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A novel approach to characterizing pulp fibres using pressure filtration and an interpretation of Canadian.. Mousavi, Payam 2007-02-23

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A novel approach to characterizing pulp fibres using pressure filtration and an interpretation of Canadian Standard Freeness by Payam Mousavi A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Applied Science in The Faculty of Graduate Studies (Mechanical Engineering) The University Of British Columbia July, 2007 © Payam Mousavi 2007 Abstract The purpose of this project is to gain physical insight into a common mea sure of the drainability of papermaking fibre suspensions, that is Canadian Standard Freeness (CSF). We do so by measuring CSF of a thermomechani-cal pulp, refined over the range of 200 - 1200 kWh/t, and comparing this to the permeability and compressibility of the network obtained by conducting pressure filtration. Also, approximate analytical solutions to the filtration equations are presented for different regimes of the problem. We find that the changes in permeability are linearly related to the multiple of permeabil ity and compressibility of the network. From this we are able to gain some insight into the changes in fibre morphology caused by the refining effect. ii Table of Contents Abstract ii Table of Contents iiList of Tables v List of Figures vi Acknowledgements . viDedication viii 1 Introduction 1 2 Background 4 2.1 Canadian Standard Freeness 4 2.2 Pressure Filtration 1 . . ^ 7 2.3 Research Objectives • • • 14 3 Analytical Solution 15 3.1 A >> 1 . • 15 3.2 A « 1 7 iii Table of Contents 4 Methods and Materials 19 4.1 Estimation of the Compressibility Function Py 20 4.2 Method to Estimate Sv 21 5 Results and Discussion 3 6 Summary and Conclusion 3Bibliography 35 Appendices A Experimental Apparatus and Settings 40 B Matlab Code 42 t C Data Tables 8 D Raw Pressure Data 50 iv List of Tables 4.1 The total energy applied and the strategies used to apply the energy through the series of refiners 20 C.l Pulp Properties .49 C.2 Mill Data 4List of Figures 2.1 Canadian Standard Freeness tester 5 2.2 Experimental apparatus 7 5.1 The Canadian Standard Freeness measured after the different refining treatments 25 5.2 Bulk vs. Energy 6 5.3 Breaking Length vs. Energy 27 5.4 Tear vs. Energy 28 5.5 Tensile vs. Energy 9 5.6 Work vs. Energy 30 5.7 Permeability vs. Energy 31 5.8 A comparison of freeness and the filtration diffusivity of dif ferently refined pulps 32 A.l CAD drawing of a piston O-ring adaptor added to the device 41 D.l An example of a pressure data set where A..E are different stages of the refining 51 Acknowledgements I would like to thank my advisors Mark Martinez and James Olson for their active involvement and support in this project. I would also like to thank Tim Patterson and Ken Wong for their technical and administrative support. vii Dedication To my family, Ziba and Mir Mousavi for all their support and encouragement throughout the years. viii Chapter 1 Introduction In this work we examine Canadian Standard Freeness (CSF) and its relation ship to the traditional parameters describing pressure filtration. Part of the motivation for the present investigation stems from an interest in optimizing multi-stage high consistency (HC) reject refining operations. In particular, we are interested in understanding the changes in fibre properties, after dif ferent refining treatments, and relating this to macroscopic properties useful in controlling the paper machine and related to final paper properties. There are a number of research studies found in the literature which have attempted somewhat similar work; see for example, Forgacs [10], Mohlin [24], Kibblewhite & Bailey [16], or Reme et al [25] and the references contained therein. In essence, the goals of these authors were to develop a set of suspension parameters which are related to the final paper prop erties. In what we consider to be the landmark work in this area, Forgacs [10] attempted to characterize the suspension in terms of two fundamental parameters, i.e., the length and the hydrodynamic specific surface. With regards to the first parameter, Forgacs demonstrates that all paper strength properties are related to the fraction of fibres retained on a 48-mesh screen during separation in a Bauer Mcnett. This finding indicates that the length 1 Chapter 1. Introduction distribution of the suspension is a fundamental parameter related to paper strength. This has been confirmed by Mohlin [24] in latter work. In addition to fibre length, Forgacs advances the argument that the specific surface of the fibre, as defined by Mason [23], should also be related to paper strength as this is indirectly related to bonded area. The experimental method to measure the specific area (Mason [23]) is. time consuming so Forgacs substi tuted the rigorous method with a simpler CSF test on a particular fraction of the papermaking suspension. Since this work, Kibblewhite & Bailey [16] and Reme et al [25] have increased, the fundamental set of parameters and used microscopy to characterize the change in fibre diameter and cell wall thickness. We interpret these parameters to be related indirectly to the stiffness or compressibility of the fibre network. In this thesis, we attempt to build on this previous work and present our results in a line of research attempting to develop an understanding of the changes in the furnish during refining. In this, we focus on developing (i) a rapid method to determine specific surface of a paper making fibre suspension through a pressure filtration experiment and (ii) a rigorous in terpretation of CSF in terms of filtration theory. To determine the specific surface, we will measure the pressure required to drain a pulp suspension at a fixed rate and then compare this result to a model given by Landman et al [18]. We will treat the specific surface as an unknown parameter and esti mate its value by comparing the model to experimental data using standard optimization techniques. The pressure filtration experiments and the subsequent analysis are all done on pulp samples collected from the four different stages of a multi-2 Chapter 1. Introduction stage reject refining system currently deployed at Catalyst Paper in Crofton, British Columbia. The details of the experiments are discussed in subsequent sections of this thesis. 