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Hubbe, M. A., Sjöstrand, B., Nilsson, L., Koponen, A., and McDonald, J. D. (2020). "Rate-limiting mechanisms of water removal during the formation, vacuum dewatering, and wet-pressing of paper webs: A review," BioRes. 15(4), 9672-9755.

Abstract

Because some of the critical events during the removal of water before the dryer section on a paper machine happen very rapidly within enclosed spaces – such as wet-press nips – there have been persistent challenges in understanding the governing mechanisms. In principle, a fuller understanding of the controlling mechanisms, based on evidence, should permit progress in achieving both higher rates of production of paper and more reliable control of paper attributes. In addition, energy can be saved, reducing environmental impacts. The goal of this article is to review published work dealing both with the concepts involved in water removal and evidence upon which existing and new theories can be based. The scope of this review includes all of the papermaking unit operations between the jet coming from the headbox and the final wet-press nip of an industrial-scale paper machine. Published findings support a hypothesis that dewatering rates can be decreased by densification of surface layers, plugging of drainage channels by fines, sealing effects, flocculation, and rewetting. Ways to overcome such effects are also reviewed.


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Rate-limiting Mechanisms of Water Removal during the Formation, Vacuum Dewatering, and Wet-pressing of Paper Webs: A Review

Martin A. Hubbe,a,* Björn Sjöstrand,b Lars Nilsson,b Antti Koponen,c and J. David McDonald d

Because some of the critical events during the removal of water before the dryer section on a paper machine happen very rapidly within enclosed spaces – such as wet-press nips – there have been persistent challenges in understanding the governing mechanisms. In principle, a fuller understanding of the controlling mechanisms, based on evidence, should permit progress in achieving both higher rates of production of paper and more reliable control of paper attributes. In addition, energy can be saved, reducing environmental impacts. The goal of this article is to review published work dealing both with the concepts involved in water removal and evidence upon which existing and new theories can be based. The scope of this review includes all of the papermaking unit operations between the jet coming from the headbox and the final wet-press nip of an industrial-scale paper machine. Published findings support a hypothesis that dewatering rates can be decreased by densification of surface layers, plugging of drainage channels by fines, sealing effects, flocculation, and rewetting. Ways to overcome such effects are also reviewed.

Keywords: Drainage rate; Hydrofoil; Vacuum flatbox; Couch roll; Press felt; Extended-nip press

Contact information: a: Department of Forest Biomaterials, North Carolina State University, Campus Box 8005, Raleigh, NC 27695-8005; b: Department of Engineering and Chemical Sciences, Karlstad University; Karlstad, Sweden; c: VTT Tech. Res. Ctr. Finland Ltd, POB 1603, Jyväskylä 40401, Finland; d: JDMcD Consulting Inc., 97 rue Kerr, Vaudreuil-Dorion, Quebec, Canada J7V OG1;

* Corresponding author: hubbe@ncsu.edu

Contents

INTRODUCTION

Given the capital-intensive nature of papermaking operations, there is a strong motivation to achieve high rates of production on the paper machine itself. Many paper machines are drier-limited, meaning that the maximum rate of production is essentially limited by the ability of the system to evaporate water from the sheet (Paulapuro 2000). In such situations, by achieving higher solids content in the wet-web of paper by the time it leaves the final nip of the press section may lead to a higher speed of production. In addition, a high-solids web entering the press section typically yields higher runnability in the press section; not only is the web stronger, but less water needs to be removed. Higher nip loading may then be possible, leading to higher outgoing solids and ultimately higher overall production (Räisänen 2000a).

The production of pulp and paper requires large amounts of energy, but much of that energy comes from the incineration of biorenewable resources. In particular, the combustion of lignin in the black liquor from alkaline pulping processes can provide a major proportion of the steam and electrical energy needed to run paper mill equipment and evaporate moisture as the paper is being dried (Empie 2009; Bajpai 2017). However, most pulp and paper facilities share power with the electrical grid, and others use any excess steam for heating of nearby facilities. As a consequence, savings in energy usage during papermaking can provide large benefits for both profitability and the environment. In addition, steam that can be saved by improved efficiency of dewatering can be used for other purposes in the mill, such as the drying of market pulp.

