Karlstads universitet 651 88 Karlstad

Tfn 054-700 10 00 Fax 054-700 14 60

Information@kau.se www.kau.se

Faculty of technology and science

Department of Chemical Engineering

ARIF HUSSAIN

Evaluation of Different

Models for Flow through Paper

Chemical Engineering

Master thesis

Supervisor Lars Nilsson

Examiner Lars Jarnström

2 | P a g e

This thesis is dedicated to my parents and my family for their love, endless support and

encouragement.

3 | P a g e

Table of Contents ABSTRACT .................................................................................................................................................. 4

SAMMANFATTNING PÅ SVENSKA ....................................................................................................... 4

1 SUMMARY .......................................................................................................................................... 4

2 INTRODUCTION ................................................................................................................................ 5

2.1 Flow Models. ................................................................................................................................ 8

2.1.1 Darcy‟s flow Equation. ......................................................................................................... 8

2.1.2 Forchheimer flow Equation. ................................................................................................. 9

2.1.3 Air Flow-Considering Compressibility Effects. ................................................................. 10

2.1.4 Missbach flow Model.......................................................................................................... 11

2.2 Flow Regimes in Porous Media .................................................................................................. 11

2.3 Aim of the present study. ............................................................................................................ 12

3 MATERIALS AND METHODS ........................................................................................................ 14

3.1 Laboratory Hand Sheet Former................................................................................................... 14

3.2 Bendtsen Air Permeance ............................................................................................................. 14

3.3 Modified Hand Sheet Former ..................................................................................................... 15

3.4 Air Flow Using Dewatering Equipment ..................................................................................... 15

3.5 Estimation of Pressure Increase. ................................................................................................. 15

3.6 Thickness Measurements ............................................................................................................ 16

3.7 Fiber Master Analysis ................................................................................................................. 16

3.8 Reproducability of Results. ......................................................................................................... 16

3.9 Air Leakage Experiments............................................................................................................ 16

4 RESULTS AND DISCUSSION ......................................................................................................... 17

4.1 Bendtsen Air Flow ...................................................................................................................... 17

4.2 Reynolds number for Bendtsen air flow. .................................................................................... 21

4.3 (Dewatering Equipment) Pressure Increase vs Dwell time. ........................................................ 21

4.4 Air Velocity vs. Sheet Basis Weight (Dewatering Equipment) .................................................. 22

4.5 Inertial effects and Turbulent flow. ............................................................................................. 24

4.6 Flow Models for High Velocity Air Flow. ................................................................................. 24

4.7 Leakage Experiments .................................................................................................................. 26

5 CONCLUSION ................................................................................................................................... 27

6 NOMENCLATURE ........................................................................................................................... 28

7 REFERENCES ................................................................................................................................... 29

8 ACKNOWLEDGEMENT .................................................................................................................. 30

9 APPENDIX ......................................................................................................................................... 31

4 | P a g e

ABSTRACT

For understanding the energy use during vacuum dewatering and through air drying

process, air flow through highly complex structure of paper has been investigated.

Experiments were performed for a wide range of pressure drops and basis weights. In

addition the pulp samples are refined to three different beating degrees. The calculated

Reynolds numbers, based on the fiber diameter, varies in a wide range between 0.0002 and

80. The majority of data at low Reynolds number (below approximately 0.2) agree rather

well with Darcy‟s law, so that the air flow is proportional to the pressure drop and inversely

proportional to the grammage. However, the data at high Reynolds number obtained from

air flow experiments using vacuum dewatering equipment, where large amount of air

sucked through the web have more news value. Different mathematical models for flow

through porous media are investigated to see how well they can describe the experimental

findings at high Reynolds numbers. It was found that for high Reynolds number flow, the

flow rate is a unique function of the quotient of pressure drop and grammage for a specific

degree of beating. It was also found that increased beating leads to a reduced air flow

through the sample. However, no clear conclusion regarding the importance of

compressibility and inertial forces when modeling the process could be made.

SAMMANFATTNING PÅ SVENSKA

För att bättre kunna beskriva energianvändning vid vakuumavvattning och

genomblåsningstorkning har luftflödet genom det komplexa pappersmaterialet mätts upp

för en lång rad olika tryckfall och ytvikter. Även malningens inverkan på luftflödet genom

pappersstrukturen har undersökts. Reynolds tal har bestämts baserat på fiberdiametern och

för de redovisade försöken varierar Reynolds tal i ett stort område mellan 0.0002 och 80.

Huvuddelen av de uppmätta flödeshastigheterna vid låga Reynolds tal (upp till ungefär 0.2)

stämmer relativt väl överens med Darcys lag, så att luftflödet är proportionellt mot

tryckfallet och omvänt proportionellt mot ytvikten. Vid högre värden på Reynolds tal har

luftflödesmätningar utförts i en utrustning konstruerad för att studera vakuumavvattning.

Vid vakuumavvattning strömmar stora luftmängder genom arket och de här data har större

nyhetsvärde. Olika matematiska modeller för strömning genom porösa material utvärderas

avseende hur väl de beskriver de uppmätta data vid höga värden på Reynolds tal. Det visar

sig att även vid höga värden på Reynolds tal är strömningshastigheten en unik funktion av

kvoten mellan tryckfall och ytvikt för en specifik malgrad. Ett annat resultat är att ökad

malning leder till ett minskat flöde genom arket. Det gick inte att dra några definitiva

slutsatser beträffande bidraget av friktion respektive tröghetskrafter till det totala tryckfallet

över arket.

1 SUMMARY The flow rate of air through a porous material depends on the thickness, the pore size, pore shape and on

the viscosity of the flowing material and on the pressure drop. Usually the velocity (u), of a fluid flowing

through a porous material is modelled according to Darcy‟s law:

Equation 1

5 | P a g e

where K represents the permeability of the material (influenced by pore size and shape); µ is the

viscosity, ΔP is the pressure drop and L is the thickness of the material.

Darcy‟s law is strictly applicable only for incompressible fluids. For higher flow rates, Darcy‟s law can

no longer be applied. The limit for applying Darcy‟s law is determined by the Reynolds number, and

often a limit for the applicability of Darcy‟s law is stated as Re < 1, although it is sometimes not so easy

to define the characteristic pore diameter in a stringent way. The purpose of the study is to give an

overview of flow rate of air through material in paper manufacturing, which is of great importance when

calculating the energy use for vacuum dewatering. Bendtsen air permeance tester and the vacuum

dewatering equipments were used. For measuring air flow through paper at lower pressure drops by

Bendtsen air permeance tester, sheets with different basis weights were prepared using laboratory hand

sheet former from unbeaten pulp and pulp beaten at three different numbers of revolutions. On the other

hand, for measuring air flow through paper at higher pressure drop or high air velocity by vacuum

dewatering equipment, sheets were prepared using modified hand sheet former typically designed for

dewatering equipment. Pressure drops of 0.74, 1.47 and 2.20 kPa were used to estimate air flow rate using

Bendtsen air permeance tester. Similarly for dewatering experiments, pressure drops of 20, 40 and 60 kPa

were used to estimate air flow through paper. Each laboratory sheets (20-300) g/m2 basis weight made

from unbeaten pulp and pup beaten at 1000, 2000 and 3000 revolutions was then investigated for air flow

at three different pressure drops of Bendtsen air permeance tester. For vacuum dewatering experiments,

the formed sheets were then placed into the sample holder of the vacuum dewatering apparatus. The

velocity was set so that dwell times of 1, 1.5, 2, 4, 8, 12, 16 and 20 ms were achieved. The plate is

accelerated rapidly and the air is able to pass through the sample at different dwell times and pressure

drop. The pressure difference in the vacuum tank was then recorded using Dewa-soft software by

exporting the files into MS-Excel. The sheets were then saved to measure the thickness later on. For

Bendtsen air permeance experiments, the applicability of Darcy‟s law was confirmed for sheets of

different basis weights (20-300) g/m2, produced from unbeaten pulp and pulp beaten at three different

revolutions. However, there are deviations from Darcy‟s law for low grammage sheets i.e. 20 g/m2. The

majority of the calculated Reynolds numbers are also in the range where Darcy‟s law is normally

expected to be applicable. Other results are that increased refining leads to less amount of air flow

through the sheets. Also, it was found that a lower grammage sheet accommodates large flow rates as

compared to higher grammage sheets.

However, the results from vacuum dewatering experiments show deviation from Darcy‟s law. The

calculated Reynolds numbers are high enough to follow laminar or viscous flow. The experimental results

are then compared with different theoretical models for flow through porous media. The model based on

theory in which inertial forces are dominating when taking compressibility into account seems to be

suitable for experiments at 2 ms dwell time. The deviations from Darcy‟s law are smaller for the 12 ms

dwell time. The reason behind this is not clear. However, the influence of any type of “offset” effects will

be greater when evaluating the flow rate based on the shorter dwell time 2 ms. It was found that for high

Reynolds number flow, the flow rate is a unique function of the quotient of pressure drop and grammage

for a specific degree of beating. Also the air flow, by decreasing the sheet basis weight increases at first

slightly, then with a big jump between 50 g/m2

and 20 g/m2 sheets basis weight. Further results are that,

the lower basis weight sheet allows more air to penetrate in terms of pressure increase through it. An

important finding was that superficial air velocity decreases as degree of beating increases.

2 INTRODUCTION For predicting through air drying process and for the understanding of energy use during vacuum

dewatering in paper manufacturing, adequate description of the transport mechanisms involved is crucial.

Previously research made by different researchers is based on theory originally developed for flow

through porous media. This study dealt with the characterization of the paper structure and the description

of flow through porous media, especially its applicability to paper. Most of the theories presented by

different researchers were originally developed for well defined geometries of porous media, such as

packed spheres, and application to the highly complex structure of paper provides a new challenge.

6 | P a g e

Paper is highly complex porous medium made up from wood which consists mainly of three different

polymeric substances: cellulose, hemicelluloses and lignin. Dullien (1979), define porous media as a

material or a structure which passes at least one of the following two tests.

1. “It must contain spaces, so called pores or voids, free of solids, imbedded in the solid or

semisolid matrix. The pores usually contain some fluid, such as air, water, oil, etc., or a

mixture of different fluids”.

2. “It must be permeable to a variety of fluids, i.e., fluids should be able to penetrate through

one face of a septum made of the material and emerge on the other side. In this case one

refers to a „permeable porous material”.

The structure of paper is strongly influenced by the raw material, i.e. tree species and the pulping process,

and also by the paper formation technique. Within the paper structure, fibers are oriented approximately

parallel to the sheet surface; in this plane however the fibers are more or less randomly oriented. The

process of dewatering and paper drying highly depends on the porous paper structure. The main

parameters describing the porous structure of paper are porosity, specific surface area, pore size

distribution and permeability. There are many different techniques for determining these parameters and it

is important to be aware that the obtained results depend on both the method used and on other factors

previously mentioned, such as pulp type and the paper formation process. The most important factor

determining the drying rate is the air permeability (Polat et al. 1992). “Permeability” is the term used for

the conductivity of the porous medium with respect to permeation by a Newtonian fluid. “Permeability”,

used in this general sense, is of limited usefulness only because its value in the same porous sample may

vary with the properties of the permeating fluid and the mechanism of permeation (Dullien, 1979).

Porosity is also an important parameter when discussing flow through porous medium. This is same as

volume fraction of gas in the material. When dealing with paper drying, where besides fibers and air also

water is present, it is often convenient to define the porosity or volume fraction of gas as follows:

Equation 2

Where εg, εs and εw are the volume fraction of gas, solid and water respectively, ρs is the fiber density, ρw

is the water density, G is the basis weight, R is the paper moisture ratio and z is the paper thickness. In

order to determine the porosity the fiber density, paper thickness, basis weight and moisture ratio have to

be determined. Measured porosities may vary slightly depending on method due to the compressibility of

paper and due to surface effects.

Another important parameter when discussing flow through porous medium is the specific surface area.

The specific surface area of paper is usually determined through optical methods (based on reflectance) or

solution or gas (N2) adsorption, in each case in conjunction with the BET method (Braunauer, Emmet and

Teller). By using some form of the Kozeny-Carman equation, which relates properties like porosity,

tortuosity and specific surface area to permeability, it is possible to determine the specific surface area

from gas and liquid permeation experiments. The average pore size and pore size distribution are also

important factors when it comes to flow through porous medium. There is no experimental technique to

directly describe the actual pore size (radius) of a paper structure since the shapes of the pores are highly

irregular and this parameter is not a single value but can be described only as an average pore size or by

the pore size distribution within the structure. A porous medium can be defined as a solid body which

contains void spaces or pores that are distributed randomly; without any conceivable pattern throughout

the structure of the solid body. Extremely small voids are called molecular interstices and very large ones

are called caverns or vugs. Pores (intergranular and intercrystalline) are intermediate between caverns and

molecular interstices. Fluid flow can only take place in the inter-connected pore space of the porous

media; this is called effective pore space.

Fluid flow through porous medium is an important subject. For flow through porous medium, it is

desirable to be able to predict the flow rate obtainable for a given energy input (usually measured as

7 | P a g e

pressure drop) or to be able to predict the pressure drop necessary to achieve a specific flow rate. As the

drying rate in through-drying is very sensitive to the air flow rate, knowledge about the relationship

between air flow rate and applied pressure difference is critical for any prediction regarding dryer

capacity or economics. To describe the relationship between pressure drop and superficial velocity for

flow through porous media in case of paper material accurate models for describing this process are

lacking in the open literature. A few studies by previous researchers are; Polat et al. (1989), determined

for 25 and 50 g/m2

sheets basis weight and for superficial velocities in the range of 0.1 to 1.2 m/s. They

found the Missbach equation (equation 3) exponent (n) to range between 1.24 and 1.07.

Equation 3

Polat et al. (1992) measured the rate of through drying paper in the constant drying rate period for 210

combinations of temperature and through flow rate of air, basis weight, and initial moisture content of

paper. They found that for paper heavier than that which is through dried industrially, the Sherwood

number at high Reynolds numbers approaches independence from the paper thickness. However for thin

paper, they found that end effects predominate. Polat et al. (1993), in their experiments clearly

demonstrate that air flow through paper cannot be treated as purely viscous even at a flow rate of 0.6 m/s

for 150 g/m2 paper. They did experiments with through flow rates of 0.08-0.70 kg/m

2s (0.07-0.60 m/s

superficial velocity) with air and with much higher kinematic viscosity, helium at through flow rates of

0.02-0.20 kg/m2s (0.12-1.20 m/s superficial velocity). The averaged measurements were then fitted to the

equation 3 to obtain the value of exponent n listed in Table 1.

The results presented in Table 1 also indicate that when air is replaced by helium, which has a kinematic

viscosity about 7.5 times higher than that of air, the inertial contribution to the pressure drop decreases. It

is however evident that even for helium flow there is substantial inertial contribution to the pressure drop

for the lowest basis weight i.e. 25 g/m2, since the value of the exponent n in equation 3 is higher than 1.0.

A value of n of 1.0 corresponds to a case without an inertial contribution.

Table 1 Exponent n for flow through dry paper of different basis weight sheets. (Polat et al. 1993)

Fluid Basis weight, g/m

2

25 50 100 150 250

Air Flow 1.24 1.07 1.05 1.02 1.01

Helium Flow 1.08 1.01 1.00 1.00 1.00

Polat et al. (1992-93), in their analysis of through air drying of paper have shown that basis weight,

moisture content, and furnish type can significantly affect the water removal rate during through air

drying. Weineisen et al. (2005) studied the effects of pore size distribution on the average drying rate.