3 Chapter 2 Background 2.1 Canadian Standard Freeness One of the basic tools in evaluating pulp characteristics is the Canadian Standard Freeness test. This parameter (or alternatively Schopper Rielgler tester), is a measure of the degree of work done on pulp fibres during various processes. When fibres are subjected to any treatment such as mixing, or re fining, their morphology changes. The following physical changes commonly occur: 1. External fibrillation (the outer walls of the fibre are changed). 2. Fibre shortening (which generally occurs as a result of beating or re fining) 3. Formation of cellulose debris or fines generation The freeness tester was originally designed as a control for groundwood pulp production. However, nowadays, it is used in nearly all aspects of pulp evaluation. The apparatus (Figure 2.1), consists of a drainage chamber and a funnel for measuring the rate of drainage.The drainage chamber includes a standard screen through which the water can drain creating a pad of pulp. 4 Chapter 2. Background stopcock cone cup volume = Vc overflow spout Figure 2.1: Canadian Standard Freeness tester The measuring funnel, consists of a conical shape underneath a cylindrical top. The rate of discharge of water through the cone is directly controlled by the sizes of the orifices (which are standardized). When the lid is opened to start the test, the excess water (which doesn't have enough time to get through the screen) is collected and the volume collected is the freeness value (in mL). This method give values which are highly correlated with the specific surface of the fibres. Therefore, traditional permeability tests (such as sedi mentation or pressure filtration) could also be used. But they are generally more complicated and time consuming than the freeness test, and therefore 5 Chapter 2. Background in many cases are avoided. However, the CSF might produce misleading results. Treatments which produce a large volume of fines may sometimes cause an anomalous rise in freeness. Also, freeness doesn't necessarily corre late with drainability on a commercial paper machine as mentioned above. Freeness is an empirical test and the test results should be interpreted with caution by someone familiar with the particular application. It should be noted that there are many parameters that could cause big variations in the test results as freeness (drainability) is in actuality many different pa rameters combined into one. For example, water quality is very critical, and the use of de-ionized water is recommended. Also, the concentration of fines/debris in the sample could affect the results of the measurement as these could go through the filter more easily resulting in faulty measure ments. Finally, if there are chemicals mixed in with the stock, the results of the test could be affected and as a result, measurements done on pulp stocks don't necessarily correlate with those of pulps from commercial paper machines. Therefore, it can be argued that a more elaborate test which is fast and based on scientific principles is required to properly characterize the pulp. A mathematical treatment of the freeness test by Swodzinski et al [31] shows that, freeness is closely related to the specific surface (i.e. per meability). This work aims to further the understanding of this relationship and using it to characterize pulp fibres from multi-stage reject refiners. 6 Chapter 2. Background Mixer & Pump Co it.tr ol Bo x X=H(t) Data Acquisition System Displacement Trans ducer Figure 2.2: Experimental apparatus 2.2 Pressure Filtration Pressure nitration is a common technique for separating solids from liquids in suspensions. The subject has been thoroughly studied in the past, both experimentally and theoretically. The pioneers of these studies are Wake-man et al [34], Shirato et al [29], Terzaghi & Peck [32], and Sivaram & Swamee [30]. Filtration, and in particular pressure filtration, is a process commonly used in various industries such as medicine, chemical engineering, mining, and paper making. Filtration is part of a larger field, namely solid-liquid separation. The fundamental principle behind filtration is that of flow through porous media first analyzed by Darcy [7]. The theory of filtration was created and developed during the 1970's, and was formulated in paral lel with that of sedimentation ([1, 2, 5, 6]). However, the full mathematical model and suitable numerical methods were not developed till recently. 