As a general rule, the removal of water from paper during its production tends to become increasingly expensive, on a mass basis, as the process proceeds (Kullander et al. 2012). Gravity drainage through a screen can require large amounts of capital expense, but in other respects it is very cost-effective. Removing water from a paper web by means of vacuum boxes requires the running of vacuum pumps (Räisänen 2000a), and increased electrical power is needed to overcome the friction between the forming fabric and the cover of each vacuum box (Eames and Moore 1976; Hansen 1985). It has been estimated that vacuum boxes can consume one-fifth of the electricity used on a typical paper machine (Håkansson 2010; Nilsson 2014b). Since evaporation requires the highest amount of energy, based on the mass of water, there is an inherent advantage when the web solids are as high as practical once it leaves the final nip of the wet-press section (Afshar et al. 2012).

The manner of water removal during paper manufacturing also has a large impact on product quality. Examples of paper attributes that can be profoundly affected by water removal procedures include wiremark, pinholes, densification of surface layers, as well as the overall density, smoothness, and porosity of the resulting paper. Published literature dealing with the dewatering of paper tends to be disproportionately represented by some of the most traditional designs of equipment, such as the Fourdrinier forming section, in which filtrate (or “white water”) is mainly removed through the bottom side of the wet web. Readers will need to bear in mind that a corresponding emphasis in the present review article is partly a consequence of what topics have been most studied. It seems likely that many of the principles that can be derived from study of Fourdrinier dewatering and conventional wet-press nips, etc. can provide insights into other kinds of forming devices and presses, etc.

In addition to the practical issues mentioned above, a further motivation for the present review article is scientific curiosity. Much progress has been made in predicting the effects of various factors on different water-removing unit operations in paper machine systems (Ingmanson 1964; Wahlström 1969; Kerekes and McDonald 1991; Ramarao and Kumar 1996; McDonald et al. 2000; Nilsson 2014a; Koponen et al. 2016; Sjöstrand et al. 2017, 2020). But there are remaining questions concerning the implications and underlying assumptions used in the related models. Some key issues to be considered in this article include non-uniform distributions of solids within the paper web during water removal, mechanisms by which water removal rates can deviate from the predictions of some established models of dewatering, and mechanisms of rewetting of the paper web after vacuum dewatering and after wet-pressing. By better understanding the underlying causes, there may be opportunities to improve the design and adjustment of papermaking equipment, and optimize papermaking chemical programs to achieve better overall results.

 

Earlier Review Articles

As shown in Table 1, there have been many previous review articles and chapters dealing with water removal during papermaking processes. Regarding the historical development of studies of wet-pressing, MacGregor (1989) has provided a detailed overview. The present article attempts to build upon the existing progress, as documented in the works shown in Table 1, but with an emphasis on some phenomena that are not easily included in mathematical models.

Table 1. Notable Review Articles Dealing with Water Removal before the Dryer Section of Paper Machines

Organization of the Article

The remainder of this article will be organized into four main sections, of which the next will be very short – introducing some working hypotheses. Next, to provide background, the operations of key dewatering equipment present in typical paper machine systems will be described. Then the next section will consider various mechanisms to account for dewatering effects, along with reported evidence relative to such mechanisms. Finally, before the concluding statements, a section will be devoted to strategies for achieving more effective dewatering in various unit operations of papermaking.

WORKING HYPOTHESES

Purpose of Proposing Hypotheses

A set of hypotheses will be considered in this article as a means to focus the discussion. Some of these hypotheses may pertain to more than one unit operation of papermaking. The overall goal is to provide background for more realistic prediction and estimates of dewatering effects in the future. There is a well-known saying that every mathematical model is incorrect, but some of them are useful (Box 1976). Early concepts that have been used to fit dewatering data from papermaking operations tended to be overly simple, not accounting for the compressibility of the materials (Sullivan and Hertel 1942). But even with advances in mathematical approaches, some aspects, such as the plugging and sealing to be described in this work, are inherently difficult to capture in a mathematical sense. Thus there is a need for creative work to incorporate additional mechanistic features into quantitative estimates of dewatering rates.