They have shown how larger pores dry out and then act as bypass channels for the drying air. They

developed model in combination with correlations for heat and mass transfer for through drying of tissue

based on the equation of continuity. The model incorporates different geometric descriptions together

with corresponding heat and mass transfer correlations for flow through cylindrical conduits and flow

through packed beds of cylindrical fibers. At low air flow rates and low drying temperature, the model

shows very good agreement, however at higher drying intensities, the model predicts drying rates that are

generally higher than what is found in experimental studies described in the literature. Their results also

show that the early onset of the falling rate period in through drying at higher intensities could be

explained by channelling effects caused by a nonuniform pore size distribution. Weineisen et al. (2006),

present experimental data on through-drying of tissue sheets with three different basis weights i.e. 20, 30

and 40 g/m2 at intensities comparable to industrial conditions. Their superficial velocity was in the range 4

to 10 m/s and the corresponding pressure drop in the range 2 to 3.5 kPa. A power function was fitted to

the data and the exponent n of equation 3 was found to be 1.69, 1.59 and 1.56 for basis weight of 20, 30

and 40 g/m2 respectively. The higher values of the exponent n as compared to the work by Polat et al.

(1993) reflect a greater influence of inertial forces at the comparatively higher superficial velocities.

Weineisen et al. (2007) developed a model for through-drying of paper at high drying air temperature and

8 | P a g e

constant pressure drop. Their model was solved for different combinations of the variables basis weight,

drying air temperature and pressure drop corresponding to industrial conditions and the results were

compared with data from bench-scale experiments. Their simulation show that the drying rate curve is

very sensitive to the air flow rate and that correctly modelling the correlation between pressure drop and

air flow rate is the most important factor. However, for a given basis weight, an increase in pressure drop

yielded fitted parameters that were somewhat different, i.e. a lower initial gas fraction and a higher

tortuosity, a change which increases the resistance to air flow. This means that in their model the

correlation between pressure drop and air flow rate does not quite capture the nonlinear relationship

shown by the experiments.

Ramaswamy (2003), describe the role of air flow in vacuum dewatering. He lists models based on physics

of the process primarily related to flow through porous media. First he shows the very basic equation

describing flow through a straight capillary of known radius i.e. well known Hagen-Poiseuille equation

for creeping flow through single straight capillary relating the frictional pressure drop to the liquid

velocity, and is given by

Equation 4

Then he describes the Darcy‟s law for flow through porous media, which is originally an extension of the

Hagen-Poiseuille equation for laminar flow through straight capillary. Darcy‟s law considers only the

fluid viscous effects neglecting the inertial effects, and is generally said to be valid for Reynolds numbers

less than unity. Commonly accepted form of Darcy‟s law is given as

Equation 5

Then he describes the fluid flow in which both viscous and inertial effects are taken into account.

Ramaswamy explain the findings by (Polat et. al. 1992-93), that the relationship between air flow rate and

pressure difference across the mat can be given by the Forchheimer relation as

Equation 6

Ramaswamy (2003) also describes one model for air flow during vacuum dewatering considering

compressibility effects. He explains that the applied pressure differences during the vacuum dewatering

can be quite high, of the order of 80 kPa; therefore one has to consider the compressibility effects of the

air as it passes through the sheet. For isothermal compressible flow, the modified form of Forchheimer

relation including viscous and inertial effects can be given as

Equation 7

Nilsson and Stenstrom, (1996) studied the permeability of pulp and paper. They modelled a sheet of paper

as a two dimensional network of cellulose fibers. They calculate the permeabilities and compared them

with measured values by solving stokes equation or equation for creeping flow through the structure.

They assumed structure to be highly ordered, when a fiber aspect ratio of 3.5 is used, and structure has

random distribution of fibers when a fiber aspect ratio of 5 is used.

2.1 Flow Models.

2.1.1 Darcy’s flow Equation. Henri Darcy, a French civil engineer, in his 1856 publication laid the real foundation of the quantitative

theory of the flow of homogenous fluids through porous media. As a civil engineer, he was interested in

the flow characteristics of sand filters used to filter public water in the city of Dijon in France. The result

9 | P a g e

of his classic experiments, globally known as Darcy‟s law, is thus stated: “The rate of flow V of water

through the filter bed is directly proportional to the area A of the sand and to the difference Δh in the

height between the fluid heads at the inlet and outlet of the bed, and inversely proportional to the

thickness L of the bed” and is given by,

Equation 8

Darcy‟s law represents a linear

relationship between the flow rate V and

the head (pressure gradient) Δh/L. Figure

1 shows how superficial velocity (mass

flow rate) depends on the pressure drop

according to Darcy‟s law. The constant

of proportionality K in the original Darcy

equation has been expressed as /k; is

the viscosity of the fluid and is called the

permeability of the porous medium.

Darcy‟s law is the most common way of

describing the laminar or viscous flow

i.e. “linear relationship between the flow

rate and the pressure drop” through

porous media. According to Dullien

(1979);

1. “Darcy‟s law assumes laminar or viscous flow (creep velocity); it does not involve the inertia

term (the fluid density). This implies that the inertia or acceleration forces in the fluid are being

neglected when compared to the classical Navier-Stokes equations”.

2. “Darcy‟s law assumes that in a porous medium a large surface area is exposed to fluid flow,

hence the viscous resistance will greatly exceed acceleration forces in the fluid unless turbulence

sets in”.

2.1.2 Forchheimer flow Equation. Darcy‟s empirical flow model represents a simple linear relationship between flow rate and pressure drop

in porous media; any deviation from the Darcy flow scenario is termed non-Darcy flow. Physical causes

for these deviations are grouped under the following headings.

1. High velocity flow effects.

2. Molecular effects.

3. Ionic effects.

4. Non-Newtonian fluids phenomena.

However, in petroleum engineering, the most common phenomenon is the high flow rate effect. High

flow rate beyond the assumed laminar flow regime can occur in the following scenarios in petroleum

reservoirs. In 1901, Philippe Forchheimer, a Dutch man, while flowing gas thorough coal beds discovered

that the relationship between flow rate and potential gradient is nonlinear at sufficiently high velocity, and

that this non-linearity increases with flow rate. The additional pressure drop due to inertial losses is

primarily due to the acceleration and deceleration effects of the fluid as it travels through the tortuous

flow path of the porous media. The total pressure drop is thus given by Forchheimer empirical flow model

stated traditionally as;

Equation 9

0

1

2

3

4

5

0 1 2 3 4 5Fl

ow

rat

e

Pressure drop

Darcy

Figure 1 Graphical illustration of relationship between Flow rate and

Pressure drop according to Darcy's law.

10 | P a g e

The Forchheimer equation

assumes that Darcy‟s law is

still valid, but that an

additional term must be added

to account for the increased

pressure drop. Hence this

equation will be called the

Darcy-Forchheimer flow

model. Equation 9 is based on

fitting an empirical equation

through experimental data. A

theoritical model was

constructed graphically, based

on the Forchheimer relation in

terms of incompressible flow

to compare it with the

experimental results. For this purpose, maximum values of superficial velocity and the pressure drop were

assumed to be 1 m/s and 0.6 kPa respectively. The atmospheric pressure was assumed to be 1 bar. Then a

graph is constructed (Figure 2), which shows how the superficial velocity depends on pressure drop when

assuming only frictional forces, only inertial forces and 50% frictional & 50% inertial forces.

2.1.3 Air Flow-Considering Compressibility Effects. Ramaswamy, S. (2003), explained that for air flow through porous media under lower pressure drop i.e.

as in the case of through air drying, the Forchheimer relation is directly applicable. He explained that the

applied pressure differences can be quite high during vacuum dewatering. Hence the compressibility

characteristics of the air as it passes through the sheet must be considered. He gives the modified form of

Forchheimer relation including viscous and inertial effects when considering compressibility

characteristics as.

Equation 10

A theoretical model was constructed based on the modified Forchheimer equation considering

compressibility effects. For this purpose, maximum values of superficial velocity and the pressure drop

were assumed to be 1 m/s and 0.6 kPa respectively. The atmospheric pressure was assumed to be 1 bar, so

that the assumptions are the same as those used for constructing Figure 2. Then a graph is constructed

(Figure 3), which shows how superficial velocity depends on the pressure drop when assuming only

frictional forces, only inertial forces and 50% frictional & 50% inertial forces.

Figure 2 Graphical illustration of relationship between Flow rate and Pressure

drop according to Forchheimer relation in terms of incompressible flow.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8Su

pe

rfic

ial vel

oci

ty, (m

/s)

Pressure drop, (kPa)

Incompressible flow Only frictionalforces

Only intertial forces

50 % frictionalforces and 50 %inertial forces

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8

Sup

erf

icia

l ve

loci

ty,

(m/s

)

Pressure drop, (kPa)

Compressible flow Only frictionalforces

Only intertialforces

50 % frictionalforces and 50 %inertial forces

Figure 3 Graphical illustration of relationship between Flow rate and Pressure

drop according to modified Forchheimer relation in terms of compressible flow.

11 | P a g e

2.1.4 Missbach flow Model. In 1937 Missbach suggested that flow through porous media could be described by a power law model

(Weineisen et al 2006), and is given by:

Equation 11

Generally the exponent, n, in

equation 11 is in the range of 1 to

2. For n=1, the equation reduces to

Darcy‟s law (equation 9) with a =

/k. For n=2 the inertial losses

dominate and may be interpreted as

the constant βρ in equation 10. A

model was constructed graphically,

based on the Missbach flow

equation. For this purpose,

maximum values of superficial

velocity and the pressure drop were

assumed to be 1 m/s and 0.6 kPa

respectively as when constructing

Figure 2 and 3. Then a graph is

constructed (Figure 4), which

shows how superficial velocity

depends on pressure drop when assuming only frictional forces i.e. n=1, only inertial forces i.e. n=2 and

50% frictional & 50% inertial forces i.e. n=1.5.

2.2 Flow Regimes in Porous Media In fluid mechanics, the Reynolds number (Re) is a dimensionless number that gives a measure of the ratio

of inertial forces to viscous forces. Laminar flow occurs at low Reynolds number, where viscous forces

are dominant, and is characterized by smooth, constant fluid motion, while turbulent flow occurs at high

Reynolds numbers and is dominated by inertial forces. It was pointed out by Scheidegger (1960) that for

various porous media the value of the Reynolds number above which Darcy‟s law is no longer valid has

been found to range between 0.1 and 75. Change between laminar and turbulent flow is not distinct. There

is a transition which means that there is no accurate value for Reynolds number where a flow can be

considered to be laminar or turbulent. In general it can be said that transition to turbulent happens at

Reynolds number between 1000 and 10000. Since the transition from viscous to turbulent flow should

occur at an even higher Reynolds number the breakdown of Darcy‟s law must be due to some other

process than the transition from viscous to

turbulent flow. Polat et al. (1992) explain the

brake down of Darcy‟s law as being associated

with inertial effects occurring when the

streamlines of the flowing medium are distorted

due to changes in direction of motion big

enough for inertial forces to become significant

compared to viscous forces. The mechanisms of

losses due to inertial effects at relatively low

Reynolds numbers and due to turbulent losses

are identical. The mechanism behind inertial

effects in porous media differs from the effects

of turbulence only in that the change in direction of motion is induced by the structure of the porous

medium rather than being the result of directional change due to turbulent eddies. Because of this

mechanistic similarity, flow through paper in regions where inertial effects are important even though the

Figure 5 Laminar vs. Turbulent Flow Regimes

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8

Sup

erf

icia

l ve

loci

ty,

(m/s

)

Pressure Drop, (kPa)

n = 1, Only frictionalforces (Darcy's Law)n = 2 (Inertial forcesdominating)n = 1.5 (frictional andInertial forces)

Figure 4 Graphical illustration of relationship between Flow rate and Pressure

drop according to Missbach Flow Model.

12 | P a g e

flow is not yet turbulent can be described by the same equations as those used for turbulent flow through

porous media.

Equation 12

In the literature, depending on the flow velocity and the nature of the porous media different flow patterns

have been observed. However four major regimes, using laser anemometry and visualization technique

proposed were.

These four regimes are;

a) “Darcy or laminar flow where the flow is dominated by viscous forces, here the pressure gradient

varies strictly linearly with the flow velocity. The Reynolds number at this point is less than 1”.

b) “At increasing Reynolds number, a transition zone is observed leading to flow dominated by inertia

effects. This begins in the range Re=1~10. This laminar inertia flow dominated region persists up to

and Re of ~150”.

c) “An unsteady laminar flow regime for Re =150 ~ 300 is characterized by occurrence of wake

oscillations and development of vortices in the flow profile”.

d) “A highly unsteady and chaotic flow regime for Re > 300, it resembles turbulent flow in pipes and is

dominated by eddies and high head losses”.

However there is large variation in the limiting Reynolds number for these transition zones as published

in the literature, therefore one cannot be too categorical about limits and transition zones as it relates to

the Reynolds number in porous media.

2.3 Aim of the present study. This study presents experiments for evaluating the flow rate through paper material using two different

equipments. The Bendtsen air permeance tester which corresponds to low volumetric flow rates and

pressure drops. The other equipment should be vacuum dewatering which is relevant for industrial

conditions in terms of pressure drop over the sample and the flow rates. In paper manufacturing, the flow

rate of air through the material is of great importance when calculating the energy use for vacuum

dewatering. Darcy‟s law is only applicable to incompressible fluids and for low flow rates. The aim of

this study is to evaluate different

models and proposed some

suitable model for higher pressure

drops and higher flow rates

through paper sheets of different

basis weights. The most relevant

experimental data on through

drying has previously been

published by other researchers,

i.e. (Polat et al 1993 &

Weineisen et al. 2006). However,

most of the previously published

data originate from experiments

performed at relatively low

intensities, i.e. low air flow rates

and pressure drop. In present

study, pressure drops of 0.74,

1.47 and 2.20 kPa were used to

estimate air flow rate through the

paper of different basis weight

using Bendtsen equipment. The superficial air velocity was in the range of (0.00015-0.147) m/s. Similarly

Figure 6 Superficial velocity as a function of sheet basis weight, for comparison

between present study and relevant study did by previous researches.

0.0001

0.001

0.01

0.1

1

10

100

0 20 40 60 80

Sup

erf

icia

l ve

loci

ty,

(m/s

)

Pressure drop, (kPa)

Polat et al. (1993)

Weineisen et al. (2006)

Hussain (2011)

13 | P a g e

for dewatering experiments, pressure drops of 20, 40 and 60 kPa were used to estimate air flow through

paper of different basis weight. The superficial air velocity was in the range of (1.64-68) m/s. Figure 6

and 7 shows the comparison between the estimated superficial velocities, working pressure drop and sheet

basis weight used in experiments of air flow through the paper material in this study with relevant studies

done by previous researchers.

1 2 3 4 5 6 7 8 9 10

Weieisen et al. (2006) 20 30 40

Polat et al. (1993) 25 50 100 150 250

Hussain (2011) 20 50 80 100 120 150 180 200 250 300

0

50

100

150

200

250

300

350

Shee

t b

asis

wei

ght

(g/

m2)

Figure 7 Paper with different basis weights, for comparison between present

study and previously research.