7 Chapter 2. Background At this point it is instructive to review the mathematical model which we will employ to describe pressure filtration. In this section we consider the pressure o(t) required to maintain a constant rate filtration velocity V of a dilute papermaking suspension at an initial solidity of <f>0 (see Figure 2.2). We consider a filtration event in which a filter is located at x = 0 and the domain extends upwards to a piston located at x = H(t). The papermaking suspension fills this domain and is drained under the pressure generated as the piston moves towards the filter. The height of the suspension is varies as a function of time according to H(t) = H0 — Vt, where HQ is the initial height. Using both the continuity and equations of motion, Landman et al [18] report that a one-dimensional filtration event is modeled reasonably well using a convective-diffusive type relationship. The system of equations reported by these authors, for a constant velocity experiment, is given by dcf) dt = £(»<«£) (2.1) (f>(x, 0) = 4>o (2.2) d(f> dx = 0 (x = H(t)) (2-3) Py(<P) = a(t) (x = 0) rH(t) (2.4) 4>oH0 = / 4>dx Jo (2-5) D(4>) p (2-6) where k(<j>) is the permeability of the suspension; and Py(4>) is the solid stress or "compressibility relationship". From this point forward we will Chapter 2. Background refer to Py(4>) as the compressibility relationship. Equation 2.3 represents a no penetration condition at the surface of pistom It was derived from the fact that at this point the fluid and fibres must be moving at the same velocity. The second boundary condition, Equation 2.4, is derived essentially from Terazaghi's principle and results from the fact that at the surface of the filter membrane, the hydraulic pressure is equal to the atmospheric pressure. It must be noted that Equation 2.1 is a convective-diffusive type equation where the parameter £>(</>) has the units of m2/s and represents, in the traditional sense, a diffusivity. For convenience we name D((f>) as the filtration diffusivity. It is instructive to discuss the two functions used in this work, namely k((j>) and f(<p). We begin this discussion with permeability. Traditionally permeability is defined using Darcy's law which relates the change in pressure AP required to maintain a superfi cial velocity V through a porous medium of thickness L. There is no physical justification of the utility of this equation, except for empirical evidence that it works for most porous medium under creeping flow conditions. There are various experimental methods for determining fc. Most of these methods simply involve the measurement of the superficial flow rate of the fluid for a given pressure drop and comparing these data to Equation 2.7. Perhaps the most comprehensive study of the permeability of various porous materials has been done by Jackson & James [11] where they experimen-9 Chapter 2. Background tally determined the permeability of low Reynolds number flows through fibrous porous media and compared the results to existing theoretical mod els. More sophisticated techniques have been developed in the recent years. For example, Young [37] used sedimentation techniques to determine k. Intuitively it can be expected that permeability is a function of the so lidity cj). Clearly, as the medium densities, there is a corresponding increase in the resistance to flow. Perhaps the most common expression outlining this dependency is given by the Kozeny-Carman relationship ([28]), i.e. where Sv is the specific surface of the particles in the porous medium. There are many other functional forms of permeability that are developed for various ranges of volume fraction. These models have been both the oretically and experimentally studied thoroughly for various applications ([8, 13, 17]). It is worth mentioning that permeability in fibre suspensions is an anisotropic parameter. Thus far, what actually has been discussed here is transverse permeability. It is however also possible to study lateral (in-plane) permeability. Lindsay & Brady [21] have published a series of papers in which they experimentally determine both transverse and lateral permeabilities for various applications . They determined that the ratio of lateral to transverse permeability was 2-3 in most cases, and does not change as a result of compression. They [22] also performed studies, on the factors affecting permeability. These include refining, yield, fines content, pH and sheet formation. For example, it was verified by Carlsson [3], Carlsson et 10 Chapter 2. Background al [4], and Ellis [9] that permeability decreased with increased refining. And, as expected intuitively, high freeness pulp tend to have higher per meability. Traditionally ([10]), freeness is sometimes used as a measure of permeability. This is to simplify the otherwise laborious procedures that exist for measuring permeability. However, Lindsay [19] presents that, it is dangerous to rely on freeness as a measure for permeability or water removal capability of a sheet, as freeness only does this to a degree. Values for free ness are in general correlated with those of permeability. Consequently, any process that results in a reduction in freeness will also often result in the same effect on permeability. However, this correlation is non-linear and path dependent. The path-dependence implies that different treatments that will result in a given freeness might give different permeability. This suggests that CSF might be1 a poor measure of water removal behaviour. Moreover, small changes in freeness may cause large changes in permeability. For in stance Lindsay [19], demonstrates that a reduction in freeness of 700mL to 500mL, may correspond to a permeability change of over 2 orders of mag nitude. Therefore, concerning the water removal ability, permeability is a more sensitive parameter. It is from this literature that we base our work. We now continue with the discussion of the second parameter Py(<j>)-Compressibility or the solid stress is a property of the network of fibres. During compression, once the average volume fraction of the fibres becomes large enough, a network is created which has properties similar to those of solids. As a result of this, compressive stresses on the suspension can be transmitted throughout the system and the structure develops the ability to support itself. As the pressure is increased further, at some point, the net-11 Chapter 2. Background work is no longer able to preserve its structure and it irreversibly deforms. The pressure at which this occurs is denned as the solid stress for the given volume fraction. This function is an implicit function of fibre-fibre inter action forces, and possibly the shear history of the system. Based on the above definition, it is possible to formally define the compressibility function as follows, Py = mi>" - 4>na) (2.9) Py = m(4>-<j>g)n (2.10) where <pg is the gel concentration, i.e. the concentration at which the net work may support load; and m and n are empirical constant that must be determined from experiment ([12, 14, 15, 35, 36]). Before proceeding, it is instructive to scale equations 2.1-2.5. We do so by introducing T </> x - Hit) - tV a , <p0 H0h(t) H0 H0 m With this the governing equations now read 1 .2fT.d<l> _ . d ( .