The Hypotheses

The hypotheses to set the stage for discussions in this article are listed in Table 2.

Table 2. Some Working Hypothesis Concerning Factors Affecting Rates of Release from the Wet-web of Paper During its Manufacturing

PAPER MACHINE DEWATERING OPERATIONS

Paper Machine Overview

The scope of the discussion will begin more-or-less as the suspension of cellulosic fibers and fine matter (i.e. the “thin stock”) emerges as a wide jet from the headbox of a typical paper machine and heads toward a forming fabric or fabrics. The fabric or fabrics will likely then pass over such dewatering elements as hydrofoils, forming blades, and vacuum boxes, and a vacuum couch roll. Then the paper will pass through a series of wet-press nips, which are often three in number, after which any additional water to be removed will require evaporation, which is the slowest and most expensive process, based on the mass of water to be removed.

Before discussing each of the main unit operations associated with dewatering, an overview is provided in Table 3, giving some approximate ranges for the consistency (percent filterable solids), as well as the main types of forces affecting dewatering in each operation.

Table 3. Overview of Unit Operations Contributing to Dewatering in a Paper Machine System

In view of issues raised in the hypothesis statements (Table 2), one can consider how the dominant mechanisms affecting dewatering are likely to be different in different parts of the paper machine system. Early in the process, especially between the forming board and the dry line of a Fourdrinier paper machine, it is reasonable to expect a filtration mechanism to be dominant. After the dry line (meaning that the surface of the wet web no longer looks smooth and water-like), some additional terms may be used to describe aspects of the process. The term displacement dewatering will be used here to indicate sub-processes in which the water held within a wet-web of paper is being displaced by air. The term compression dewatering will mean that water is expelled when the net volume of air-free paper is decreased due to an applied pressure, resulting in outward flow of water. For example, it is reasonable to expect air to begin to displace water within the wet web once a sufficient level of vacuum is applied, using a suction box (or vacuum flatbox). The ingoing part of a wet press nip is clearly dominated by a compression mechanism. Rewetting phenomena can be important following certain vacuum dewatering and wet-pressing operations. All of these issues will be considered more deeply in the sections that follow.

Impingement of the Jet on the Wire

At the headbox of a conventional paper machine, the fiber suspension already has been prepared by mechanical refining and addition of selected chemicals. Because the stock at that point has been already diluted by process water (white water), it has the lowest value of consistency that it will achieve anywhere in the process. Part of the reason for the relatively low consistency at the headbox is to avoid excessive crowding of the fibers, which would lead to a flocky appearance of the paper (Kerekes and Schell 1992; Kerekes 2006; Hubbe 2007). The low consistency also facilitates the action of hydrocyclones, which remove dense particles such as sand from the stock before it reaches the forming section. However, the high proportion of water, for instance about 99.5% of the mass present in the jet coming from the headbox, presents a tremendous challenge. Not only must the water be separated from the solids, but also this must be done in a way that results in a relatively uniform distribution of fibers. In addition, those fibers individually need to be relatively straight, generally oriented within the X-Y plane of the paper. If there is a preferred orientation, the mean value of orientation needs to be aligned with the direction of manufacture, not at an angle.

Some basics related to the flow from the slice of a headbox have been explained concisely by Zhao and Kerekes (2017). A detail that is particularly worth noting, when attempting to predict what will happen to the jet of furnish coming from the headbox, is the fact that the thickness of the jet typically contracts after it emerges from the slice opening. The contraction factor can be as low as 0.62 when comparing the height of the slice opening with the thickness at the vena contractai.e. the point of highest velocity and minimum jet thickness.