14 | P a g e

3 MATERIALS AND METHODS The material used was Södra gold eucalyptus pulp. The pulp samples were divided into four test portions:

one for unbeaten and three for beaten grades. The four test portions, each corresponding to (30.0 ± 0.5) g

of oven dry pulp, were soaked in 1.5 liters of water for more than four hours according to standard

procedure, as the dry matter content of the pulp was > 60 %. The pulps were then disintegrated according

to standard ISO 5263-1:2004 for 30,000 revolutions, as the dry matter content was > 20%. Following

disintegration the pulp suspensions were drained in a Buchner funnel before being diluted to a total mass

of 300±5 grams, corresponding to a mass fraction of 10 % stock. Three of four thickened pulp samples

were then beaten in the PFI mill to three different degrees (1000, 2000 and 3000 revolutions, respectively)

according to standard procedure (ISO 5264-2:2002). Each test portion i.e. unbeaten and beaten pulp

samples were then diluted with 15 liters distilled water to get 0.2 % stock consistency. For measuring air

flow through paper at lower pressure drops by Bendtsen air permeance tester, sheets with different basis

weights were prepared using laboratory hand sheet former from unbeaten and three different beaten pulp

samples. On the other hand, for measuring air flow through paper at higher pressure drop or high air

velocity by vacuum dewatering equipment, sheets were prepared using modified hand sheet former

typically designed for dewatering equipment.

3.1 Laboratory Hand Sheet Former Paper of basis weight 25, 50, 80, 100, 120, 150, 180, 200, 250 and 300 g/m

2 from unbeaten and beaten

stock consistencies was prepared. The upper section of the laboratory hand sheet former is prefilled with

water to half its volume, followed by adding exact amount of stock to give desired basis weight sheet; to

ensure that fibres are not trapped in the wire during filling. The stock is filled up to the mark and

compressed air is used to agitate the system to ensure uniformity. After the agitation the drainage valve is

opened. The sheet formed on the wire is allowed to drain under reduced pressure for about 20 seconds.

Paper sheets of different basis weight from the laboratory hand sheet former were pressed between two

blotters and pressure is exerted on it by placing a couch on top of the blotters for 15 seconds after which

the couch is removed and the top blotter is removed and the sheet is allowed to stick to the lower blotter

from the wire. The complete stack of laboratory sheets was then wet pressed to 410 kPa for 25 seconds.

After the first pressing, a second pressing is carried out, for which the laboratory sheets were reversed and

all the blotters are replaced followed by raising the pressing pressure rapidly to 410 kPa for 2 minutes.

The laboratory sheets with different basis weight were then carefully separated from the blotters and are

mounted in a suitable manner in a conditioning room to prevent shrinkage. The sheets were then allowed

to dry for one day to be ready for air permeance testing.

3.2 Bendtsen Air Permeance Laboratory sheets with different basis weight are tested

according to ISO standard (5636-3:1992E) method to determine

the air permeance at low pressure drops. Air permeance is

defined as “The mean flow of air through unit area under unit

pressure difference in unit time, under specified conditions and

at operating pressure” (ISO 5636-3:1992E) It is expressed in

micrometers per Pascal second [1 ml/ (m2Pas) = 1µm/ (Pas)].

The Bendtsen air permeance apparatus (Figure 8) consists of a

compressor, pressure controlling weights, sample clamping

device and the flow meter. The measuring head consists of a

device in which the test piece is clamped between an angular flat

surface and a circular rubber gasket. Each laboratory sheet (20-

300 g/m2 basis weight) made from unbeaten as well as beaten

was then clamped between an angular flat surface and a circular

rubber gasket. The test area of each sheet was 10 cm2

± 0.2 cm2. The air pressure was controlled by three

manostat weights provided with Bendtsen air permeance tester, which control the air pressure at 0.74

kPa±0.01 kPa, 1.47 kPa±0.02 kPa and 2.20 kPa±0.03 kPa. Air flow at three different pressure drops was

then recorded by pressing the handle above the measuring head to allow air to flow through the paper

Figure 8 Bendtsen air Permeance Tester.

15 | P a g e

sheets. For each sheet of different grammage air flow reading from flow meter was recorded. The sheets

were then saved to measure the thickness later on.

3.3 Modified Hand Sheet Former Paper of basis weight 25, 50, 80, 100, 120, 150, 180, and 200 g/m

2 from unbeaten and beaten stock

consistencies was prepared. A hand sheet mould with a rectangular top was slightly modified to be able to

produce circular sheets of 184 mm diameter. The modified hand sheet mould differed in some aspects

from the standard hand sheet mould in SCAN-CM 26:99. The hand sheet mould was filled up with water

to a total volume of 3.5 litres in the upper section. The exact amount of stock to give the desired basis

weight was added which results in a thin stock concentration of about 0.01 %. The stock was stirred by

moving a mechanical device up and down five times before the water was evacuated. The sheets were

formed by pulling the handle upwards to drain off the water.

3.4 Air Flow Using Dewatering Equipment A bench-scale, laboratory vacuum dewatering was constructed as shown in Figure 9. Vacuum level, dwell

time and frequency of single vacuum pulses are in the range

typical for a Through Air Drying (TAD) tissue machine. The

vacuum dewatering equipment consists of two linear drives,

servo motor, and plate with slot width of 5 mm. The forming

fabric along with the formed sheet was taken from the

modified hand sheet former and placed into the sample

holder of the vacuum dewatering apparatus. The clamping

device was attached to the sample by two clamps. The

velocity was set so that dwell times of 1, 1.5, 2, 4, 8, 12, 16

and 20 ms were achieved and the start button was pressed for

each test to move the plate for the purpose of dewatering. For

each sheet sample having different basis weights prepared

from unbeaten and beaten pulp samples, the vacuum pressure

was maintained at 20, 40 and 60 kPa in a vacuum tank using

a vacuum pump. When the plate is accelerated rapidly and

the slot passes under the sample holder, air is able to pass through the sample at different dwell times and

pressure drops resulting in sheet dewatering. The pressure difference in the vacuum tank was then

recorded using Dewa-soft software by exporting the files into MS-Excel.

3.5 Estimation of Pressure Increase. Pressure increase/ difference from pressure

data obtained by Dewa-soft software are

something very difficult to evaluate. However

the approach used to estimate pressure

difference after exporting the pressure data

from Dewa-soft software into MS-Excel is

discussed below. By exporting pressure data

into MS-Excel following graph as shown in

Figure 10 in which pressure data as a function

of time is plotted was obtained. When the slot

of the plate passes over the vacuum tank a

vacuum pulse is created; air passes through the

sheet and the pressure in the vacuum tank

increases as shown in Figure 10. The set

pressure drop i.e. 20 kPa in Figure 10 was

named as P1, and the point where vacuum

pulse ends was named as P2. The pressure

Figure 9 Vacuum Dewatering Apparatus.

Figure 10 Graph obtained after exporting data from dewatering

equipment into MS-Excel.

16 | P a g e

difference ΔP, was then calculated as ΔP = P2 – P1.

The sheets are then carefully detached from the forming fabric and are allowed to dry in a conditioning

room for thickness measurements. The mass flow rate (kg/sec) and superficial velocity (m/sec) was then

calculated from estimated pressure difference for each sheet sample using equation 13 and 14

respectively.

Equation 13

Equation 14

3.6 Thickness Measurements Sheets with different basis weights, produced from unbeaten and beaten pulp samples are then tested to

measure thickness according to standard (ISO 534:1998); using thickness tester TJT-Teknik

manufactured by Lorentzen and Wettres AB. Sheet samples with different basis weight prepared from

laboratory hand sheet former and modified hand sheet former were then scanned between two opposite

measurement points so that a profile of the paper was obtained which gives a peak value corresponding to

the thickness of the sheet.

3.7 Fiber Master Analysis The pulp samples unbeaten and beaten at three different beating

revolutions i.e. 1000, 2000 and 3000 revolutions are then collected for the

fiber analysis. L&W Fiber Tester measures bra length, width, fines, shape

factor and coarseness. The instrument has a sample feeder with six

positions designed as a rotating disc (Figure 11). This automates the

measurement procedure, making it easier for the operator. The total

measurement cycle is made within six minutes. One feature is that images

of fibers are displayed during measurements. It is also possible to save

images of detected objects for later viewing.

3.8 Reproducibility of Results. There is some spread in the data obtained during dewatering experiment; therefore some attention was

given to the reproducibility of these results. For this purpose a sheet of 20 g/m2 was prepared using

modified hand sheet former. After that sheet was carefully transfer to sample holder of vacuum

dewatering equipment. Parameters are set as 2.5 m/s plate velocity and 20 kPa pressure drop. The plate is

accelerated for allowing air to pass through the sheet. The same sheet is then tested for air flow up to five

times to see the difference in pressure increase. Another experiment was performed by making 50 g/m2

sheets using modified hand sheet former. All sheets were carefully transferred to sample holder of

dewatering equipment. Parameters are adjusted as 0.41 m/s velocity and 20 kPa pressure drop. Different

50 g/m2 sheets prepared exactly in the same way are tested for air flow up to four times. Finally three

sheets of 20 g/m2 were prepared. Parameters are set as 2.5m/s plate velocity and 20, 40 and 60 kPa

pressure drops for three consecutive sheets respectively. The plate is then accelerated for allowing air to

pass through the sheets at 20, 40 and 60 kPa. Sheets of grammage 50 g/m2 were then allowed to dry in an

oven at 105°C for basis weight estimation later on.

3.9 Air Leakage Experiments. Finally some attention was given to investigate, if there is any leakage of air from the walls of sample

holder; when determining the air flow through paper. For this purpose, a rubber pad which does not allow

air to penetrate through it; was transfer to the sample holder of the vacuum dewatering equipment. The

plate velocities were set as 0.25, 0.41 and 2.5 m/s. For each velocity, plate is then accelerated up to four

times for allowing air to pass around the rubber pad at 20, 40 and 60 kPa pressure drops.

Figure 11 Fiber Master Tester.

17 | P a g e

4 RESULTS AND DISCUSSION

4.1 Bendtsen Air Flow A quantitative description of flow through porous media begins with an experimental rule found by

Darcy. This rule, describing that the rate of flow passing through a powder bed is proportional to the

pressure gradient of the flow, has been extended to a variety of porous media. There are various equations

to express this rule and its modification, known collectively as Darcy‟s law (equation 1).

The majority of the experimental results obtained for sheets of different basis weights (20-300) g/m2,

produced from unbeaten and beaten pulps using Bendtsen air permeance tester confirmed the applicability

of Darcy‟s law. Figures 12, 13, 14 and 15 shows the volumetric air flow rate, (ml/min) as a function of

pressure difference divided by sheet grammage (ΔP/G), for unbeaten pulp and pulp beaten at 1000, 2000

and 3000 beating revolutions respectively.

Figure 12 Volumetric air flow rate as a function of pressure difference/ grammage, for unbeaten pulp.

Figure 13 Volumetric air flow rate as a function of pressure difference/ grammage, for pulp beaten at 1000 revolutions.

0

1000

2000

3000

4000

5000

6000

0 0.01 0.02 0.03 0.04 0.05

Vo

lum

etr

ic a

ir f

low

rate

, (m

l/m

in)

ΔP/G, (m2kPa/g)

0.74KPa

1.47KPa

2.20KPa

0

500

1000

1500

2000

2500

3000

0 0.01 0.02 0.03 0.04 0.05

Vo

lum

etr

ic a

ir f

low

rate

, (m

l/m

in)

ΔP/G, (m2kPa/g)

0.74KPa

1.47KPa

2.20KPa

18 | P a g e

Figure 14 Volumetric air flow rate as a function of pressure difference/ grammage, for pulp beaten at 2000 revolutions.

Figure 15 Volumetric air flow rate as a function of pressure difference/ grammage, for pulp beaten at 3000 revolutions.

It can be seen in Figures 12, 13, 14 and 15 that there is a linear relationship between the volumetric air

flow and the ΔP/G; which confirms the applicability of Darcy‟s law. One important finding during the

estimation of air flow through paper of different basis weights using Bendtsen equipment was that; by

increasing the degree of beating less amount of air flow through the sheets. The possible explanation is

the creation of fines during beating. Refinement and other mechanical treatment have been shown to

increase the specific surface area of fibers, as well as increase their swelling capacity, flexibility and

compressibility (Ramaswamy 2003). Although previous research on refining describes how it affects

sheet solid contents, how difficult vacuum dewatering will be then, but these entire findings correlate very

well to air flow through paper. Nordman, L. (1954) showed that increasing the content of fines decreases

the solids content obtainable by suction in a linear fashion. Britt and Unbehend (1985), on the other hand,

0

200

400

600

800

1000

1200

0 0.01 0.02 0.03 0.04 0.05

Vo

lum

etr

ic a

ir f

low

rate

, (m

l/m

in)

ΔP/G, (m2kPa/g)

0.74KPa

1.47KPa

2.20KPa

0

20

40

60

80

100

120

0 0.01 0.02 0.03 0.04 0.05

Vo

lum

etr

ic a

ir f

low

rate

, (m

l/m

in)

ΔP/G, (m2kPa/g)

0.74KPa

1.47KPa

2.20KPa

19 | P a g e

show that increasing the fines initially increases the level of dryness after vacuum dewatering but further

increase in the amount of fines makes vacuum dewatering more difficult.

Refining of pulp also improves the bonding ability of fibers, causing a variety of simultaneous changes in

fibers such as; internal fibrillation, external fibrillation, fiber shortening or cutting. Internal fibrillation of

fibers improves the flexibility and collapsibility of fibers, which further improves inter-fiber bonding.

Another explanation of low air flow by increasing degree of refining is that, refining makes the paper

more dense i.e. reduces the pore space between the fibers. The results from Fiber master analysis

however, show that there is slightly increase in fines by increasing degree of beating. Table 2 below

shows the results obtained from fiber master analysis for unbeaten and pulp beaten at three different

beating revolutions.

Table 2 Fiber master results for unbeaten and beaten pulp at three different revolutions.

Variable Unbeaten Beaten 1000 Beaten 2000 Beaten 3000

Length 0,714 mm 0,726 mm 0,723 mm 0,716 mm

Width 16,8 μm 17,1 μm 17,3 μm 17,5 μm

Shape 90.44% 91.00% 91.17% 91.29%

Fines 4.80% 4.80% 5.10% 5.50%

Coarseness 59,0 μg/m 59,5 μg/m 63,5 μg/m 69,4 μg/m

No. Fibers in sample 2950558 2886976 2737249 2578134

The flow rate of air through a porous material depends on the porosity. Results obtained from thickness

measurements also confirm that thickness and thereby porosity decreases as degree of beating increases.

Figure 16 shows the results obtained from thickness measurements for paper sheets produced from

unbeaten and beaten pulp.

Figure 16 Thickness as a function of sheet basis weight, measured for sheets made from laboratory hand sheet former for

Bendtsen experiments.

0

100

200

300

400

500

600

0 100 200 300 400

Thic

knes

s, (

µm

)

Basis Weight, (g/m2)

UnBeaten

B1000

B2000

B3000

20 | P a g e

It can also be seen in Figure 16 that thickness increases as the sheet basis weight increases. As mentioned

above that flow rate of air though a porous material depends on the thickness, due to this low air flow

through higher grammage sheets are found.

The data obtained using Bendtsen air permeance show deviations from Darcy‟s law for low grammage

sheets i.e. 20 g/m2 for unbeaten and beaten pulp samples Figures (17, 18, 19 and 20). The possible reason

might be that the maximum range of measuring air flow using Bendtsen air permeance tester was 8820

ml/min, or for lower grammage sheets pin hole counts increases exponentially which accommodates large

flow rates. This is what Polat et. al. (1993), also observed in their experiments, they found that air flow

through paper cannot be treated as purely viscous even at a flow rate of 0.6 m/s for 150 g/m2 paper. They

did experiments with through flow rates of 0.08-0/70 kg/m2s (0.07-0.60 m/s superficial velocity) with air

and with much higher kinematic viscosity, helium at through flow rates of 0.02-0.20 kg/m2s (0.12-1.20

m/s superficial velocity). The results presented in Table 1 also indicate that when air is replaced by

helium, which has a kinematic viscosity about 7.5 times higher than that of air, the inertial contribution to

the pressure drop decreases. It is however evident that even for helium flow there is substantial inertial

contribution to the pressure drop for the lowest basis weight (25 g/m2). Weineisen at al. (2006), also in

their experiments found the value of exponent n in equation 3 for sheets of basis weight 20, 30 and 40

g/m2 in the range of 1.56 and 1.69. This indicates that, for flow through paper at high air velocities, the

pressure drop due to inertial effects cannot be neglected.