-.d<t>\ , ^d<P (j>(x,0) = 1 (2.13) dx = 0 (x = l) (2.14) m-4>g)n = a(t) (5 = 0) (2.15) It should be noted that for computational purposes we expanded the term (1-1 — 3<f> + 0((j>2) and used this for the optimization 12 Chapter 2. Background 1 = (1- r) P <f>dx (2.16) . Jo where A = 5.5S?/iV^/""2 (2-17) g(4>) = 4>n-2(l-4>otf (2.18) 13 Chapter 2. Background 2.3 Research Objectives The goal of this study is twofold:(i) to gain a better understanding of the Canadian Standard Freeness (CSF) through its correlation to permeabil ity and compressibility parameters and (ii) to exploit these correlations to characterize pulp collected from multi-stage reject refiners (Catalyst Paper, Crofton BC). Also, a variety of standard pulp tests are performed and the results are compared. 14 Chapter 3 Analytical Solution In this section we use asymptotic methods to solve the model equations (2.12-2.18), in order to gain insight into the inverse problem. In addition to this, these limiting cases, serve as known solutions when bench marking the numerical work. In this section we examine two limiting cases. In the first case, we examine the solution with j « 1. Physically, this condition is met when the piston velocity is small (i.e. v —> 0). The second case considered is when A << 1 (i.e. the fast moving piston). 3.1 A»l We start with this case as regular perturbation methods may be used to obtain a solution. Here we seek a solution of the form, oo (3.1) n=0 and can easily show that to the lowest order of approximation, equation 2.12 can be reduced to two linear differential equations, W'0 = l(»t> (32» 15 Chapter 3. Analytical Solution 1 d(p0 d d(f>i d(f>0 0(A): -at = Yx{9^)+^ (3-3) subject to, and, l l (1 - t) = J~4>0dx , 0 = J~4>xdx (3.6) o o The lowest order approximation, equation 3.2, can be integrated directly. When the boundary conditions are applied, the solution reads, *° = Tzrt (3-7) Physically, the solution indicates that mass is conserved at all times and the concentration field is uniform spatially. The first order solution, equation 3.3, can be solved directly with the solution for <p0. This reads, = \rt^-W=t)X+Tg (3-8) with this the approximate solution of (j) is, 16 Chapter 3. Analytical Solution The usefulness of the approximation becomes apparent when we substitute this into equation 2.15, €(7^-^)" = ^) (3-10) The expression implies that if <j(t) is known experimentally, then the un known constant n maybe determined by linear regression. We will use this relationship in the experimental section to determine the compressibility relationship. 3.2 A « 1 This case is somewhat more challenging as it requires singular perturbation methods. In this case, we seek a solution of the form, i + 4>(v,t), V = £ (3-11) where a is a constant. If we set a = 1, after elimination of terms smaller than order A, the governing equation reduces to, Although this equation is much simpler than the original PDE, we still can not obtain a closed form solution. To do so, we linearize the function g((f>) using a Taylor series approximation. When we retain the zeroth order term 17 Chapter 3. Analytical Solution g(<p(0,t)) the equation can be integrated to yield, As(0(O,i)) with the full solution given as, 4>(x,t) = 1+ ,-,n e *«(*(o.O) (3.14) \g(<j>(0,t)) The usefulness of this expression is apparent when we apply equation 2.15. With this we get a direct measure of the function D(<f>), D(4>) = (3.15) This expression will not be used in the remaining part of the thesis as we could not experimentally obtain conditions of A << 1. The determination of D(4>) in this case is done numerically by comparison to experiment. 18 Chapter 4 Methods and Materials In this section we focus our efforts on determining the filtration diffusivity D(4>) of different pulps and comparing this to the measured Canadian Stan dard Freeness. To do so, pulps of differing freeness were prepared using a 4 stage TMP reject refining system located at Catalyst Paper (Crofton, British Columbia, Canada). The refining system consisted of 4 Bauer 480 refiners operated in series. The plate pattern for the first one was Andritz 52-066. The other three had plate patterns J&L 52-135. The rotational speed was 1200 rpm. The refiners were fed with a mechanical pulp suspension at 30% (wt/wt) to a total energy of approximately 1200 kWh/t using the strategies outlined in Table 4.1. In total, five pulp samples were acquired along the length of the refining system, for each refining strategy, and tests were con ducted at the mill to characterize the change in CSF, breaking length, bulk, tear, and tensile strength. Samples were also collected for pressure filtration to determine -D (</>). Latency was removed prior to testing using a Domtar disintegrator. The filtration diffusivity D(<p) was determined in a two step procedure. In the first step, we determine the compressibility function Py. The perme-19 Chapter 4. Methods and Materials Refiner 1 Refiner 