An interesting conceptual model of dewatering, starting at the point of jet impingement on the forming fabric, was presented by Herzig and Johnson (1999). Figure 1 is a new drawing inspired by an original in the cited work, but with some clarifications and updated terminology. As depicted in the diagram, this model is consistent with a process of simple filtration, analogous to the formation of a paper handsheet from a highly dilute aqueous suspension (see TAPPI Method T205). The model envisions basically two phases present within the wet web. Near to the forming fabric, which is the point at which water is being removed due to pressure resulting from the inertia of the jet, there is a “mat” or “boundary layer” phase, where the consistency is distinctly higher than the headbox consistency (Herzig and Johnson 1999; Helmer et al. 2006). But above that zone, the rest of the wet web is modeled as still having essentially the same proportion of water as it did within the headbox. A key argument in favor of the essential validity of the relatively simple model presented in Fig. 1 is the fact that most fibers in a typical sheet of paper are oriented in a layered structure, as if they belong to a series of two-dimensional sheets (Kufereth 1982a). Though many additional concepts will be discussed in this review article, it will be important to keep in mind that a filtration mechanism tends to be dominant in typical papermaking operations.

Fig. 1. Concept of paper mat buildup on the forming fabric of a Fourdrinier paper machine starting at the point of jet impingement (based on Herzig and Johnson 1999)

According to Herzig and Johnson (1999), resistance to the flow of water through a forming fabric will increase in direct proportion to the amount of fiber mass deposited onto it, at least up to an amount between 15 and 25 g/m2. In fact, the flow-resistance attributable to the mat of fibers quickly becomes a more dominant factor than the flow-resistance of the forming fabric, especially if the pulp is well refined. The cited authors also pointed out something unique about the point of jet impingement on the forming fabric; that is the only location throughout the rest of the dewatering process where the momentum and inertia of the stock suspension itself provides a major component of force contributing to rapid release of water. Ingmanson and Andrews (1959) estimated that the velocity of water downward through the forming fabric near the beginning of the dewatering process can be as fast as 150 cm/s. Whether or not such rapid dewatering at the point of jet impingement is good papermaking practice will be questioned in later sections of this article, however, when some mechanistic issues are considered in more detail.

Three prominent aspects of the flow patterns associated with the jet impingement area can be called oriented shear, turbulence, and drainage (Parker 1972; Kufereth 1982a; Norman 1989, 2001; Kiviranta 1992). Oriented shear in the impingement zone comes from two sources. First, the fibers within the jet of furnish coming from the headbox tend to be preferentially oriented in the machine direction. Though the reasons for this orientation are not strictly within the scope of this article, they are related to elongational shear within the contracting zone of the headbox slice (Aidun 1998; Hubbe 2007). The other source of oriented shear is the fact that, in a great many cases, papermakers adjust the speeds of the jet and the forming fabric to be slightly unequal. The resulting “rush” or “drag” of the stock gives rise to oriented vorticity. This imparts an oriented rotational motion of elements of fluid, which further contributes to an average preferential alignment of fibers in the direction of flow or manufacture (Jeffery 1922; Stover et al. 1992; Orts et al. 1995; Gunes et al. 2008; Mortensen et al. 2008; Perumal et al. 2019). As part of this effect, an individual fiber can be drawn into machine-direction alignment when one end of the fiber is influenced by the fabric surface and the other end is influenced by fluid having a difference in velocity relative to the fabric. The word “turbulence” merely means that the flow is chaotic and contains multi-scale vortex flow (Aidun 1998). The word “drainage” means, in the case of a Fourdrinier paper machine, that there is a net movement of water downwards.

As will be discussed in more detail later in this article, there is some evidence that interactions between individual fibers at the forming fabric sometimes can result in resistance to dewatering that would not be predicted from either the fibers or the fabric alone. Such effects, even when imprecisely defined, have become known as “sheet sealing” or perhaps more accurately as “fabric sealing” (Kufereth 1983). In particular, it has become accepted wisdom among some papermakers that fabric sealing tends to be more of a problem if initial drainage is too rapid, for instance when the angle of impingement of the jet onto the forming fabric is too steep.