Figure 17 Volumetric air flow rate as a function of

pressure difference/ grammage, for low grammage

sheets of unbeaten pulp

Figure 18 Volumetric air flow rate as a function of

pressure difference/ grammage, for low grammage

sheets of 2000 rev beaten pulp

Figure 19 Volumetric air flow rate as a function of

pressure difference/ grammage, for low grammage

sheets of 1000 rev beaten pulp

Figure 20 Volumetric air flow rate as a function of

pressure difference/ grammage, for low grammage

sheets of 3000 rev beaten pulp

0

2000

4000

6000

8000

10000

0 0.05 0.1 0.15

Vo

lum

etr

ica

air

flo

w,

(ml/

min

)

ΔP/G, (m2kPa/g)

0.74KPa

1.47KPa

2.20KPa

0

2000

4000

6000

8000

10000

0 0.05 0.1 0.15

Vo

lum

etr

ic a

ir f

low

, (m

l/m

in)

ΔP/G, (m2kPa/g)

0.74KPa

1.47KPa

2.20KPa

0

2000

4000

6000

8000

10000

0 0.05 0.1 0.15

Vo

lum

etr

ic a

ir f

low

, (m

l/m

in)

ΔP/G, (m2kPa/g)

0.74KPa

1.47KPa

2.20KPa

0

2000

4000

6000

8000

0 0.05 0.1 0.15

Vo

lum

etr

ic a

ir f

low

, (m

l/m

in)

ΔP/G, (m2kPa/g)

0.74KPa

1.47KPa

2.20KPa

21 | P a g e

4.2 Reynolds number for Bendtsen air flow. In fluid mechanics, the Reynolds number (Re) is a dimensionless number that gives a measure of the ratio

of inertial forces to viscous forces. Laminar flow occurs at low Reynolds number, where viscous forces

are dominant, and is characterized by smooth,

constant fluid motion, while turbulent flow

occurs at high Reynolds numbers and is

dominated by inertial forces, which tends to

produce eddies, vortices and other flow

instabilities.

Equation 15

The Reynolds number at which Darcy‟s law is

no longer applicable ranges between 0.1-75

depending on the porous structure and the

choice of characteristic dimension used (Polat et

al. 1992). The calculated Reynolds numbers for

unbeaten and beaten pulp to three revolutions

using Bendtsen air flow experiments are very

low, even the higher value is near to 0.18. Figure

21 shows the calculated Reynolds numbers as a function of sheet basis weights.

4.3 (Dewatering Equipment) Pressure

Increase vs. Dwell time. In order to investigate the relationship between

the air flow in terms of pressure increase and the

vacuum dwell time, eight sheets of 20 g/m2 were

prepared. The velocity was set so that dwell

times of 1, 1.5, 2, 4, 8, 12, 16 and 20 ms were

achieved and the start button was pressed for

each test sheet to move the plate at above

mentioned dwell times for the purpose of

dewatering. For each sheet sample, the vacuum

pressure was maintained at 60 kPa in a vacuum

tank using a vacuum pump. Figure 22 shows the

way in which the air that penetrated the sample

as given by the pressure increase in the vacuum

tank increases when the dwell time is increased.

The results showed that when the dwell time

was increased, the amount of air flowing

through the sample (in terms of pressure

increase in the vacuum tank) was also increased:

there is simply more time available for the air to

be sucked through the slots in the plate. The

increase in the air flow through the sheet that

resulted from increasing the dwell time was

observed for the unbeaten pulp samples. Figure

22 shows that there is a linear relationship

between the pressure increases as a function of

vacuum dwell time. This leads to the conclusion

that the flow rate through the sample can be

calculated from one dwell time only. For the

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 100 200 300 400

Re

yno

ld's

nu

mb

er, (

Re

)

Sheet basis weight, (g/m2)

y = 0.3551x + 0.4072 R² = 0.9934

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0 5 10 15 20 25

Pre

ssu

re In

cre

ase

, (kP

a)

Vacuum dwell time, (ms)

0

1

2

3

4

5

6

7

0 10 20

Pre

ssu

re In

cre

ase

, (kP

a)

Vacuum dwell time, (ms)

20g/m2

80g/m2

120g/m2

180g/m2

250g/m2

Figure 21 Calculated Reynolds numbers as a function of sheet

basis weight for Bendtsen air permeance experiments.

Figure 22 Pressure increase as a function of vacuum dwell time.

Figure 23 Pressure increase as a function of vacuum dwell time

for sheets of different basis weights.

22 | P a g e

majority of flow rates presented, a dwell time of 12 ms was used. However, a shorter dwell time of 2 ms

was also used.

Figure 23 shows the same relationship between the pressure increases as a function of vacuum dwell time

for sheets of different basis weight at 60 kPa. It can be seen a lower basis weight sheet allows more air to

penetrate in terms of pressure increase through it. The possible explanation is that, as the sheet basis

weight increases the thickness of the sheet increases; which means that by increasing paper thickness,

mean pore size decreases and the pore size distribution becomes narrower.

4.4 Air Velocity vs. Sheet Basis Weight (Dewatering Equipment) The results from the dewatering experiments show that, air flow decreases as the sheet basis weight

increases. Also the air flow, by decreasing the sheet basis weight increases at first slightly, then with a big

jump between 50 g/m2

and 20 g/m2 sheets basis weight Figure 25, 26 and 27. The possible reason is that

as the sheet basis weight increases the thickness of sheet increases. In accord with Darcy‟s law, fluid flow

through porous media depends on the thickness of the porous material. Polat et al., (1993) also confirm in

their experiments on sheets basis weight between 25-250 g/m2 that “With decreasing basis weight the

permeability increases, at first slightly, then with a big jump between 50 g/m2

and 20 g/m2

paper”.

According to Polat et al. (1993) “the small increase in air flow with decreasing basis weight from 250 to

50 g/m2 probably derives from small changes in pore size and pore size distribution”. They also quote the

finding of Bliesner that “as paper thickness increases, mean pore size decreases and the pore size

distribution becomes narrower”. Another explanation of this is given by (Corte & Kallmes) and (Corte &

Lloyd) as quoted in article by Polat et al. that “For commercial paper, pin hole counts increases

exponentially with decreasing basis weight. Pin holes accommodate disproportionately large flow rates.

In other words, at high basis weight three-dimensional pores control the flow but, as basis weight

decreases, Z-directional pores

become increasingly important. The

large increase in permeability at

such a low basis weight thus reflects

a substantial fraction of flow

through Z-directional pores”. Less

amount of air flow through higher

grammage sheets was also found

during estimation of air flow at low

pressure drops using Bendtsen air

permeance tester.

Figure 24 shows the thickness

values obtained for different

grammage sheets made from

unbeaten and beaten pulp samples. It

can be seen that thickness increases

as the sheet basis weight increases.

However, the thickness values

obtained from sheets prepared with

laboratory hand sheet former are

lower as compared to modified sheet former due to pressing effects.

The mass flow rate and the superficial air velocity was calculated at dwell time of 12 ms and at three

different pressure drops of 20, 40 and 60 kPa according to equation 16 and 17 respectively.

Equation 16

0

100

200

300

400

500

600

0 50 100 150 200 250

Thic

kne

ss, (μ

m)

Sheet basis Weight, (g/m2)

UnBeaten

B1000

B2000

B3000

Figure 24 Thickness measurements of sheets made from modified hand

sheet former for dewatering experiments obtained using thickness tester-

TJT-Teknik.

23 | P a g e

Equation 17

Figures 25, 26 and 27 below show the superficial air velocity as a function of sheet basis weight, for

dwell time of 12 ms. It can also be seen that superficial air velocity decreases as degree of beating

increases. This again confirms the theory of refining, which was observed in the case of Bendtsen

experiments. Refinement and other mechanical treatment have been shown to increase the specific surface

area of fibers. Ramaswamy (2003) describe that “Potential mechanisms of water removal by air flow

during vacuum dewatering include viscous drag by flowing air on the water present in the fiber interstices

or pores and compression by surface tension forces. Due to the level of fines, paper and board grades

offer significant resistance to air flow thus minimizing the amount of air flow under vacuum dewatering

conditions”. Although previous research on refining describes how it affects sheet solid contents, how

difficult vacuum dewatering will be then, but these entire findings correlate very well to air flow through

paper. The results from Fiber master analysis also confirm that an increase beating decreases the

permeance as fines are created. Table 2 above shows the results obtained from fiber master analysis for

unbeaten and pulp beaten at three different beating revolutions.

Figure 25 Superficial air velocity (m/s) as a function of

sheet basis weight (g/m2), estimated at 20kPa and at 12

ms dwell time.

Figure 26 Superficial air velocity (m/s) as a function of

sheet basis weight (g/m2), estimated at 40 kPa and at 12

ms dwell time.

Figure 27 Superficial air velocity (m/s) as a function of sheet basis weight (g/m2), estimated at 60 kPa and at 12 ms dwell

time.

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

0 100 200 300

Sup

erf

icia

l Air

Ve

loci

ty,

(m/s

)

Sheet basis weight, (g/m2)

Unbeaten

1000 deg

2000deg

3000 deg

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

0 100 200 300

Sup

erf

icia

l Air

Ve

loci

ty,

(m/s

)

Sheet basis weight, (g/m2)

Unbeaten

1000 deg

2000deg

3000 deg

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

0 100 200 300

Sup

erf

icia

l Air

Ve

loci

ty,

(m/s

)

Sheet basis weight, (g/m2)

Unbeaten

1000 deg

2000deg

3000 deg

24 | P a g e

Figure 28 Calculated Reynolds numbers as a function of Sheet

basis weight for dewatering experiments at12 ms dwell time.

4.5 Inertial effects and Turbulent flow. The application of Darcy‟s law has been the predominant way of describing air flow through paper, i.e.

flow through paper has generally been considered as being purely viscous. However, later research has

shown that when pinholes become evident the flow is no longer purely viscous and thus Darcy‟s law does

no longer apply. According to Polat et al. (1989 and 1992), since the findings that flow through thin paper

is not always purely viscous, many researchers have instead of treating this fact, made sure to perform

their experiments at viscous flow, i.e. by increasing paper thickness or decreasing flow rate. The

Reynolds number at which Darcy‟s law are no longer applicable ranges between 0.1-75 depending on the

porous structure and the choice of characteristic dimension used Polat et al. (1992). The calculated

Reynolds numbers at 2 and 12 ms dwell time for unbeaten and beaten pulps using dewatering equipment

experiments are high. Figure 28 shows the calculated Reynolds numbers as a function of sheet basis

weights for dewatering experiments performed at 2 and 12 ms dwell time. Polat et al. (1992) explain the

breakdown of Darcy‟s law being associated with inertial effects occurring when the streamlines of the

flowing medium are distorted due to changes in direction of motion big enough for inertial forces to

become significant compared to viscous forces. The mechanisms of losses due to inertial effects at

relatively low Reynolds numbers and

due to turbulent losses are identical. The

mechanism behind inertial effects in

porous media differs from the effects of

turbulence only in that the change in

direction of motion is induced by the

structure of the porous medium rather

than being the result of directional

change due to turbulent eddies. Because

of this mechanistic similarity, flow

through paper in regions where inertial

effects are important but the flow is not

yet turbulent can be described by the

same equations as those used for

turbulent flow through porous media.

Thus the Forchheimer relation (equation

9) and the equation of Missbach

(equation 11) are both on principal

applicable to flow through paper. The

only difference is the interpretation of the

second order term in the former and the

deviation from unity of the exponent, n in the latter, which for flow through paper at moderate Reynolds

number should be interpreted as the effects of inertial forces due to deflections in the structure rather than

describing the effect of inertial forces due to turbulent eddies.

4.6 Flow Models for High Velocity Air Flow. The experimental results obtained for flow of air through unbeaten and beaten paper sheets of different

grammage using vacuum dewatering equipment are shown in Figures 29 and 30 below. Figure 29 reports

data for a dwell time of 2 ms and Figure 30 for a dwell time of 12 ms. The data include a total of seven

different basis weights, three different pressure drops and four different degrees of beating (unbeaten and

beaten for 1000, 2000 and 3000 revolutions). One conclusion is that the flow rate is very much influenced

by the degree of beating so that increased beating of the pulp will lead to a decrease in the flow rate

through the paper, just as for the Bendtsen air permeance measurements reported earlier. Refining of pulp

improves the bonding ability of fibers, causing a variety of simultaneous changes in fibers such as;

internal fibrillation, external fibrillation, fiber shortening or cutting. Internal fibrillation of fibers improves

the flexibility and collapsibility of fibers, which further improves inter-fiber bonding. Another

explanation of low air flow by increasing degree of refining is that, refining makes the paper more dense

i.e. reduces the pore space between the fibers.

0

10

20

30

40

50

60

70

80

90

0 100 200

Re

yno

lds

nu

mb

ers

, (R

e)

Sheet basis weight, (g/m2)

20 kPa

40 kPa

60 kPa

25 | P a g e

It is also clear from the data in Figures 29 and 30 that the parameter P/G seems to very relevant for

describing the flow rate so that the flow rate through the sample can be regarded as being a function of

P/G alone, as long as the degree of beating remains constant.

When it comes to the shape of the curves and the applicability of different types of mathematical models,

the results are not conclusive when comparing both graphs. The data in Figure 29 correspond to the

shorter dwell time are better described in terms of one of the models including inertial pressure drop and

compressibility effects, such as the one presented by Ramaswamy (Equation 10 and Figure 3). It can be

seen that the relationship between the pressure drop and the air flow rate is a non-linear expression and

that Darcy‟s law is not applicable. The possible explanation for such deviation is that Reynolds numbers

are high enough to correspond to laminar flow. The deviation from Darcy‟s law for paper from laminar to

turbulent conditions must be due to effect other than the transition. Polat explained the deviation from

linearity as being the result of inertial pressure losses as the air flow is subjected to rapid changes in the

direction of flow as it passes through the paper structure. For paper, which can be considered a very thin

porous bed, entrance and exit effects, i.e. irreversible losses due to acceleration and deceleration of the

fluid, are also likely to contribute significantly to the overall pressure drop.

Figure 29 show the experimental data of superficial velocity as a function of pressure drop obtained using

vacuum dewatering equipment; for unbeaten and beaten pulp samples at pressure drops of 20, 40 and 60

kPa for 2 ms dwell time.

Figure 29 Superficial air velocities as a function of pressure drop/ grammage for unbeaten and beaten pulp at 20, 40 and

60 kPa pressure drops for 2 ms dwell time experiments.

By assuming a constant density, behavior of such flows in which density does not vary significantly may

be simplified. This theory is termed as incompressible flow. However, the significant variations in density

can occur in many cases especially at higher velocities with large pressure changes. If a fluid exhibits

significant variations in density, its flow is considered to be compressible flow. Ramaswamy, (2003)

explained that during vacuum dewatering, the applied pressure differences can be quite high. Hence one

has to consider the compressibility effects of air as it passes through the sheet. It seems that the results

from the dewatering experiments are more likely similar to the model in which inertial forces are

dominating when taking compressibility into account.