2 Refiner 3 Refiner 4 Total Energy (kWh/t) A 390 308 279 248 1225 B 210 264 282 367 1123 C 282 271 261 285 1099 Table 4.1: The total energy applied and the strategies used to apply the energy through the series of refiners ability function is determined in the second step. These two functions are combined in order to estimate D(4>). The filtration experiments were conducted in a 203 mm diamter plex iglass tube with an effective length of 203 mm. The piston is made from stainless steel and is driven using high pressure air. Two sensors are em ployed in collecting the required data. An LVDT displacement (Celesco Transducer Products- PT8420-0010-111-1110) and a pressure transducer to measure the position of the piston and the applied pressure as a function of time, respectively. The filtration experiments were conducted as follows: a 0.06 % (wt/wt) suspension was poured into the apparatus and then stirred; and finally motion of the piston was initiated at a prescribed velocity V 4.1 Estimation of the Compressibility Function Py In this subsection, the experimental method to determined the parameters m, n, and <j>g are given. The method is based upon an asymptotic solution to Equation 2.12, with the boundary conditions.given by 2.13, 2.14 and 2.16, for the limiting case where 1/A <C 1. Physically, this represents the case in 20 Chapter 4. Methods and Materials which the velocity of the piston is very slow, i.e. V C 1 and represents a quasi-static case. With this assumption, we seek a solution for <j> using an expansion of the form = £^n (4.1) and solve using standard perturbation methods to yield cP{x,t) = ^—l + 0(l/\) (4.2) With this Equation 2.15 reads from which the constants TO, n, 4>g can be determined using non-linear re gression techniques (see Appendix B) 4.2 Method to Estimate Sv The details of the numerical methods used to estimate the specific surface of the fibre Sv are presented here. We do so by conducting the filtration experiments at V = 1 mm/s and use the following procedure: 1. First the values of TO, n, <pg are determined by fitting a curve through the pressure filtration data (non-linear least squares method). 2. A trial value of Sv (i.e. specific surface) is assumed. Care should be taken that this guess has the correct order of magnitude as there 21 Chapter 4, Methods and Materials are multiple solutions possible. This can be done by making a rough estimate of the value by looking at the values of different parameters and dimensions of the apparatus. 3. We solve Equations 2.12-2.15 using a(t) as input generated from the experimental results. The parameters m, n, <j>g are also considered to be known. Matlab's 'fminsearch' and 'pdepe' are used towards this goal (see Appendix B). 4. We update the value of Sv using a root-finding procedure until the continuity relationship, i.e. Equation 2.16, is satisfied at every time step. 5. Once Sv is known, the permeability function can be easily calculated from its functional form. 22 Chapter 5 Results and Discussion In this section we present the results in two subsections. In the first part of the discussion we examine the paper properties resulting from the different refining treatments. We do so to examine the effect of the different refining strategies on the pulp. In the second section we present the main findings of this work, a comparison of freeness to the filtration diffusivity D(<f>). To begin, we.examine the effect of refining treatment on freeness, see Figure 5.1. As with all graphs from this point forward, the properties have been normalized to the initial value measured before the refining treatment. The first observation that can be made is that there is no statistical difference between the different refining strategies on the measured freeness. This indicates that for the conditions tested we only need to examine the total of the energy applied and it is path independent. The second observation that can be made is that the slope of the curve diminishes with increasing energy. Similar observations can be made regarding the other properties measured, see Figures 5.2-5.5. Clearly we can draw no physical insight into the changes in fibre morphology, from this data. From our laboratory experiments we measured the compressibility func tion Py and the specific surface Sv. As shown we do not report the value of 23 Chapter 5. Results and Discussion the function Py but instead, report the integral of this function; this repre sents the work required to compress the network during the filtration. We report the values normalized to the initial unrefined pulp. What is clear from this data is that the work increased with increasing energy whilst the permeability decreased over the same range. We attempt to interpret this trend in terms of the changes in physical properties of the network. We attempt to advance the argument that these trends result from changes in external fibrillation of the fibre. This causes a reduced external pore space resulting in a decreased permeability. This also would increase the num ber of inter-fiber contact points resulting in an increased stiffness through decreased fibre mobility. At this point, it is interesting to estimate the filtra tion diffusivity D(<p) using both of these functions. We do so as the filtration theory presented indicates that the filtration event is governed by only one-lumped material parameter: this parameter contains both a compressibility and permeability functions. As a result there should be a direct relation ship between this and freeness. We show this relationship in Figure 5.8 where it is seen that freeness is proportional to the filtration diffusivity. In determination of the property values at the mill, as many as six different experiments were conducted for measuring each parameter. The average is taken as the value while standard protocols axe followed to ensure that the measurements are consistent. 