Optimization of Water Removal in the Press Section of a Paper Machine                                                         277 

 

 

Brazilian Journal of Chemical Engineering Vol. 27,  No. 02,  pp. 275 - 288,  April - June,  2010 

 
 
 
 

1st 

Press

Felt

Pick Up

Felt

3rd Press

Felt

4th Press

Felt

1st 

Press

Felt

Pick Up

Felt

3rd Press

Felt

4th Press

Felt

1st 

Press

Felt

Pick Up

Felt

3rd Press

Felt

4th Press

Felt

 

 

Figure 2: Press section. 

 
Felts are responsible for guiding the web, 

removing the maximum amount of water, smoothing 
the surface, and removing small marks left in the 
formation section (Reese, 2006a). The felts have 
different sizes, costs and physical characteristics. 
The felts lifetime depends on the amount of water 
they remove during their useful life. According to 
Roux and Vincent (1991), the water removal by 
pressing is usually 20 times cheaper than by drying.  
 
 

PROBLEM STATEMENT 

 

The objective is to minimize the total cost, which 

involves the cost of new felts (replacement), the cost 
of pressing and the cost of steam for the drying 
section. The assumptions are a fixed time horizon, 
different types and amount of paper that can be 
processed in the same paper machine, and the use of 
new felts at the start of the production. 
 
 

MATHEMATICAL MODEL 

 

Initially the amount of reels to be produced is 

defined. Each set of reels contains a specific type of 
paper. The total production time 

T  is given by: 

 

N

i

i 1

T

T

=

=

∑

                           (1) 

 
in which 

i

T  is the processing time for each set of reels. 

In this work the total time did not regard 

shutdowns due to unexpected events, such as rupture 

of the paper. A variable for the reels is then defined 
as follows:  
 

ik

1

for reel i processed in time interval k

x

0

otherwise

⎧

= ⎨

⎩

 

 
where each time interval does not necessarily have 
the same time length, since it depends on the 
processing time of each reel. The following 
constraints then hold: each reel (or set of reels) can 
only be processed in one interval; each interval can 
only process one reel (or set of reels). These 
assignment constraints are given by: 
 

N

ik

k 1

x

1

=

=

∑

   

i 1, , N

= …

                 (2) 

 

N

ik

i 1

x

1

=

=

∑

   

k 1, , N

= …

                 (3) 

 

Therefore, the time for each interval is given by: 

 

N

k

i

ik

i 1

t

T x

=

=

⋅

∑

                        (4) 

 
in which these variables are related to the total time 
T as follows: 
 

N

k

k 1

T

t

=

=

∑

                           (5)