0

10

20

30

40

50

60

70

80

0 1 2 3 4

Sup

erf

icia

l Ve

loci

ty, (

m/s

)

(ΔP/G), (m2kPa/g)

Unbeaten

Beaten 1000

Beaten 2000

Beaten 3000

26 | P a g e

The deviations from Darcy‟s law are smaller for the 12 ms dwell time data in Figure 30. The reason

behind this is not clear. However, the influence of any type of “offset” effects will be greater when

evaluating the flow rate according to Equations 16 and 17 based on only one dwell time. Due to the time

and effort involved it was not possible to evaluate every flow rate for a number of different dwell times as

was done for the data presented in Figure 22. However, one more way of evaluating the flow rate would

be using both dwell times so that flow rate is evaluated as

Equation 18

Figure 30 show the experimental data of superficial velocity as a function of pressure drop obtained using

vacuum dewatering equipment; for unbeaten and beaten pulp samples at pressure drops of 20, 40 and 60

kPa for 12 ms dwell time.

Figure 30 Superficial air velocities as a function of pressure drop/ grammage for unbeaten and beaten pulp at 20, 40 and

60 kPa pressure drops for 12 ms dwell time experiments.

4.7 Leakage Experiments The leakage was determined to investigate if air enters the vacuum tank without flowing through paper

sheets. The air flow results show that the higher leakages mean value i.e 0.44 kPa in terms of pressure

increase comes at 20 ms dwell time and 60 kPa pressure drop. The present study involves experiments at

2 ms and 12 ms dwell time. The higher mean value 0.36 kPa comes at 12 ms for 60 kPa pressure drop.

However the leakage values are so small that leakage can be neglected when calculating the air flow

0

10

20

30

40

50

60

70

0 1 2 3 4

Sup

erf

icia

l air

ve

loci

ty,

(m/s

)

ΔP/G, (m2kPa/g)

Unbeaten

Beaten 1000

Beaten 2000

Beaten 3000

27 | P a g e

through paper. Figure 31 show the leakage in terms of pressure increase as a function of dwell time for

20, 40 and 60 kPa pressure drops.

Figure 31 Air leakage in terms of pressure increase as a function of dwell time at 20, 40 and 60 kPa.

5 CONCLUSION Air flow through paper of basis weight (20-300) g/m

2 was investigated experimentally. The Bendtsen air

permeance tester was used to investigate the air flow at pressure drop of 0.74, 1.47 and 2.20 kPa; while

the vacuum dewatering equipment was used to investigate air flow at pressure drop of 20, 40 and 60 kPa.

For Bendtsen air permeance tester, the majority of the experimental data from unbeaten and beaten pulp

sample agree rather well with Darcy‟s law i.e. there is a linear relationship between the volumetric flow

rate and the pressure drop/ grammage. However, for lower grammage sheet i.e. 20 g/m2 the obtained data

shows deviation from Darcy‟s law. The majority of the calculated Reynolds numbers are also in the

range, that they satisfy the applicability of Darcy‟s law. Further results from Bendtsen experiments are

that increased refining leads to less amount of air flow through the sheets. Also, it was found that a lower

grammage sheet accommodates large flow rates as compared to higher grammage sheets. However, when

comparing the vacuum dewatering experimental results with different theoretical models for flow through

porous media, it was found that the flow model in which inertial forces are dominating when taking

compressibility into account is applicable for experimental results at 2 ms dwell time. The deviation from

Darcy‟s law is smaller for the results of 12 ms dwell time experiments. The reason might be that the

influence of any type of “offset” effects will be greater when evaluating the flow rate according to

Equations 16 and 17 based on only one dwell time. Further results are that the parameter P/G, or

pressure drop divided by grammage seems to be very relevant for describing the flow rate so that the flow

rate through the sample can be regarded as being a function of P/G alone, as long as the degree of

beating remains constant. Also the air flow, by decreasing the sheet basis weight increases at first slightly,

then with a big jump between 50 g/m2 and 20 g/m

2 sheets basis weight. It was also observed that the lower

basis weight sheet allows more air to penetrate in terms of pressure increase through it.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 5 10 15 20 25

Pre

ssu

re In

cre

ase

, kP

a

Vacuum dwell time, (ms)

20 kPa

40 kPa

60 kPa

28 | P a g e

6 NOMENCLATURE

ΔP Pressure difference Pa

Fluid viscosity Pa.s

k Material Permeability

L Thickness of Material m

εg, εs and εw volume fraction of gas solid and water

ρs Fiber density kgm-3

/

ρw Water density kgm-3

G Basis Weight gm-2

a Regression constant

n exponent

L Length of capillary m

U Superficial velocity ms-1

α Viscous Parameter m-2

β Inertial parameter m-1

1 Inlet conditions

2 Outlet conditions

R Gas constant Pa m3/kg mol K

Re Reynolds number

m Mass flow rate, Kg/sec

M Molecular mass of air, kg-mol-1

V Volume of tank, m3

T Temperature, K

Δt Dwell time, second

A Cross section area, m2

29 | P a g e

7 REFERENCES Britt, K.W. and Unbehend, J.E, (1985), Water removal during paper formation, published in Tappi

journal, 68. (4), pp. 104-107.

Dullien, F.A.L, (1979), Porous media Fluid transport and pore structure.

Granevald, R., (2005), Doctoral thesis, Vacuum dewatering of low-grammage paper webs and fabrics.

Macdonald, I.F., El-Sayed, M.S., Mow, K, and Dullien, F.A.L., (1979), Flow through porous media-the

Ergun equation revisited., Published in Ind. Eng. Chem. Fundamental., Vol 18, No. 3.

Massey, B.S., (1990), Mechanics of fluids, Sixth edition.

Nordman, L. (1954), Laboratory investigation of water removal by a dynamic suction box, published in

Tappi journal, 37. (11), pp. 553-560.

Nilsson, L., (1996), Doctoral thesis, Some studies of the transport coefficients of pulp and paper.

Nilsson, L, and Stenstrom, S., (1996), A study of the permeability of pulp and paper, Published in

International journal for Multiphase Flow, Vol. 23, No 1, pp. 131-153.

Nilsson, L, Hussain, A. Abbas, A., (2011), Energy aspects on tissue production with the through air

drying technique, Paper accepted for publication in Nordic Drying Conference to be held in

Helsinki on June 19-21.

Polat, O., Crotogino, R.H., and Douglas, W.J.M (1992), Transport phenomena analysis of through drying

paper, published in Ind. Eng. Chem. Res, 21, 736-743.

Polat, O., Crotogino, R.H., Heiningen, V.A.R.P, and Douglas, W.J.M (1993), Permeability and specific

surface of paper, published in Journal of pulp and paper science: Vol. 19 No. 4.

Ramaswamy, S. (2003), Vacuum dewatering during paper manufacturing, Published in Drying

technology, Vol 21, No. 4, pp. 685-717.

Scheidegger, A.E. (1960), Physics of flow through porous media.

Tiller, F.M, Li, W.P, and Lee, J.B, (2001), Determination of the critical pressure drop for filtration of

super-compactible cakes, published in Water science and technology, Vol 44 No 10, pp. 171-176.

Weineisen, H, and Stenstrom, S., (2005), Modelling through drying of tissue-Effect of pore size

distribution on drying characteristics, Published in Drying technology, 23: 1909-1923.

Weineisen, H, Parent, L, Morrison, D, and Stenstrom, S. (2006), Experimental study of through-drying of

tissue at industrial conditions-Drying results and flow analysis, Published in 15th International

drying symposium, pp. 1026-1033.

Weineisen, H., Parent, L., Morrison, D., and Stenstrom, S., (2007), Through-drying of tissue at high

intensities- An experimental study, Published in journal of pulp and paper science, Vol. 33 No. 1.

Weineisen, H, (2007), Doctoral Thesis, Through drying of tissue paper.

30 | P a g e

8 ACKNOWLEDGEMENT My supervisor, Dr. Lars Nilsson, is gratefully acknowledged for his skilled and confident guidance,

support and help throughout the studies and for his courage to take on this project. I am very grateful to

you for always have being available for discussion and support for my project. I really appreciate his

contribution during the last months when the structure of thesis was set.

All my colleagues at Karlstad University are greatly acknowledged for all their support and for creating a

pleasant atmosphere in which to work. I also express my gratitude to all staff at department of Chemical

Engineering at Karlstad University for always being helpful. Special thanks to Johan Kalender for

valuable discussion during data evaluation of dewatering equipment.

I would like to thanks Vesna for providing me the opportunity of using Bendtsen Air Permeance Tester at

StoraEnso Research Centre. I appreciated the pleasant cooperation we had during those measurements.

Staff at Karlstad Technical Centre is acknowledged for allowing me to perform Fiber testing analysis.

I would like to thanks Mikael Nilsson (Area Sales Manager) at Lorentzen & Wettre Skandinavien AB for

his technical comments regarding Bendtsen Air permeance tester.

I would also like to thanks my family for their prayers and their encouraging calls during my entire master

program. My friends for their support and encouragement are gratefully acknowledged.

31 | P a g e

9 APPENDIX

Table 3 Measured superficial velocities from Bendtsen Air Permeance Tester.

Pressure

Drop

Pulp

Sample 20 50 80 100 120 150 180 200 250 300

Superficial air Velocity, (ml/min)

0.7

4k

Pa Unbeaten 2600 2100 1700 1300 1180 800 600 480 420 400

1000 rev 2500 900 500 280 220 180 170 160 150 130

2000 rev 2200 500 320 220 190 170 110 90 80 60

3000 rev 2000 90 35 25 15 14 10 10 10 9

1.4

7k

Pa Unbeaten 8820 3580 3000 2500 2250 1550 1250 1000 900 800

1000 rev 8820 1800 1000 700 450 370 360 350 340 320

2000 rev 8820 700 480 350 290 210 150 110 90 70

3000 rev 4200 220 70 45 35 30 25 20 18 15

2.2

0 k

Pa Unbeaten 8820 5600 3550 2880 2650 2400 2000 1700 1500 1300

1000 rev 8820 2600 1700 1000 800 550 480 470 460 430

2000 rev 8820 1000 920 750 500 460 350 240 140 95

3000 rev 5850 280 110 80 55 45 35 30 30 25

32 | P a g e

Table 4 Thickness values obtained for sheets made from hand sheet former.

Basis Weight (g/m2)

Unbeaten Beaten 1000 Beaten 2000 Beaten 3000

Thickness, (μm)

20 47 41 37 34

50 112 86 84 74

80 164 145 124 105

100 207 189 154 138

120 247 218 187 148

150 309 244 219 197

180 361 301 255 230

200 396 326 300 254

250 498 401 341 300

300 530 462 401 309

Table 5 Thickness values obtained for sheets made from moified hand sheet former.

Basis weight (g/m2)

Unbeaten Beaten1000 Beaten2000 Beaten3000

Thickness, (μm)

20 67 61 58 55

50 194 173 164 151

80 279 233 226 219

100 283 281 252 242

120 331 325 277 274

150 396 375 330 301

180 434 428 387 381

200 484 479 417 341

33 | P a g e

Table 6 Calculated Reynolds number for unbeaten pulp sheets, after measuring air flow using Bendtsen air permeance tester.

Air Flow

(ml/min)

Air Flow

(m/s)

Hydrostatic

diameter,

Dh

(meter)

Air

Density(δ)

kg/m3

Air

Viscosity

(μ)

Pas

Reynolds

Number

2500 0.0417 0.0000169 1.29 0.000018 0.050

900 0.0150 0.0000169 1.29 0.000018 0.018

500 0.0083 0.0000169 1.29 0.000018 0.010

280 0.0047 0.0000169 1.29 0.000018 0.006

220 0.0037 0.0000169 1.29 0.000018 0.004

180 0.0030 0.0000169 1.29 0.000018 0.004

170 0.0028 0.0000169 1.29 0.000018 0.003

160 0.0027 0.0000169 1.29 0.000018 0.003

150 0.0025 0.0000169 1.29 0.000018 0.003

130 0.0022 0.0000169 1.29 0.000018 0.003

8820 0.1470 0.0000169 1.29 0.000018 0.178

1800 0.0300 0.0000169 1.29 0.000018 0.036

1000 0.0167 0.0000169 1.29 0.000018 0.020

700 0.0117 0.0000169 1.29 0.000018 0.014

450 0.0075 0.0000169 1.29 0.000018 0.009

370 0.0062 0.0000169 1.29 0.000018 0.007

360 0.0060 0.0000169 1.29 0.000018 0.007

350 0.0058 0.0000169 1.29 0.000018 0.007

340 0.0057 0.0000169 1.29 0.000018 0.007

320 0.0053 0.0000169 1.29 0.000018 0.006

8820 0.1470 0.0000169 1.29 0.000018 0.178

2600 0.0433 0.0000169 1.29 0.000018 0.052

1700 0.0283 0.0000169 1.29 0.000018 0.034

1000 0.0167 0.0000169 1.29 0.000018 0.020

800 0.0133 0.0000169 1.29 0.000018 0.016

550 0.0092 0.0000169 1.29 0.000018 0.011

480 0.0080 0.0000169 1.29 0.000018 0.010

470 0.0078 0.0000169 1.29 0.000018 0.009

460 0.0077 0.0000169 1.29 0.000018 0.009

430 0.0072 0.0000169 1.29 0.000018 0.009

34 | P a g e

Table 7 Calculated Reynolds number for beaten pulp sheets at 1000 revolution, after measuring air flow using Bendtsen air permeance tester.

Air Flow

(ml/min)

Air Flow

(m/s)

Hydrostatic

Diameter,

Dh

(meter)

Air

Density(δ)

kg/m3

Air

Viscosity

(μ)

Pas

Reynolds

Number

2600 0.0433 0.0000169 1.29 0.000018 0.052

2100 0.0350 0.0000169 1.29 0.000018 0.042

1700 0.0283 0.0000169 1.29 0.000018 0.034

1300 0.0217 0.0000169 1.29 0.000018 0.026

1180 0.0197 0.0000169 1.29 0.000018 0.024

800 0.0133 0.0000169 1.29 0.000018 0.016

600 0.0100 0.0000169 1.29 0.000018 0.012

480 0.0080 0.0000169 1.29 0.000018 0.010

420 0.0070 0.0000169 1.29 0.000018 0.008

400 0.0067 0.0000169 1.29 0.000018 0.008

8820 0.1470 0.0000169 1.29 0.000018 0.178

3580 0.0597 0.0000169 1.29 0.000018 0.072

3000 0.0500 0.0000169 1.29 0.000018 0.061

2500 0.0417 0.0000169 1.29 0.000018 0.050

2250 0.0375 0.0000169 1.29 0.000018 0.045

1550 0.0258 0.0000169 1.29 0.000018 0.031

1250 0.0208 0.0000169 1.29 0.000018 0.025

1000 0.0167 0.0000169 1.29 0.000018 0.020

900 0.0150 0.0000169 1.29 0.000018 0.018

800 0.0133 0.0000169 1.29 0.000018 0.016

8820 0.1470 0.0000169 1.29 0.000018 0.178

5600 0.0933 0.0000169 1.29 0.000018 0.113

3550 0.0592 0.0000169 1.29 0.000018 0.072

2880 0.0480 0.0000169 1.29 0.000018 0.058

2650 0.0442 0.0000169 1.29 0.000018 0.053

2400 0.0400 0.0000169 1.29 0.000018 0.048

2000 0.0333 0.0000169 1.29 0.000018 0.040

1700 0.0283 0.0000169 1.29 0.000018 0.034

1500 0.0250 0.0000169 1.29 0.000018 0.030

1300 0.0217 0.0000169 1.29 0.000018 0.026

35 | P a g e

Table 8 Calculated Reynolds number for beaten pulp sheets at 2000 revolution, after measuring air flow using Bendtsen air permeance tester.