24 Chapter 5. Results and Discussion <D N ro E 1* 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 A • B A C A' • •0 A" 0 ••••H--0 A 200 400 600 800 1000 Energy (KWh/t) 1200 1400 Figure 5.1: The Canadian Standard Freeness measured after the different refining treatments 25 Chapter 5. Results and Discussion 10-0.95 "D 0J M 0.9 \ CO E \ o 0.85 0.8 0.751 0 A • B A C A N • N A V 200 400 600 800 1000 1200 1400 Energy (KWh/t) Figure 5.2: Bulk vs. Energy 26 Chapter 5. Results and Discussion 1.7 •o QJ ^ 1.5 0 A • B 1.6 - A C £ 1.4 o 1.3 _1 c ro 12 CO 1.1 1£-0 0 0 0 A 200 400 600 800 1000 Energy (KWh/t) 1200 1400 Figure 5.3: Breaking Length vs. Energy 27 Chapter 5. Results and Discussion 400 600 800 1000 Energy (KWh/t) 1200 1400 Figure 5.4: Tear vs. Energy 28 Chapter 5. Results and Discussion 0 200 400 600 800 1000 1200 1400 Energy (KWh/t) Figure 5.5: Tensile vs. Energy 29 Chapter 5. Results and Discussion 4.5 3.5 <x> N "co 3 E o 2.5 1:5 1 • A • B A C 0 0 200 . 400 600 800 1000 Energy (KWh/t) 1200 1400 Figure 5.6: Work vs. Energy 30 Chapter 5. Results and Discussion 0.45 0.4 -o 0.35 <B ro E 0.3 0.25 -Q 0.2 £ S. 0.15 0.1 0.05 n r-0 A 0 A • B A C 0 • A._ 0 -J I I I I l_ _l l_ 300 400 500 600 700 800 900 1000 1100 1200 1300 Energy (KWh/t) Figure 5.7: Permeability vs. Energy 31 Chapter 5. Results and Discussion 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Filtration Diffusivity (Normalized) 0.4 Figure 5.8: A comparison of freeness and the filtration diffusivity of differ ently refined pulps 32 Chapter 6 Summary and Conclusion In this work we demonstrated that freeness is proportional to a filtration diffusivity D(<j>), defined using Equation 2.6. Freeness is a widely used pa rameter within the industry and is an excellent measure of the drainage characteristics of the suspension. This parameter has been found to scale with many other resulting paper properties and thus its use is wide spread. The trouble with freeness is that the method and the interpretation of the results are not based on empiricism and conservation laws. Our work demon strates the utility of freeness by relating this commonly used parameter to scientifically-defined conservation laws. Also, pulp samples from different stages of a multi-stage reject refining system (Catalyst Paper), are collected and analyzed using the new tools developed. It is inferred from the analysis that the final pulp qualities are in fact energy path independent. This implies that the only important factor in obtaining the desired results is the total amount of energy that's applied to the sample. Also, there seems to be less effect (less change in some properties) as more energy is applied past 700-800 KWh/t. Therefore, it is recommended that this be taken into consideration for specific applications. Further work could encompass some or all of the following: 33 Chapter 6. Summary and Conclusion 1. /A more reliable pressure filtration device should be designed that can handle higher consistencies and velocities. It is desirable to have the capability for maximum consistency or around 4 — 5%. This would significantly improve the range and accuracy of the results. One idea is to adapt an existing instrument (i.e. the Instron) for this purpose. 2. The Matlab code should be converted to C or Fortran. As it exists, the program is slow. 3. The filtration tests could be done on samples from different stages of paper production. 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Japan 14, 527-532 [18] LANDMAN, K.A., SIRAKOF, C, WHITE, L.R. 1991, "Dewatering of flocculated suspensions by pressure filtration" Phys. of Fluids A 3(6), 1495-1509 [19] LINDSAY, J.D. 1990, "The anisotropic permeability of paper" TAP PI J. 73(5), 223-229 [20] LINDSAY, J.D., & BRADY, P. 1993, "Studies of anisotropic permeabil ity with applications to water removal in fibrous webs, part 1" TAPPI J. 76(9), 119 [21] LINDSAY, J.D., BRADY, P.H. 1993, "Studies of anisotropic perme ability with applications to water removal in fibrous webs - Part 1" TAPPI J. 76(9), 119-127 [22] LINDSAY, J.D., BRADY, P.H. 1993, "Studies of anisotropic perme ability with applications to water removal in fibrous webs - Part 2" TAPPI J. 76(11), 167-174 37 Bibliography [23] MASON, S. G., 1950, "The Specific Surface of Fibres - Its Measurement and Application" TAPPI J, 33(8), 403 [24] MOHLIN, U.B., 1989, "Fiber-Bonding Ability Key Pulp Quality Param eter for Mechanical Pulps to Be Used in Printing Papers" International Mechanical Pulping Conference 49-57, Helsiniki [25] REME, P.A., JOHNSEN, P.O. & HELLE, T. 2001, "Assessment of fibre transverse dimensions using SEM and image analysis" J Pulp Pap. Sci. 28(4), 122-128 [26] ROBERTSON, A.A.,1958, Proceedings of the Third International Me chanical Pulping Conference 180-181, Quebec, QC [27] ROBETRSON, A.A., MASON, S.G. 1949, "Specific surface of cellulose fibres by the liquid permeability method" Pulp and Paper Magazine of Canada 12,103-110 [28] SCHEIDEGGER, A. 