Forming Board Issues

The function of a forming board, though consistent with the issue of fabric sealing, may at first seem out of step with an overall goal of removing as much water as practical from paper in a relatively short period of time. The forming board is a relatively flat platform just below the forming fabric of a Fourdrinier forming section that temporarily blocks or slows down the progress of water through the forming fabric. One can consider the forming board as a way to achieve a stable layer of suspension on top of a fast-moving fabric. Papermakers call this “setting the sheet”. Typically about a quarter of the fluid is drawn from the impinging jet before the forming board so that no air can be drawn in between the forming fabric and the wet web when it is resting on the flat part of the forming board. Otherwise, the jet may bounce, creating an unstable situation and operational problems.

Hydrofoils (Fourdrinier paper machines)

Though terms such as “gravity drainage” are widely used within the paper industry (Britt 1981; Ahonen et al. 1992; Rezk et al. 2013; Nilsson 2014b; Singh and Green 2015), there are essentially no modern paper machines that rely on gravity alone during the formation of the sheet. During the early years of Fourdrinier-type papermaking, the forming fabric was held horizontal by “table rolls,” which were found to provide some benefits in terms of dewatering within favorable speed ranges (Victory 1969; Cadieux 1983; Zhao and Kerekes 2017). Wrist (1954) and Taylor (1956, 1958) provided a way to estimate the suction that can occur just behind the mid-point position of a table roll. Such suction helps to remove water from the wet web. The subsequent release of suction creates instabilities that, in moderate amounts, can improve the uniformity of formation. However, as further developments of technology allowed paper machine speeds to climb well beyond 300 m/min, surface instabilities caused by the sudden release of suction produced by table rolls became strong enough to disrupt the wet webs.

The problems with table rolls, as mentioned above, were overcome by the development of hydrofoils (often called “foils”), which are illustrated schematically in Fig. 2. The original development is attributed to Burkhard and Wrist (1956) of the Quebec North Shore Paper Co. The design of the most basic type of hydrofoil can be described as having a land area parallel to the forming fabric, followed by a surface having a diverging angle, often about 3 degrees (Miller 1998). Typical widths of blades were estimated to be about 50 to 89 mm. Hydrofoils became widely used after the introduction of plastic-type forming fabrics, which are many times more durable than the bronze “wires” that had been used on paper machines up to that point (Zhao and Kerekes 2017). Though hydrofoils have been found to be effective for removal of water during the initial part of a Fourdrinier forming section, they do not have the ability to achieve high levels of solids, as indicated in Table 3.

Two types of pressure effects are believed to act upon the wet web of paper as it passes over a typical hydrofoil. First, at the leading edge of the hydrofoil it is expected that some water will tend to be pushed up into the wet web, i.e. a brief pressure pulse (Eames 1993). Then, especially as the web passes over the area where the hydrofoil surface diverges from the linear path of the forming fabric, a vacuum event is expected (Taylor 1958). Cadieux (1983) reported that the maximum vacuum is generated relatively early as the sheet passes over a hydrofoil. These pressure and vacuum effects are indicated schematically in Fig. 2, which indicates a suction effect occurring where the surface of the foil is diverging from the linear path of the fabric. In addition to tending to dewater the wet web, the action of the hydrofoil tends to promote microturbulence within the wet web. The intensity of microturbulence (which is often called “action”) can be judged from the appearance of images obtained with stroboscopic illumination (Miller 1998). The intensity of microturbulence can be optimized by adjusting the design, alignment, and spacing between subsequent hydrofoils (Kawka et al. 1981; Ahonen et al. 1992; Miller 1998). Also, various details of the shape of a hydrofoil can be changed (Sodergren and Neun 2000).