Air Flow

(ml/min)

Air Flow

(m/s)

Hydrostatic

diameter,

Dh

(meter)

Air

Density(δ)

kg/m3

Air

Viscosity

(μ)

Pas

Reynolds

Number

2200 0.0367 0.0000169 1.29 0.000018 0.044

500 0.0083 0.0000169 1.29 0.000018 0.010

320 0.0053 0.0000169 1.29 0.000018 0.006

220 0.0037 0.0000169 1.29 0.000018 0.004

190 0.0032 0.0000169 1.29 0.000018 0.004

170 0.0028 0.0000169 1.29 0.000018 0.003

110 0.0018 0.0000169 1.29 0.000018 0.002

90 0.0015 0.0000169 1.29 0.000018 0.002

80 0.0013 0.0000169 1.29 0.000018 0.002

60 0.0010 0.0000169 1.29 0.000018 0.001

8820 0.1470 0.0000169 1.29 0.000018 0.178

700 0.0117 0.0000169 1.29 0.000018 0.014

480 0.0080 0.0000169 1.29 0.000018 0.010

350 0.0058 0.0000169 1.29 0.000018 0.007

290 0.0048 0.0000169 1.29 0.000018 0.006

210 0.0035 0.0000169 1.29 0.000018 0.004

150 0.0025 0.0000169 1.29 0.000018 0.003

110 0.0018 0.0000169 1.29 0.000018 0.002

90 0.0015 0.0000169 1.29 0.000018 0.002

70 0.0012 0.0000169 1.29 0.000018 0.001

8820 0.1470 0.0000169 1.29 0.000018 0.178

1000 0.0167 0.0000169 1.29 0.000018 0.020

920 0.0153 0.0000169 1.29 0.000018 0.019

750 0.0125 0.0000169 1.29 0.000018 0.015

500 0.0083 0.0000169 1.29 0.000018 0.010

460 0.0077 0.0000169 1.29 0.000018 0.009

350 0.0058 0.0000169 1.29 0.000018 0.007

240 0.0040 0.0000169 1.29 0.000018 0.005

140 0.0023 0.0000169 1.29 0.000018 0.003

95 0.0016 0.0000169 1.29 0.000018 0.002

36 | P a g e

Table 9 Calculated Reynolds number for beaten pulp sheets at 3000 revolution, after measuring air flow using Bendtsen air permeance tester.

Air Flow

(ml/min)

Air Flow

(m/s)

Hydrostatic

diameter,

Dh

(meter)

Air

Density(δ)

kg/m3

Air

Viscosity

(μ)

Pas

Reynolds

Number

2000 0.0333 0.0000169 1.29 0.000018 0.040

90 0.0015 0.0000169 1.29 0.000018 0.002

35 0.0006 0.0000169 1.29 0.000018 0.001

25 0.0004 0.0000169 1.29 0.000018 0.001

15 0.0003 0.0000169 1.29 0.000018 0.000

14 0.0002 0.0000169 1.29 0.000018 0.000

10 0.0002 0.0000169 1.29 0.000018 0.000

10 0.0002 0.0000169 1.29 0.000018 0.000

10 0.0002 0.0000169 1.29 0.000018 0.000

9 0.0002 0.0000169 1.29 0.000018 0.000

4200 0.0700 0.0000169 1.29 0.000018 0.085

220 0.0037 0.0000169 1.29 0.000018 0.004

70 0.0012 0.0000169 1.29 0.000018 0.001

45 0.0008 0.0000169 1.29 0.000018 0.001

35 0.0006 0.0000169 1.29 0.000018 0.001

30 0.0005 0.0000169 1.29 0.000018 0.001

25 0.0004 0.0000169 1.29 0.000018 0.001

20 0.0003 0.0000169 1.29 0.000018 0.000

18 0.0003 0.0000169 1.29 0.000018 0.000

15 0.0003 0.0000169 1.29 0.000018 0.000

5850 0.0975 0.0000169 1.29 0.000018 0.118

280 0.0047 0.0000169 1.29 0.000018 0.006

110 0.0018 0.0000169 1.29 0.000018 0.002

80 0.0013 0.0000169 1.29 0.000018 0.002

55 0.0009 0.0000169 1.29 0.000018 0.001

45 0.0008 0.0000169 1.29 0.000018 0.001

35 0.0006 0.0000169 1.29 0.000018 0.001

30 0.0005 0.0000169 1.29 0.000018 0.001

30 0.0005 0.0000169 1.29 0.000018 0.001

25 0.0004 0.0000169 1.29 0.000018 0.001

37 | P a g e

Table 10 Mass flows for unbeaten and beaten pulp sheets to different revolutions, after measuring pressure increase at 20 kPa using vacuum dewatering equipment at 2 ms dwell time.

Un

bea

ten

Pulp

Dwell Time

Δt

Pressure

difference

ΔP

Molecular

mass of

air

M

(kg.mol-1

)

Tank

Volume

V

(m3)

Gas

Constant

R

(Nm.mol-

1.K

-1)

Temperature

T

(K)

Mass Flow

m

(kg/sec) (msec) (sec) (kPa) (Pa)

2 0.002 1 1000 0.029 0.3 8.31 293 1.78657

2 0.002 0.95 950 0.029 0.3 8.31 293 1.69724

2 0.002 0.8 800 0.029 0.3 8.31 293 1.42926

2 0.002 0.75 750 0.029 0.3 8.31 293 1.33993

2 0.002 0.65 650 0.029 0.3 8.31 293 1.16127

2 0.002 0.6 600 0.029 0.3 8.31 293 1.07194

2 0.002 0.5 500 0.029 0.3 8.31 293 0.89329

2 0.002 0.4 400 0.029 0.3 8.31 293 0.71463

Bea

ten 1

000

2 0.002 0.9 900 0.029 0.3 8.31 293 1.60792

2 0.002 0.75 750 0.029 0.3 8.31 293 1.33993

2 0.002 0.7 700 0.029 0.3 8.31 293 1.25060

2 0.002 0.65 650 0.029 0.3 8.31 293 1.16127

2 0.002 0.6 600 0.029 0.3 8.31 293 1.07194

2 0.002 0.5 500 0.029 0.3 8.31 293 0.89329

2 0.002 0.4 400 0.029 0.3 8.31 293 0.71463

2 0.002 0.4 400 0.029 0.3 8.31 293 0.71463

Bea

ten 2

000

2 0.002 0.8 800 0.029 0.3 8.31 293 1.42926

2 0.002 0.7 700 0.029 0.3 8.31 293 1.25060

2 0.002 0.65 650 0.029 0.3 8.31 293 1.16127

2 0.002 0.6 600 0.029 0.3 8.31 293 1.07194

2 0.002 0.55 550 0.029 0.3 8.31 293 0.98261

2 0.002 0.45 450 0.029 0.3 8.31 293 0.80396

2 0.002 0.35 350 0.029 0.3 8.31 293 0.62530

2 0.002 0.35 350 0.029 0.3 8.31 293 0.62530

Bea

ten 3

00

0

2 0.002 0.6 600 0.029 0.3 8.31 293 1.07194

2 0.002 0.55 550 0.029 0.3 8.31 293 0.98261

2 0.002 0.5 500 0.029 0.3 8.31 293 0.89329

2 0.002 0.45 450 0.029 0.3 8.31 293 0.80396

2 0.002 0.4 400 0.029 0.3 8.31 293 0.71463

2 0.002 0.35 350 0.029 0.3 8.31 293 0.62530

2 0.002 0.3 300 0.029 0.3 8.31 293 0.53597

2 0.002 0.3 300 0.029 0.3 8.31 293 0.53597

38 | P a g e

Table 11 Mass flows for unbeaten and beaten pulp sheets to different revolutions, after measuring pressure increase at 40 kPa using vacuum dewatering equipment at 2 ms dwell time.

U

nb

eate

n P

ulp

Dwell Time

Δt

Pressure

difference

ΔP

Molecular

mass of

air

M

(kg.mol-1

)

Tank

Volume

V

(m3)

Gas

Constant

R

(Nm.mol-

1.K

-1)

Temperature

T

(K)

Mass Flow

m

(kg/sec) (msec) (sec) (kPa) (Pa)

2 0.002 1.37 1370 0.029 0.3 8.31 293 2.44760

2 0.002 1.24 1240 0.029 0.3 8.31 293 2.21535

2 0.002 1.04 1040 0.029 0.3 8.31 293 1.85804

2 0.002 0.98 980 0.029 0.3 8.31 293 1.75084

2 0.002 0.89 890 0.029 0.3 8.31 293 1.59005

2 0.002 0.65 650 0.029 0.3 8.31 293 1.16127

2 0.002 0.55 550 0.029 0.3 8.31 293 0.98261

2 0.002 0.5 500 0.029 0.3 8.31 293 0.89329

Bea

ten 1

000

2 0.002 0.91 910 0.029 0.3 8.31 293 1.62578

2 0.002 0.85 850 0.029 0.3 8.31 293 1.51859

2 0.002 0.8 800 0.029 0.3 8.31 293 1.42926

2 0.002 0.75 750 0.029 0.3 8.31 293 1.33993

2 0.002 0.7 700 0.029 0.3 8.31 293 1.25060

2 0.002 0.65 650 0.029 0.3 8.31 293 1.16127

2 0.002 0.5 500 0.029 0.3 8.31 293 0.89329

2 0.002 0.4 400 0.029 0.3 8.31 293 0.71463

Bea

ten 2

000

2 0.002 0.83 830 0.029 0.3 8.31 293 1.48286

2 0.002 0.8 800 0.029 0.3 8.31 293 1.42926

2 0.002 0.75 750 0.029 0.3 8.31 293 1.33993

2 0.002 0.7 700 0.029 0.3 8.31 293 1.25060

2 0.002 0.65 650 0.029 0.3 8.31 293 1.16127

2 0.002 0.6 600 0.029 0.3 8.31 293 1.07194

2 0.002 0.55 550 0.029 0.3 8.31 293 0.98261

2 0.002 0.45 450 0.029 0.3 8.31 293 0.80396

Bea

ten 3

00

0

2 0.002 0.78 780 0.029 0.3 8.31 293 1.39353

2 0.002 0.78 780 0.029 0.3 8.31 293 1.39353

2 0.002 0.7 700 0.029 0.3 8.31 293 1.25060

2 0.002 0.65 650 0.029 0.3 8.31 293 1.16127

2 0.002 0.6 600 0.029 0.3 8.31 293 1.07194

2 0.002 0.55 550 0.029 0.3 8.31 293 0.98261

2 0.002 0.5 500 0.029 0.3 8.31 293 0.89329

2 0.002 0.4 400 0.029 0.3 8.31 293 0.71463

39 | P a g e

Table 12 Mass flows for unbeaten and beaten pulp sheets to different revolutions, after measuring pressure increase at 60 kPa using vacuum dewatering equipment at 2 ms dwell time.

U

nb

eate

n P

ulp

Dwell Time

Δt

Pressure

difference

ΔP

Molecular

mass of

air

M

(kg.mol-1

)

Tank

Volume

V

(m3)

Gas

Constant

R

(Nm.mol-

1.K

-1)

Temperature

T

(K)

Mass Flow

m

(kg/sec) (msec) (sec) (kPa) (Pa)

2 0.002 1.39 1390 0.029 0.3 8.31 293 2.48334

2 0.002 1.25 1250 0.029 0.3 8.31 293 2.23322

2 0.002 1.05 1050 0.029 0.3 8.31 293 1.87590

2 0.002 0.98 980 0.029 0.3 8.31 293 1.75084

2 0.002 0.75 750 0.029 0.3 8.31 293 1.33993

2 0.002 0.65 650 0.029 0.3 8.31 293 1.16127

2 0.002 0.55 550 0.029 0.3 8.31 293 0.98261

2 0.002 0.5 500 0.029 0.3 8.31 293 0.89329

Bea

ten 1

000

2 0.002 0.94 940 0.029 0.3 8.31 293 1.67938

2 0.002 0.9 900 0.029 0.3 8.31 293 1.60792

2 0.002 0.85 850 0.029 0.3 8.31 293 1.51859

2 0.002 0.8 800 0.029 0.3 8.31 293 1.42926

2 0.002 0.75 750 0.029 0.3 8.31 293 1.33993

2 0.002 0.6 600 0.029 0.3 8.31 293 1.07194

2 0.002 0.5 500 0.029 0.3 8.31 293 0.89329

2 0.002 0.55 550 0.029 0.3 8.31 293 0.98261

Bea

ten 2

000

2 0.002 0.85 850 0.029 0.3 8.31 293 1.51859

2 0.002 0.8 800 0.029 0.3 8.31 293 1.42926

2 0.002 0.75 750 0.029 0.3 8.31 293 1.33993

2 0.002 0.7 700 0.029 0.3 8.31 293 1.25060

2 0.002 0.65 650 0.029 0.3 8.31 293 1.16127

2 0.002 0.55 550 0.029 0.3 8.31 293 0.98261

2 0.002 0.5 500 0.029 0.3 8.31 293 0.89329

2 0.002 0.45 450 0.029 0.3 8.31 293 0.80396

Bea

ten 3

00

0

2 0.002 0.8 800 0.029 0.3 8.31 293 1.42926

2 0.002 0.75 750 0.029 0.3 8.31 293 1.33993

2 0.002 0.7 700 0.029 0.3 8.31 293 1.25060

2 0.002 0.65 650 0.029 0.3 8.31 293 1.16127

2 0.002 0.6 600 0.029 0.3 8.31 293 1.07194

2 0.002 0.55 550 0.029 0.3 8.31 293 0.98261

2 0.002 0.5 500 0.029 0.3 8.31 293 0.89329

2 0.002 0.5 500 0.029 0.3 8.31 293 0.89329

40 | P a g e

Table 13 Mass flows for unbeaten and beaten pulp sheets to different revolutions, after measuring pressure increase at 20 kPa using vacuum dewatering equipment at 12 ms dwell time.

Un

bea

ten

Pu

lp

Dwell Time

Δt

Pressure

difference

ΔP

Molecular

mass of

air

M

(kg.mol-1

)

Tank

Volume

V

(m3)

Gas

Constant

R

(Nm.mol-

1.K

-1)

Temperature

T

(K)

Mass Flow

m

(kg/sec) (msec) (sec) (kPa) (Pas)

12 0.012 2 2000 0.029 0.3 8.31 293 0.59552

12 0.012 1 1000 0.029 0.3 8.31 293 0.29776

12 0.012 0.8 800 0.029 0.3 8.31 293 0.23821

12 0.012 0.5 500 0.029 0.3 8.31 293 0.14888

12 0.012 0.7 700 0.029 0.3 8.31 293 0.20843

12 0.012 0.5 500 0.029 0.3 8.31 293 0.14888

12 0.012 0.4 400 0.029 0.3 8.31 293 0.11910

12 0.012 0.4 400 0.029 0.3 8.31 293 0.11910

Bea

ten

10

00

12 0.012 1.9 1900 0.029 0.3 8.31 293 0.56575

12 0.012 0.9 900 0.029 0.3 8.31 293 0.26799

12 0.012 0.7 700 0.029 0.3 8.31 293 0.20843

12 0.012 0.6 600 0.029 0.3 8.31 293 0.17866

12 0.012 0.5 500 0.029 0.3 8.31 293 0.14888

12 0.012 0.5 500 0.029 0.3 8.31 293 0.14888

12 0.012 0.4 400 0.029 0.3 8.31 293 0.11910

12 0.012 0.3 300 0.029 0.3 8.31 293 0.08933

Bea

ten

20

00

12 0.012 1.4 1400 0.029 0.3 8.31 293 0.41687

12 0.012 0.4 400 0.029 0.3 8.31 293 0.11910

12 0.012 0.8 800 0.029 0.3 8.31 293 0.23821

12 0.012 0.5 500 0.029 0.3 8.31 293 0.14888

12 0.012 0.5 500 0.029 0.3 8.31 293 0.14888

12 0.012 0.4 400 0.029 0.3 8.31 293 0.11910

12 0.012 0.3 300 0.029 0.3 8.31 293 0.08933

12 0.012 0.3 300 0.029 0.3 8.31 293 0.08933

Bea

ten

30

00

12 0.012 1.3 1300 0.029 0.3 8.31 293 0.38709

12 0.012 0.7 700 0.029 0.3 8.31 293 0.20843

12 0.012 0.5 500 0.029 0.3 8.31 293 0.14888

12 0.012 0.5 500 0.029 0.3 8.31 293 0.14888

12 0.012 0.4 400 0.029 0.3 8.31 293 0.11910

12 0.012 0.3 300 0.029 0.3 8.31 293 0.08933

12 0.012 0.3 300 0.029 0.3 8.31 293 0.08933

12 0.012 0.2 200 0.029 0.3 8.31 293 0.05955

41 | P a g e

Table 14 Mass flows for unbeaten and beaten pulp sheets to different revolutions, after measuring pressure increase at 40 kPa using vacuum dewatering equipment at 12 ms dwell time.