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Powder Tech nology 65(1), 283-292 [35] WILDER, H.D. 1960, "The compression creep properties of wet pulp mats" TAPPI J. 43(8), 715-720 [36] WRIST, P.E. 1964, "The present state of our knowledge on the fun damentals of wet pressing" Pulp and Paper Magazine of Canada 65(7), T284-T296 [37] YOUNG E.W.K. 2004, "The permeability and compressibility of semi-dilute pulp fibre suspensions: inversely solving the governing PDE of sed imentation" PhD Dissertation, Department of Mechanical Engineering, University of British Columbia, Vancouver, Canada 39 Appendix A Experimental Apparatus and Settings 40 Appendix A. Experimental Apparatus and Settings 4 X Figure A.l: CAD drawing of a piston O-ring adaptor added to the device 41 Appendix B Matlab Code '/main function clear all;clc; hold on format long; global Xo XX; global pressure displacement time velocity m_f thephi phil; 70 Running the function to input the data analyze; '/.Optimizing to get f(phi) 7„x=[m n phi_g] ; [my_phi pp] = analyze_comp('E3_5g_lp0_08029_l.txt',160000); xo = [le4 .5 le-6] ;*/, .05] ; '/initial guess thephi = linspace(6.3536e-004,10e-4,20); '/.picked based on the data '/, fitting a polynomial through pressure data so that, the fit is simpler. temp_l = polyfit(my_phi,pp,5); temp_p = polyval(temp_l,thephi); options = optimset('TolFun', le-14,'MaxFunEvals',10000,'TolX',le-14,'Maxlter',10000); XX = lsqcurvefit(Of_phi,xo.thephi,temp_p,xo,[lelO 5 1],options); XX = real(XX) '/. plot (thephi ,f_phi (XX, thephi) ) ; 7, D(phi) Optimizationp global phi; myPDE(0.11904199218750); "/. global XXX; '/. Xo = [.01] ; '/. options = optimsetCMaxlter' ,10000, 'TolFun', le-6, 'TolX',le-6, 'Display', 'iter') 42 Appendix B. Matlab Code % [XXX.EXITFLAG] = fminsearchCmyPDE',Xo, opt ions); '/. XXX I % '/, Evaluation and plotting of permeability '/. ksv2 = XX(l)*XX(2)/XXX/MU_water(22) % dl = K(thephi,ksv2); % hold on % plot(thephi,dl,'rs-'); '/, title ('Permeability as a function of phi'); xlabeK 'phi ' ) ; •/.ylabeK'K(phi) [mm-2] ' ) ; 1 70 /.Calculating the work: '/. Area = pi* (203/2) ~2; '/, W = 10e-6*Area*velocity*trapz(pressure,time) °/. Function to solve the pde given D the value of the diffusion equation. % This function is used in the optimization routine main.m. It is assumed % enfrocing this condition is a sufficient optimization scheme. This will be checked later by switching the boundary conditions, function [Error] = myPDE(Xo) m = 0; %slab global phi_o Ho time m_f XX; global gamma; '/.gamma = m*n/(k*S_v~2)/mu(T) gamma = Xo; global thephi; global velocity pressure displacement; global alpha t; global PC; 70testing the forward solver '/.plot(time,pressure); /.some initial parameters Ho = 237; */. mm ho = 32.23; */. the height below the filter displacement(1); °/»phi_o = t2c_conv(0,m_f .velocity,displacement(1)); phi_o = t2c_conv(m_f.displacement(1)); alpha = velocity * Ho; "/.picked for convenience x=linspace(0,1,200); 43 Appendix B. Matlab Code '/.Calculating the appropriate time span: the time for which we have pressure data /,time_final = (displacement(end)-displacement(1))/velocity time_final = time(end); t_final = time_final * alpha / Ho~2; t=linspace(7e-2,t_final,200); global temp; /.temp = (time. *alpha. /Ho. ~2); /.temp = temp./temp(end) /.PC = polyf it (temp. *t_final, pressure, 10) ; t_temp = linspace(0,t_final.length(pressure)); PC = polyfit(t_temp'.pressure,4); /.Testing the polynomial fit: 7. figure(5) '/• ggg=alpha/Ho~2; 7. plot(t_temp,pressure); 7. hold on 7. plot(t_temp,polyval(PC,t_temp), 'r-'); 7. hold off 7. End of test for polynomial fit sol = pdepe(m,@pdefun,@icfun,@bcfun,x,t); global phi; phi = sol(:,:,l);' /.approximation to the solution PHI=real(phi) ; /.used in the conservation of mass 7,phi = phi . *phi_o; phi = real(phi); 7, surf (phi. *phi_o); 7. xlabel('x') 7, ylabel('t') /.Converting to the dimensional variables global xxx; xxx = linspace(0,1,200); hold on for i=l:20:length(phi) plot(xxx,phi(i,:),'-'); end /, plot (xxx, phi',' —'); '/. xlabel('x'); ylabel('Phi') ; /. /, plot (xxx ,phi(l, :)','-'); 44 Appendix B. Matlab Code 7, hold on /. plot(xxx,phi(10,:)','r-'); % '/.plot(xxx,phi(20,:)', 'b—') ; % plot(xxx,phi(30,:)\'g-'); 7. '/.plot(xxx,phi(40,:)','k— '/. plot(xxx,phi(50, :)','c-'); hold off global tt;global xx; tt = t.*(Ho~2/alpha); 7.since t will be between 0 and 1 we want to convert it to O-time(end) /.Implementing the "error" 7. (1) using the conservation of mass 7. Redefine x and t incase they have been changed by pdepe... t=linspace(le-4,t_final,200); x=linspace(0,l,200); for index=l:length(t) . tempi (index) = l/(-t(index)+l); /.assumed alpha=vHo /.defined to increase the accuracy of the integral (i.e. smaller step size) H_t = 0:le-3:l; phi_interp = interpl(x.PHI(index,:),H_t); phi_int(index) = trapz(H_t,phi_interp); end Error_vec = tempi - phi_int; °/,L2 norm is: Error = sqrt(sum(abs(Error_vec).~2)); °/. (2) using BC3 (refer to summary) • . 7. hh = 0.0001; 7. xi = 0:hh: (2*hh) ; 7. for i=l:length(t) 7, phi_interp = interpl(x,phi(i,:) ,xi); 7. temp = dif f (phi_interp) ; 7, dpdx(i) = temp(l)/hh; 7. end 7, Error_vec2=(-t+l)'-dpdx'.*(gamma.*(phi(:,1).~2-beta.*phi(:,1).~3)) 45 Appendix B. Matlab Code ./(phi(:,l)*alpha); '/ °/L2 norm is: '/, global Error2; '/ Error2 = sqrt(sum(abs(Error_vec) . ~2)) '/Error =1; '/Helper function required for pdepe '/ the pde Function. function [c,f,s] = pdefun(x,t,phi,dudx) '/global aa;global bb;global cc; global Ho; global velocity; global alpha; global XX; global phi_o; global gamma; '/ phi*phi_o = PHI which we're solving for... D = gamma * (phi*phi_o-XX(3)*phi_o)~(XX(2)-1) * (l/(phi*phi_o) -3); °/D = gamma * (phi*phi_o-0*phi_o)"(XX(2)-1) * (l/(phi*phi_o) - 3); c = (l-(velocity*Ho/alpha)*t)~2; f = (D/alpha)*dudx; s = (x-1)*(-velocity*Ho/alpha)*(1-(velocity*Ho/alpha)*t)*dudx; '/ Initial Conditions function phi_i = icfun(x) global alpha; global aa; global bb; global cc; global phi_o; phi_i = l;°/phi_o; '/ Boundary Conditions function [pi,ql,pr,qr] = bcfun(xl,phi_l,xr,phi_r,t) global alpha; global XX; global phi_o; global Ho; global velocity;global pressure;global time; global gamma; global. PC pr = 0; qr = 1; '/making time dimensionless '/ time = time.