Fig. 2. Schematic diagram of a hydrofoil below a forming fabric with a wet-web of paper on it. Deflections are greatly exaggerated in the depiction as a means to suggest the mechanisms of action.

Another consequence of hydrofoil action is a partial refluidization of the wet web structure; this results in a washing out of cellulosic fines and other small particles, especially those near to the “wire-side” of the paper web (Eames and Moore 1976; Sodergren and Neun 2000). Neun and Fielding (1994) suggest that washing effects become much less important above a solids content of about 6% due to increasing strength and integrity of the wet-web structure. Such washing and refluidization effects happening in real paper machine forming sections appear to explain the poor correlations often observed between ordinary freeness and drainage tests, using simple equipment, in comparison to results of commercial trials on paper machines (Persson and Österberg 1969; Britt 1981; Hubbe et al. 2006).

Forming Blades (some gap-former paper machines)

Though published information about dewatering events on Fourdrinier (single forming fabric) paper machines is more abundant, some excellent studies have been reported having to do with dual-fabric paper machine designs (gap formers, which are also called twin-wire formers), which have become dominant in recent paper machine installations. In situations where a wet web of paper is sandwiched between a pair of forming fabrics, the function of a hydrofoil is generally replaced by a forming blade, which touches the outside surface of one of the forming fabrics over a very brief distance (Norman 1987, 1989; Räisänen 2000b; Wildfong et al. 2003; Zhao and Kerekes 2017). As shown by Brauns (1986) of the Beloit Corporation, as the sandwich of two forming fabrics passes a blade, with a wet web of fibers between them, there is a quick rise in pressure, followed by an abrupt fall. The mathematics to account for the effects were presented by Zhao and Kerekes (1995, 1996) and by Zahrai and Bark (1995). It has been shown that these sharp changes in pressure cause displacement of material in the middle of the wet web opposite to the direction of manufacture by as much as 3 to 9 mm (Zhao and Kerekes 1996). Two main consequences of such displacement of material are an improvement in the uniformity of formation and an increased tendency for machine-direction alignment of fibers. As shown by Akesson and Norman (2006), fiber flocs in the sheet can become elongated and ruptured by such movement.

Vacuum Boxes

The idea behind vacuum dewatering is simple: apply vacuum and remove water from the paper. However, as discussed in review articles on the topic, there are many questions and details about vacuum dewatering that are not yet fully resolved (Räisänen 1996; Baldwin 1997; Räisänen 2000a; Roux and Rueff 2012). One clear consequence of vacuum box application is a compression of the wet web (Campbell 1947; Nordman 1954; Ingmanson 1964; Jönsson and Jönsson 1992a,b; Åslund and Vomhoff 2008b,c; Åslund et al. 2008). This water removal process is called compression dewatering. Another, equally important consequence (after the dryline) is air flowing into the fiber network and forcing water out of the fiber network. This process is called displacement dewatering (Åslund and Vomhoff 2008b).

On a traditional Fourdrinier paper machine, the first vacuum boxes to interact with the paper web are the low-vacuum (“lo-vac”) boxes. Figure 3 presents a schematic diagram of such equipment. A distinguishing attribute of the type of equipment shown is the use of water itself to generate the needed vacuum as it flows down tubes by gravity to a seal chest located in the basement of the paper mill. The cover is typically composed of ceramic or a hard plastic, and there are slots or holes in the cover.

For reasons that will be discussed later in this article, it is conventional practice to steadily increase the levels of vacuum applied in successive groups or individual flat boxes along the machine direction of a paper machine forming section (Eames and Moore 1976; Baldwin 1997; Jones 1998). Evans (1997) has provided a useful overview of control technology for vacuum levels on the paper machine. When the needed vacuum levels become too high to be practically generated by the siphoning action of water moving down in tubes, it is then necessary to use a vacuum pump. The use of a vacuum pump can be regarded as the practical demarcation between low-vacuum and high-vacuum boxes. Typically, the slots on a modern vacuum flatbox are in the range of 13 to 25 mm in width (Räisänen 2000a). Thus, at typical speeds of paper machines, the vacuum pulse is often in the range of half of one ms to several ms. When similar devices are employed in twin-wire forming systems, the term “suction shoes” has been used (Roshanzamir et al. 2000).

