentration, and ethylene monomer concentration using the model of step (c) together with the database of step (b);

(e) using said calculated physical properties of step (d) as a predictor of at least one physical property of said polyethylene polymer particles produced by said polymerization process; and

(f) controlling said polymerization process based on said calculated physical properties.

2. The method of claim 1 where said predicted physical property is at least one of density and melt index.