*(alpha/Ho~2); '/ time = time./time (end); . . '/ pressure data used: '/thePressure = interpKtime,pressure,t) ; thePressure = polyval(PC,t); */.pl = phi_l - (l/phi_o)*(thePressure/XX(l) + XX(3)~XX(2))~(1/XX(2)) ; '/type I f(ph '/Normal Solver pi = phi_l - (l/phi_o)*((thePressure/XX(l))*(l/XX(2)) + XX(3)); '/type II f(phi) 46 Appendix B. Matlab Code '/.pi = phi_l - (l/phi_o)*((thePressure/XX(l))-(l/XX(2)) + 0); '/.type III f(phi) ql = 0; % forward solver ' '/. pi = phi_l*alpha*(t-l); '/. DD = gamma * (phi_l*phi_o-XX(3)*phi_o) ~ (XX (2)-1) * (l/(phi_l*phi_o) - 3); % ql = -DD/alpha; function F = f_phi(x,phi) '/.F = x(l).*(phi.~x(2) - x(3)"x(2)); F = x(l).*(phi - x(3)).~x(2); •/.F = x(l).*(phi.-x(2)); function k = k_eval(gamma,beta) a=gamma*le-6/l.336e4/2.95; b=beta; phi=0.0001:.00001:.001; plot(phi, a.*exp(-b.*phi)./phi); k=l; function [data] = maindatalnput(myfile) global data; fopen(myfile); data = dlmread(myf ile); f close Call'); dt = data(2,2); %get from data function f=MU_water(T) Temperature = [20 40 60 80 100]; /units: g/mm/s viscosity = [0.001 .000653 .000467 .000355 .000282]; f = interpl(Temperature, viscosity,T); function phi = t2c_conv(t,m_f,v.Xoffset) Ho = 237 - (Xoffset -32.23); ro_w = 0.001; %g.mm-3 ro_f = 0.0015; y.g.mm-3 phi = m_f (./ ((pi*101.5"2*ro_f).*(Ho-v.*t)); 47 Appendix C Data Tables Norm Bulk g S « CD CD CO § — fe ^ 3 S§^ Norm Elongitlon r~ 3 jji 05 j^i - •$ jo Jorm. Breaking Length £j ij> rjj E -ES3S Norm. Mellen Gauge $ § « 5 normalized tear reading g 5jj p 5j "sii? normellied caliper |||| 1 S 11 | § I £ normalized tensile p S| 3 s|Si t» o c? o> rt <p AntBt IftSS "51833 ft. as I a 151 I lip il illll Ill SIS SSSSS 88888 88888 oodh'ui o o -•r tfi <•> d iv n T oi Total Energy(KWh) SSSR S 5 £ 2 K S 5 | ????? ????? ????? ???? ????? ????? §§??? 5555 E ' MSSii SIISI alSsS §p§ TEA R.adlng (J'm2) 5 8 S S S S K S 3 S KSSSS 5 8 S 3 Elongation Reading (mm) " — — — tJtJ Breaking Length Reading (km) 0 2§ili 111? Ilan Oauga Raadlng (pal) E 2 S S S 2^SK3S 2 2 R S R 3 w m §1§S§ iilli IISSs ?iss a— Tear Heading (gt) !; « J 3 ° 2 8 ? 2 * 3'3 S ; £ £ S 8 S y) SSSSS 8155: = SSSjijg g58S QJ s eneet Caliper (thou>;j88SS5 S ; 8 8 8 ? 8 8 8 3 • §1111 ISSil ?s;l Tensile Readlng(kN/m) -  rj M to -cJcJrioi - ai rj oj Q_ ±~ Fraaneaa a ffi « g « 8 8 8 8 S St^SS 8 8 2 5 0) SSSfS ????? Q. g> -Illll lilll fill 1818 % "8 m'KP"lllll lllll 11111 llll - » ^ 010 0.0,0.0. 0.0.-0.0. 3 pill lpsi pip Iii 1 ^ """,<j°"i"iliisi gisgs E • g CO Wort((Joulaa)Cotnpiaaaibility Curvan * i ^ ol si?o3 Sj lj * i § 3333 CD iisSs 2»SS5 3rSsS( tr s CD Q- SSi O PormaaOillty (k'Sv*2) - j3 £ aassa sasss Results T2 - Feed T2 -480-1 T2 - 480-2 T2 - 480-3 T2 - 480-4 T3 - Feed T3-480-1 T3 - 480-2 Freeness (CSF) mL 266 177 117 83 51 256 196 138 Brighlness 47.2 47.7 48.3 48.4 48.9 46.6 47.50 47.50 Scattering Coefficient .43.94 45.71 48.34 52.43 54.97 41.93 44.73 47.97 Absorption Coefficient 4.88 4.93 5.09 5.52 5.56 4.77 4.88 5.41 Handsheet Data # of Handsheets 6 6 6 6 6 6 6 6 Conditioned Weight g 8.17 8.11 8.37 8.27 8.27 8.04 8.28 8.39 5 sheet Caliper thou 43.4 39.4 38.3 35.5 33.7 42.5 41.8 39.6 Tear Reading gi 48.0 48.8 46.5 41.5 39.3 48.8 56.0 49.0 # of Sheets Torn 10 10 10 10 10 10 10 10 Mullen Gauge Reading psi 13.1 18.7 23.6 24.4 27.7 14.4 17.9 20.5 # of Sheets Burst 1 1' 1 1 -1 1 1 1 Tensile Reading kN/m 1.99 2.17 2.67 3.00 2.88 1.97 2.34 2.65 Breaking Length Reading km 3.32 3.66 4.37 4.97 4.75 3.34 3.85 4.31 Elongation Reading mm 1.68 1.74 1.93 2.35 2.91 1.76 1.68 1.98 TEA Reading J/m2 21.57 24.69 33.95 46.67 55.56 22.68 25.56 34.46 Calculations Oven Dry Weight g 3.80 3.74 3.85 3.81 3.80 3.72 3.83 3.88 Conditioned Weight g 4.23 4.17 4.30 4.26 4.24 4.15 4.26" 4.33 % Bone Dry % B.D. 89.83 89.69 89.53 89.44 89.62 89.64 89.91 89.61 Basis Weight g/m2 61.16 60.61 62.45 61.63 61.76 60.06 62.03 62.65 Bulk cm3/g 3.60 3.30 3.12 2.93 2.77 3.60 3.42 3.21 Tear Index mN.m2/g 12.31 12.63 11.68 10.56 9.98 12.75 14.16 12.27 Burst Index kPa.m2/g 2.95 2.13 2.60 2.73 3.09 1.65 1.99 2.25 Breaking Length m 3320 3660 4370 • 4970 4750 3340 3850 4310 Tensile Index N.m/g 32.54 35.80 42.76 48.67 46.63 32.80 37.72 42.30 Stretch % 1.68 1.74 1.93 2.35 2.91 1.76 1.68 1.98 TEA Index JTXg 353 407 544 757 900 378 412 550 #3RejRef #3RejRef #3RejRef #3RejRef TMP#1 480-3 T3 - 480-4 T4 - Feed T4 - 480-1 T4 480-2 T4 480-3 T4 480-4 Feed 4000kw 5500kw 6850kw DF 99 64 253 155 108 88 62 . 298 156 118 101 47 48.50 49.1 46.9 48.2 48.7 49.3 48.8 47.6 48.9 48.6 48.9 44.1 50.27 53.62 41.20 46.88 51.92 53.81 58.40 40.29 45.63 48.52 49.45 60.04 5.20 5.46 4.64 5.00 5.36 5.29 6.14 4.55 4.69 5.13 5.26 9.39 6 6 6 6 6 6 6 6 6 6 6 6 8.33 8.35 8.15 8.27 8.30 8.20 8.18 8.09 7.96 8.11 8.07 7.20 36.3 35.1 42.2 38.7 36.7 34.9 33.5 43.7 36.4 35.9 34.7 30.2 42.8 41.0 47.3 48.8 44.5 44.0 40.5 47.5 50.3 46.5 44.3 27.5 10 10 10 10 10 10 10 10 10 10 10 10 23.7 25.8 15.1 18.1 21.8 22.4 24.9 13.2 17.3 20.8 22.1 15.6 2.93 3.10 1.92 2.40 2.66 2.85 2.84 1.78 2.24 2.41 2.76 2.00 4.78 5.05 3.21 3.94 4.39 4.75 4.75 3.02 3.85 4.09 4.72 3.80 2.19 2.22 1.74 2.04 2.06 2.30 3.10 1.51 1.90 2.23 2.26 2.18 42.91 45.34 21.58 32.16 36.67 43.54 59.81 23.75 27.86 35.72 41.62 28.79 3.88 3.87 3.76 3.83 3.83 3.79 3.79 3.71 3.67 3.74 3.70 3.32 4.31 4.31 4.19 4.26 4.28 4.23 4.23 4.16 4.11 4.21 4.17 3.71 90.02 89.79 89.74 89.91 89.49 89.60 89.60 89.18 89.29 88.84 88.73 89.49 62.49 62.48 60.94 61.96 61.89 61.22 61.07 60.12 59.23 60.04 59.67 53.69 2.95 2.85 3.52 3.17 3.01 2.90 2.79 3.69 3.12 3.04 2.95 2.86 10.75 10.30 12.18 12.36 11.28 11.28 10.40 12.40 13.32 12.15 11.65 8.04 2.61 2.85 1.71 2.01 2.43 2.52 2.81 1.51 2.01 2.39 2.55 2.00 4780 5050 3210 3940 4390 4750 4750 3020 3850 4090 4720 3800 46.89 49.62 31.50 38.74 42.98 46.55 46.50 29.61 37.82 40.14 46.26 37.25 2.19 2.22 1.74 2.04 2.06 2.30 3.10 1.51 1.90 2.23 2.26 2.18 687 726 354 519 592 711 979 395 470 595 698 536 Table C.2 Mill Data Appendix D Raw Pressure Data Appendix D. Raw Pressure Data Figure D.l: An example of a pressure data set where A..E are different stages of the refining 


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