Un

bea

ten

Pu

lp

Dwell Time

Δt

Pressure

difference

ΔP

Molecular

mass of

air

M

(kg.mol-1

)

Tank

Volume

V

(m3)

Gas

Constant

R

(Nm.mol-

1.K

-1)

Temperature

T

(K)

Mass Flow

m

(kg/sec) (msec) (sec) (kPa) (Pas)

12 0.012 4.5 4500 0.029 0.3 8.31 293 1.33993

12 0.012 2.5 2500 0.029 0.3 8.31 293 0.74441

12 0.012 1.6 1600 0.029 0.3 8.31 293 0.47642

12 0.012 1.2 1200 0.029 0.3 8.31 293 0.35731

12 0.012 1.1 1100 0.029 0.3 8.31 293 0.32754

12 0.012 1 1000 0.029 0.3 8.31 293 0.29776

12 0.012 0.8 800 0.029 0.3 8.31 293 0.23821

12 0.012 0.8 800 0.029 0.3 8.31 293 0.23821

Bea

ten

10

00

12 0.012 3.5 3500 0.029 0.3 8.31 293 1.04217

12 0.012 2 2000 0.029 0.3 8.31 293 0.59552

12 0.012 1.1 1100 0.029 0.3 8.31 293 0.32754

12 0.012 0.8 800 0.029 0.3 8.31 293 0.23821

12 0.012 0.8 800 0.029 0.3 8.31 293 0.23821

12 0.012 0.7 700 0.029 0.3 8.31 293 0.20843

12 0.012 0.6 600 0.029 0.3 8.31 293 0.17866

12 0.012 0.6 600 0.029 0.3 8.31 293 0.17866

Bea

ten

20

00

12 0.012 2.5 2500 0.029 0.3 8.31 293 0.74441

12 0.012 1.2 1200 0.029 0.3 8.31 293 0.35731

12 0.012 0.9 900 0.029 0.3 8.31 293 0.26799

12 0.012 0.8 800 0.029 0.3 8.31 293 0.23821

12 0.012 0.7 700 0.029 0.3 8.31 293 0.20843

12 0.012 0.6 600 0.029 0.3 8.31 293 0.17866

12 0.012 0.6 600 0.029 0.3 8.31 293 0.17866

12 0.012 0.5 500 0.029 0.3 8.31 293 0.14888

Bea

ten

30

00

12 0.012 2.2 2200 0.029 0.3 8.31 293 0.65508

12 0.012 1.1 1100 0.029 0.3 8.31 293 0.32754

12 0.012 0.8 800 0.029 0.3 8.31 293 0.23821

12 0.012 0.7 700 0.029 0.3 8.31 293 0.20843

12 0.012 0.5 500 0.029 0.3 8.31 293 0.14888

12 0.012 0.6 600 0.029 0.3 8.31 293 0.17866

12 0.012 0.5 500 0.029 0.3 8.31 293 0.14888

12 0.012 0.6 600 0.029 0.3 8.31 293 0.17866

42 | P a g e

Table 15 Mass flows for unbeaten and beaten pulp sheets to different revolutions, after measuring pressure increase at 60 kPa using vacuum dewatering equipment at 12 ms dwell time.

Un

bea

ten

Pu

lp

Dwell Time

Δt

Pressure

difference

ΔP

Molecular

mass of

air

M

(kg.mol-1

)

Tank

Volume

V

(m3)

Gas

Constant

R

(Nm.mol-

1.K

-1)

Temperature

T

(K)

Mass Flow

m

(kg/sec) (msec) (sec) (kPa) (Pas)

12 0.012 8 8000 0.029 0.3 8.31 293 2.38210

12 0.012 5.4 5400 0.029 0.3 8.31 293 1.60792

12 0.012 3.8 3800 0.029 0.3 8.31 293 1.13150

12 0.012 2.4 2400 0.029 0.3 8.31 293 0.71463

12 0.012 2 2000 0.029 0.3 8.31 293 0.59552

12 0.012 1.6 1600 0.029 0.3 8.31 293 0.47642

12 0.012 1 1000 0.029 0.3 8.31 293 0.29776

12 0.012 0.8 800 0.029 0.3 8.31 293 0.23821

Bea

ten

10

00

12 0.012 4 4000 0.029 0.3 8.31 293 1.19105

12 0.012 2 2000 0.029 0.3 8.31 293 0.59552

12 0.012 1.5 1500 0.029 0.3 8.31 293 0.44664

12 0.012 1.2 1200 0.029 0.3 8.31 293 0.35731

12 0.012 1 1000 0.029 0.3 8.31 293 0.29776

12 0.012 0.8 800 0.029 0.3 8.31 293 0.23821

12 0.012 0.7 700 0.029 0.3 8.31 293 0.20843

12 0.012 0.6 600 0.029 0.3 8.31 293 0.17866

Bea

ten

20

00

12 0.012 3.6 3600 0.029 0.3 8.31 293 1.07194

12 0.012 1.6 1600 0.029 0.3 8.31 293 0.47642

12 0.012 1.2 1200 0.029 0.3 8.31 293 0.35731

12 0.012 1.2 1200 0.029 0.3 8.31 293 0.35731

12 0.012 1 1000 0.029 0.3 8.31 293 0.29776

12 0.012 0.8 800 0.029 0.3 8.31 293 0.23821

12 0.012 0.7 700 0.029 0.3 8.31 293 0.20843

12 0.012 0.5 500 0.029 0.3 8.31 293 0.14888

Bea

ten

30

00

12 0.012 3 3000 0.029 0.3 8.31 293 0.89329

12 0.012 1.4 1400 0.029 0.3 8.31 293 0.41687

12 0.012 1.2 1200 0.029 0.3 8.31 293 0.35731

12 0.012 1 1000 0.029 0.3 8.31 293 0.29776

12 0.012 0.8 800 0.029 0.3 8.31 293 0.23821

12 0.012 0.8 800 0.029 0.3 8.31 293 0.23821

12 0.012 0.7 700 0.029 0.3 8.31 293 0.20843

12 0.012 0.5 500 0.029 0.3 8.31 293 0.14888

43 | P a g e

Table 16 Superficial air velocity for unbeaten and beaten pulp sheets to different revolutions, after measuring mass flow at 20 kPa using vacuum dewatering equipment at 2 ms dwell time.

Un

bea

ten

Pulp

Mass Air Flow

(kg/sec)

Air Density

(kg/m3)

Cross

Section

Area

(m2)

Air Velocity

(m/sec)

1.79 1.29 0.028 49.462

1.70 1.29 0.028 46.989

1.43 1.29 0.028 39.570

1.34 1.29 0.028 37.097

1.16 1.29 0.028 32.150

1.07 1.29 0.028 29.677

0.89 1.29 0.028 24.731

0.71 1.29 0.028 19.785

Bea

ten 1

000

1.61 1.29 0.028 44.516

1.34 1.29 0.028 37.097

1.25 1.29 0.028 34.623

1.16 1.29 0.028 32.150

1.07 1.29 0.028 29.677

0.89 1.29 0.028 24.731

0.71 1.29 0.028 19.785

0.71 1.29 0.028 19.785

Bea

ten 2

000

1.43 1.29 0.028 39.570

1.25 1.29 0.028 34.623

1.16 1.29 0.028 32.150

1.07 1.29 0.028 29.677

0.98 1.29 0.028 27.204

0.80 1.29 0.028 22.258

0.63 1.29 0.028 17.312

0.63 1.29 0.028 17.312

Bea

ten 3

00

0

1.07 1.29 0.028 29.677

0.98 1.29 0.028 27.204

0.89 1.29 0.028 24.731

0.80 1.29 0.028 22.258

0.71 1.29 0.028 19.785

0.63 1.29 0.028 17.312

0.54 1.29 0.028 14.839

0.54 1.29 0.028 14.839

44 | P a g e

Table 17 Superficial air velocity for unbeaten and beaten pulp sheets to different revolutions, after measuring mass flow at 40 kPa using vacuum dewatering equipment at 2 ms dwell time.

Un

bea

ten

Pulp

Mass Air Flow

(kg/sec)

Air Density

(kg/m3)

Cross Section

Area

(m2)

Air Velocity

(m/sec)

2.45 1.29 0.028 67.763

2.22 1.29 0.028 61.333

1.86 1.29 0.028 51.441

1.75 1.29 0.028 48.473

1.59 1.29 0.028 44.021

1.16 1.29 0.028 32.150

0.98 1.29 0.028 27.204

0.89 1.29 0.028 24.731

Bea

ten 1

000

1.63 1.29 0.028 45.011

1.52 1.29 0.028 42.043

1.43 1.29 0.028 39.570

1.34 1.29 0.028 37.097

1.25 1.29 0.028 34.623

1.16 1.29 0.028 32.150

0.89 1.29 0.028 24.731

0.71 1.29 0.028 19.785

Bea

ten 2

000

1.48 1.29 0.028 41.054

1.43 1.29 0.028 39.570

1.34 1.29 0.028 37.097

1.25 1.29 0.028 34.623

1.16 1.29 0.028 32.150

1.07 1.29 0.028 29.677

0.98 1.29 0.028 27.204

0.80 1.29 0.028 22.258

Bea

ten 3

00

0

1.39 1.29 0.028 38.580

1.39 1.29 0.028 38.580

1.25 1.29 0.028 34.623

1.16 1.29 0.028 32.150

1.07 1.29 0.028 29.677

0.98 1.29 0.028 27.204

0.89 1.29 0.028 24.731

0.71 1.29 0.028 19.785

45 | P a g e

Table 18 Superficial air velocity for unbeaten and beaten pulp sheets to different revolutions, after measuring mass flow at 60 kPa using vacuum dewatering equipment at 2 ms dwell time.

Un

bea

ten

Pulp

Mass Air Flow

(kg/sec)

Air Density

(kg/m3)

Cross

Section

Area

(m2)

Air Velocity

(m/sec)

2.48 1.29 0.028 68.752

2.23 1.29 0.028 61.828

1.88 1.29 0.028 51.935

1.75 1.29 0.028 48.473

1.34 1.29 0.028 37.097

1.16 1.29 0.028 32.150

0.98 1.29 0.028 27.204

0.89 1.29 0.028 24.731

Bea

ten 1

000

1.68 1.29 0.028 46.494

1.61 1.29 0.028 44.516

1.52 1.29 0.028 42.043

1.43 1.29 0.028 39.570

1.34 1.29 0.028 37.097

1.07 1.29 0.028 29.677

0.89 1.29 0.028 24.731

0.98 1.29 0.028 27.204

Bea

ten 2

000

1.52 1.29 0.028 42.043

1.43 1.29 0.028 39.570

1.34 1.29 0.028 37.097

1.25 1.29 0.028 34.623

1.16 1.29 0.028 32.150

0.98 1.29 0.028 27.204

0.89 1.29 0.028 24.731

0.80 1.29 0.028 22.258

Bea

ten 3

00

0

1.43 1.29 0.028 39.570

1.34 1.29 0.028 37.097

1.25 1.29 0.028 34.623

1.16 1.29 0.028 32.150

1.07 1.29 0.028 29.677

0.98 1.29 0.028 27.204

0.89 1.29 0.028 24.731

0.89 1.29 0.028 24.731

46 | P a g e

Table 19 Superficial air velocity for unbeaten and beaten pulp sheets to different revolutions, after measuring mass flow at 20 kPa using vacuum dewatering equipment at 12 ms dwell time.

Un

bea

ten

Pulp

Mass Air Flow

(kg/sec)

Air Density

(kg/m3)

Cross

Section

Area

(m2)

Air Velocity

(m/sec)

0.60 1.29 0.028 16.487

0.30 1.29 0.028 8.244

0.24 1.29 0.028 6.595

0.15 1.29 0.028 4.122

0.21 1.29 0.028 5.771

0.15 1.29 0.028 4.122

0.12 1.29 0.028 3.297

0.12 1.29 0.028 3.297

Bea

ten 1

000

0.57 1.29 0.028 15.663

0.27 1.29 0.028 7.419

0.21 1.29 0.028 5.771

0.18 1.29 0.028 4.946

0.15 1.29 0.028 4.122

0.15 1.29 0.028 4.122

0.12 1.29 0.028 3.297

0.09 1.29 0.028 2.473

Bea

ten 2

000

0.42 1.29 0.028 11.541

0.12 1.29 0.028 3.297

0.24 1.29 0.028 6.595

0.15 1.29 0.028 4.122

0.15 1.29 0.028 4.122

0.12 1.29 0.028 3.297

0.09 1.29 0.028 2.473

0.09 1.29 0.028 2.473

Bea

ten 3

00

0

0.39 1.29 0.028 10.717

0.21 1.29 0.028 5.771

0.15 1.29 0.028 4.122

0.15 1.29 0.028 4.122

0.12 1.29 0.028 3.297

0.09 1.29 0.028 2.473

0.09 1.29 0.028 2.473

0.06 1.29 0.028 1.649

47 | P a g e

Table 20 Superficial air velocity for unbeaten and beaten pulp sheets to different revolutions, after measuring mass flow at 40 kPa using vacuum dewatering equipment at 12 ms dwell time.

Un

bea

ten

Pu

lp

Mass Air Flow

(kg/sec)

Air Density

(kg/m3)

Cross Section Area

(m2)

Air Velocity

(m/sec)

1.34 1.29 0.028 37.097

0.74 1.29 0.028 20.609

0.48 1.29 0.028 13.190

0.36 1.29 0.028 9.892

0.33 1.29 0.028 9.068

0.30 1.29 0.028 8.244

0.24 1.29 0.028 6.595

0.24 1.29 0.028 6.595

Bea

ten 1

000

1.04 1.29 0.028 28.853

0.60 1.29 0.028 16.487

0.33 1.29 0.028 9.068

0.24 1.29 0.028 6.595

0.24 1.29 0.028 6.595

0.21 1.29 0.028 5.771

0.18 1.29 0.028 4.946

0.18 1.29 0.028 4.946

Bea

ten 2

000

0.74 1.29 0.028 20.609

0.36 1.29 0.028 9.892

0.27 1.29 0.028 7.419

0.24 1.29 0.028 6.595

0.21 1.29 0.028 5.771

0.18 1.29 0.028 4.946

0.18 1.29 0.028 4.946

0.15 1.29 0.028 4.122

Bea

ten 3

00

0

0.66 1.29 0.028 18.136

0.33 1.29 0.028 9.068

0.24 1.29 0.028 6.595

0.21 1.29 0.028 5.771

0.15 1.29 0.028 4.122

0.18 1.29 0.028 4.946

0.15 1.29 0.028 4.122

0.18 1.29 0.028 4.946

48 | P a g e

Table 21 Superficial air velocity for unbeaten and beaten pulp sheets to different revolutions, after measuring mass flow at 60 kPa using vacuum dewatering equipment at 12 ms dwell time.

Un

bea

ten

Pu

lp

Mass Air Flow

(kg/sec)

Air Density

(kg/m3)

Cross

Section Area

(m2)

Air Velocity

(m/sec)

2.38 1.29 0.028 65.950

1.61 1.29 0.028 44.516

1.13 1.29 0.028 31.326

0.71 1.29 0.028 19.785

0.60 1.29 0.028 16.487

0.48 1.29 0.028 13.190

0.30 1.29 0.028 8.244

0.24 1.29 0.028 6.595

Bea

ten 1

000

1.19 1.29 0.028 32.975

0.60 1.29 0.028 16.487

0.45 1.29 0.028 12.366

0.36 1.29 0.028 9.892

0.30 1.29 0.028 8.244

0.24 1.29 0.028 6.595

0.21 1.29 0.028 5.771

0.18 1.29 0.028 4.946

Bea

ten 2

000

1.07 1.29 0.028 29.677

0.48 1.29 0.028 13.190

0.36 1.29 0.028 9.892

0.36 1.29 0.028 9.892

0.30 1.29 0.028 8.244

0.24 1.29 0.028 6.595

0.21 1.29 0.028 5.771

0.15 1.29 0.028 4.122

Bea

ten 3

000

0.89 1.29 0.028 24.731

0.42 1.29 0.028 11.541

0.36 1.29 0.028 9.892

0.30 1.29 0.028 8.244

0.24 1.29 0.028 6.595

0.24 1.29 0.028 6.595

0.21 1.29 0.028 5.771

0.15 1.29 0.028 4.122

49 | P a g e

Table 22 Calculated Reynolds numbers for unbeaten and beaten pulp sheets to different revolution, after measuring air flow at 20 kPa using vacuum dewatering equipment at 2 ms dwell time.

Air Flow

(m/s)

Hydrostatic

Diameter,

Dh

(meter)

Air

Density(δ)

kg/m3

Air

Viscosity

(μ)

Pas

Reynolds

Number

49.4621 0.0000169 1.29 0.000018 59.907

46.9890 0.0000169 1.29 0.000018 56.912

39.5697 0.0000169 1.29 0.000018 47.926

37.0966 0.0000169 1.29 0.000018 44.930

32.1504 0.0000169 1.29 0.000018 38.939

29.6773 0.0000169 1.29 0.000018 35.944

24.7311 0.0000169 1.29 0.000018 29.953

19.7849 0.0000169 1.29 0.000018 23.963

44.5159 0.0000169 1.29 0.000018 53.916

37.0966 0.0000169 1.29 0.000018 44.930

34.6235 0.0000169 1.29 0.000018 41.935

32.1504 0.0000169 1.29 0.000018 38.939

29.6773 0.0000169 1.29 0.000018 35.944

24.7311 0.0000169 1.29 0.000018 29.953

19.7849 0.0000169 1.29 0.000018 23.963

19.7849 0.0000169 1.29 0.000018 23.963

39.5697 0.0000169 1.29 0.000018 47.926

34.6235 0.0000169 1.29 0.000018 41.935

32.1504 0.0000169 1.29 0.000018 38.939

29.6773 0.0000169 1.29 0.000018 35.944

27.2042 0.0000169 1.29 0.000018 32.949

22.2580 0.0000169 1.29 0.000018 26.958

17.3117 0.0000169 1.29 0.000018 20.967

17.311748 0.0000169 1.29 0.000018 20.967

29.677282 0.0000169 1.29 0.000018 35.944

27.204175 0.0000169 1.29 0.000018 32.949

24.731068 0.0000169 1.29 0.000018 29.953

22.257961 0.0000169 1.29 0.000018 26.958

19.784855 0.0000169 1.29 0.000018 23.963

17.311748 0.0000169 1.29 0.000018 20.967

14.838641 0.0000169 1.29 0.000018 17.972

14.838641 0.0000169 1.29 0.000018 17.972

50 | P a g e

Table 23 Calculated Reynolds numbers for unbeaten and beaten pulp sheets to different revolution, after measuring air flow at 40 kPa using vacuum dewatering equipment at 2 ms dwell time.

Air Flow

(m/s)

Hydrostatic

Diameter,

Dh

(meter)

Air

Density(δ)

kg/m3

Air

Viscosity

(μ)

Pas

Reynolds

Number

67.7631 0.0000169 1.29 0.000018 82.072

61.3330 0.0000169 1.29 0.000018 74.285

51.4406 0.0000169 1.29 0.000018 62.303

48.4729 0.0000169 1.29 0.000018 58.709

44.0213 0.0000169 1.29 0.000018 53.317

32.1504 0.0000169 1.29 0.000018 38.939

27.2042 0.0000169 1.29 0.000018 32.949

24.7311 0.0000169 1.29 0.000018 29.953

45.0105 0.0000169 1.29 0.000018 54.515

42.0428 0.0000169 1.29 0.000018 50.921

39.5697 0.0000169 1.29 0.000018 47.926

37.0966 0.0000169 1.29 0.000018 44.930

34.6235 0.0000169 1.29 0.000018 41.935

32.1504 0.0000169 1.29 0.000018 38.939

24.7311 0.0000169 1.29 0.000018 29.953

19.7849 0.0000169 1.29 0.000018 23.963

41.0536 0.0000169 1.29 0.000018 49.723

39.5697 0.0000169 1.29 0.000018 47.926

37.0966 0.0000169 1.29 0.000018 44.930

34.6235 0.0000169 1.29 0.000018 41.935

32.1504 0.0000169 1.29 0.000018 38.939

29.6773 0.0000169 1.29 0.000018 35.944

27.2042 0.0000169 1.29 0.000018 32.949

22.257961 0.0000169 1.29 0.000018 26.958

38.580466 0.0000169 1.29 0.000018 46.727

38.580466 0.0000169 1.29 0.000018 46.727

34.623496 0.0000169 1.29 0.000018 41.935

32.150389 0.0000169 1.29 0.000018 38.939

29.677282 0.0000169 1.29 0.000018 35.944

27.204175 0.0000169 1.29 0.000018 32.949

24.731068 0.0000169 1.29 0.000018 29.953

19.784855 0.0000169 1.29 0.000018 23.963

51 | P a g e

Table 24 Calculated Reynolds numbers for unbeaten and beaten pulp sheets to different revolution, after measuring air flow at 60 kPa using vacuum dewatering equipment at 2 ms dwell time.

Air Flow

(m/s)

Hydrostatic

Diameter,

Dh

(meter)

Air

Density(δ)

kg/m3

Air

Viscosity

(μ)

Pas

Reynolds

Number

68.7524 0.0000169 1.29 0.000018 83.271

61.8277 0.0000169 1.29 0.000018 74.884

51.9352 0.0000169 1.29 0.000018 62.902

48.4729 0.0000169 1.29 0.000018 58.709

37.0966 0.0000169 1.29 0.000018 44.930

32.1504 0.0000169 1.29 0.000018 38.939

27.2042 0.0000169 1.29 0.000018 32.949

24.7311 0.0000169 1.29 0.000018 29.953

46.4944 0.0000169 1.29 0.000018 56.312

44.5159 0.0000169 1.29 0.000018 53.916

42.0428 0.0000169 1.29 0.000018 50.921

39.5697 0.0000169 1.29 0.000018 47.926

37.0966 0.0000169 1.29 0.000018 44.930

29.6773 0.0000169 1.29 0.000018 35.944

24.7311 0.0000169 1.29 0.000018 29.953

27.2042 0.0000169 1.29 0.000018 32.949

42.0428 0.0000169 1.29 0.000018 50.921

39.5697 0.0000169 1.29 0.000018 47.926

37.0966 0.0000169 1.29 0.000018 44.930

34.6235 0.0000169 1.29 0.000018 41.935

32.1504 0.0000169 1.29 0.000018 38.939

27.2042 0.0000169 1.29 0.000018 32.949

24.7311 0.0000169 1.29 0.000018 29.953

22.257961 0.0000169 1.29 0.000018 26.958

39.569709 0.0000169 1.29 0.000018 47.926

37.096602 0.0000169 1.29 0.000018 44.930

34.623496 0.0000169 1.29 0.000018 41.935

32.150389 0.0000169 1.29 0.000018 38.939

29.677282 0.0000169 1.29 0.000018 35.944

27.204175 0.0000169 1.29 0.000018 32.949

24.731068 0.0000169 1.29 0.000018 29.953

24.731068 0.0000169 1.29 0.000018 29.953

52 | P a g e

Table 25 Calculated Reynolds numbers for unbeaten and beaten pulp sheets to different revolution, after measuring air flow at 20 kPa using vacuum dewatering equipment at 12 ms dwell time.

Air Flow

(m/s)

Hydrostatic

Diameter,

Dh

(meter)

Air

Density(δ)

kg/m3

Air

Viscosity

(μ)

Pas

Reynolds

Number

16.4874 0.0000169 1.29 0.000018 19.969

8.2437 0.0000169 1.29 0.000018 9.984

6.5950 0.0000169 1.29 0.000018 7.988

4.1218 0.0000169 1.29 0.000018 4.992

5.7706 0.0000169 1.29 0.000018 6.989

4.1218 0.0000169 1.29 0.000018 4.992

3.2975 0.0000169 1.29 0.000018 3.994

3.2975 0.0000169 1.29 0.000018 3.994

15.6630 0.0000169 1.29 0.000018 18.971

7.4193 0.0000169 1.29 0.000018 8.986

5.7706 0.0000169 1.29 0.000018 6.989

4.9462 0.0000169 1.29 0.000018 5.991

4.1218 0.0000169 1.29 0.000018 4.992

4.1218 0.0000169 1.29 0.000018 4.992

3.2975 0.0000169 1.29 0.000018 3.994

2.4731 0.0000169 1.29 0.000018 2.995

11.5412 0.0000169 1.29 0.000018 13.978

3.2975 0.0000169 1.29 0.000018 3.994

6.5950 0.0000169 1.29 0.000018 7.988

4.1218 0.0000169 1.29 0.000018 4.992

4.1218 0.0000169 1.29 0.000018 4.992

3.2975 0.0000169 1.29 0.000018 3.994

2.4731 0.0000169 1.29 0.000018 2.995

10.716796 0.0000169 1.29 0.000018 12.980

5.7705826 0.0000169 1.29 0.000018 6.989

4.1218447 0.0000169 1.29 0.000018 4.992

4.1218447 0.0000169 1.29 0.000018 4.992

3.2974758 0.0000169 1.29 0.000018 3.994

2.4731068 0.0000169 1.29 0.000018 2.995

2.4731068 0.0000169 1.29 0.000018 2.995

1.6487379 0.0000169 1.29 0.000018 1.997

53 | P a g e

Table 26 Calculated Reynolds numbers for unbeaten and beaten pulp sheets to different revolution, after measuring air flow at 40 kPa using vacuum dewatering equipment at 12 ms dwell time.

Air Flow

(m/s)

Hydrostatic

Diameter,

Dh

(meter)

Air

Density(δ)

kg/m3

Air

Viscosity

(μ)

Pas

Reynolds

Number

37.0966 0.0000169 1.29 0.000018 44.930

20.6092 0.0000169 1.29 0.000018 24.961

13.1899 0.0000169 1.29 0.000018 15.975

9.8924 0.0000169 1.29 0.000018 11.981

9.0681 0.0000169 1.29 0.000018 10.983

8.2437 0.0000169 1.29 0.000018 9.984

6.5950 0.0000169 1.29 0.000018 7.988

6.5950 0.0000169 1.29 0.000018 7.988

28.8529 0.0000169 1.29 0.000018 34.946

16.4874 0.0000169 1.29 0.000018 19.969

9.0681 0.0000169 1.29 0.000018 10.983

6.5950 0.0000169 1.29 0.000018 7.988

6.5950 0.0000169 1.29 0.000018 7.988

5.7706 0.0000169 1.29 0.000018 6.989

4.9462 0.0000169 1.29 0.000018 5.991

4.9462 0.0000169 1.29 0.000018 5.991

20.6092 0.0000169 1.29 0.000018 24.961

9.8924 0.0000169 1.29 0.000018 11.981

7.4193 0.0000169 1.29 0.000018 8.986

6.5950 0.0000169 1.29 0.000018 7.988

5.7706 0.0000169 1.29 0.000018 6.989

4.9462 0.0000169 1.29 0.000018 5.991

4.9462 0.0000169 1.29 0.000018 5.991

18.136117 0.0000169 1.29 0.000018 21.966

9.0680583 0.0000169 1.29 0.000018 10.983

6.5949515 0.0000169 1.29 0.000018 7.988

5.7705826 0.0000169 1.29 0.000018 6.989

4.1218447 0.0000169 1.29 0.000018 4.992

4.9462136 0.0000169 1.29 0.000018 5.991

4.1218447 0.0000169 1.29 0.000018 4.992

4.9462136 0.0000169 1.29 0.000018 5.991

54 | P a g e

Table 27 Calculated Reynolds numbers for unbeaten and beaten pulp sheets to different revolution, after measuring air flow at 60 kPa using vacuum dewatering equipment at 12 ms dwell time.

Air Flow

(m/s)

Hydrostatic

Diameter,

Dh

(meter)

Air

Density(δ)

kg/m3

Air

Viscosity

(μ)

Pas

Reynolds

Number

65.9495 0.0000169 1.29 0.000018 79.876

44.5159 0.0000169 1.29 0.000018 53.916

31.3260 0.0000169 1.29 0.000018 37.941

19.7849 0.0000169 1.29 0.000018 23.963

16.4874 0.0000169 1.29 0.000018 19.969

13.1899 0.0000169 1.29 0.000018 15.975

8.2437 0.0000169 1.29 0.000018 9.984

6.5950 0.0000169 1.29 0.000018 7.988

32.9748 0.0000169 1.29 0.000018 39.938

16.4874 0.0000169 1.29 0.000018 19.969

12.3655 0.0000169 1.29 0.000018 14.977

9.8924 0.0000169 1.29 0.000018 11.981

8.2437 0.0000169 1.29 0.000018 9.984

6.5950 0.0000169 1.29 0.000018 7.988

5.7706 0.0000169 1.29 0.000018 6.989

4.9462 0.0000169 1.29 0.000018 5.991

29.6773 0.0000169 1.29 0.000018 35.944

13.1899 0.0000169 1.29 0.000018 15.975

9.8924 0.0000169 1.29 0.000018 11.981

9.8924 0.0000169 1.29 0.000018 11.981

8.2437 0.0000169 1.29 0.000018 9.984

6.5950 0.0000169 1.29 0.000018 7.988

5.7706 0.0000169 1.29 0.000018 6.989

24.731068 0.0000169 1.29 0.000018 29.953

11.541165 0.0000169 1.29 0.000018 13.978

9.8924273 0.0000169 1.29 0.000018 11.981

8.2436894 0.0000169 1.29 0.000018 9.984

6.5949515 0.0000169 1.29 0.000018 7.988

6.5949515 0.0000169 1.29 0.000018 7.988

5.7705826 0.0000169 1.29 0.000018 6.989

4.1218447 0.0000169 1.29 0.000018 4.992