Fig. 3. Schematic diagram of a low-vacuum flatbox

Many studies have shown that when vacuum is applied at the same level continuously to a wet web, the moisture content will tend toward an asymptotic value (Norman 1989; Clos et al. 1994; Neun 1994, 1995, 1996; Räisänen 1995b; Jones 1998; Räisänen 2000a; Pujara et al. 2008a,b). According to Jones (1998) the relationship between ultimate achievable dryness and the dwell time is a hyperbolic tangent. Koponen et al. (2012) studied vacuum dewatering with a filtration device, enabling pressure differences up to 70 kPa. For LWC paper the solids content rose to 11% already at a vacuum of 25 kPa, whereas for SC fibers the solids content rose to 14% at 40 kPa. This suggests that the repeating compression – expansion cycles due to the sheet traveling on the forming board from a vacuum box to a vacuum box are beneficial for water removal.

At the leading edge of a vacuum box, depending on details of geometry, there is often a doctoring effect, by which water is skimmed off from the underside of a Fourdrinier forming fabric (Attwood 1960, 1962; Miller 1998). According to Miller (1998), such a doctoring effect has been incorporated into the design of vacuum boxes preceding the dry line, i.e. the position on a Fourdrinier table in which the sheet no longer appears glossy due to increasing consistency.

Though vacuum boxes can be very effective for the removal of water from paper, they have some characteristic problems. As already mentioned at the opening of this article, a consequence of vacuum forces holding the forming fabric against the covers of flat boxes is friction, which needs to be overcome by the electrical motor driving the forming fabric (Eames and Moore 1976; Hansen 1985; Skalicky et al. 1991a,b; Räisänen 2000a). The back surface of the forming fabric tends to get abraded over time, especially if sand particles become embedded in microscopic cracks in the covers of vacuum flatboxes (Eames and Moore 1976; Skalicky et al. 1991a). Another inherent problem is the development of pinholes in the paper (Campbell 1947; Eames and Moore 1976), which often can be attributed to entrained air bubbles that get pulled through the wet web by the force of vacuum. Finally, the strong forces pulling the wet web toward the wire can leave a lasting imprint on the paper, called wire marking (Eames and Moore 1976). Brundrett and Baines (1966) estimated that high vacuum may be able to exceed the threshold of capillary pressure, giving rise to pinholes of about 51 µm or larger.

At some point, the level of vacuum will be sufficient to pull air through the wet web (Brundrett and Baines 1966; Åslund and Vomhoff 2008b). As was shown by Britt and Unbehend (1985), a non-uniform formation of the wet web can render vacuum dewatering much less effective. The presumed reason is that air is able to essentially leak through thin areas of the paper, using up vacuum pumping energy without effectively removing the water from the denser, floc areas of the paper.

The air flow can be decreased by adding microfibrillated cellulose to the pulp. In (Koponen et al. 2015) the addition of microfibrillated cellulose (MFC) slowed down the drainage of handsheets but increased the final consistency. The same effect was observed at the pilot scale; the consistency was increased after the forming section when MFC was added. A possible reason for this behavior is MFC’s film-making tendency. In this situation, the MFC possibly seals the sheet surfaces so that the applied vacuum becomes more effective because less air is flowing through the sheet after the dry line. As the airflow through the sheet decreases, the vacuum compresses the sheet more, which leads to higher solids content after the forming section.

Vacuum Couch Roll

Before the wet web passes forward to the wet-press section, there is one more chance to remove water as it passes over a vacuum couch roll (Brundrett and Bains 1996; Hansen 1987), if one is present on the machine. Because the couch roll is rotating, with its outer surface matching that of the forming fabric, the problem of high frictional drag, which is characteristic of high-vacuum flatboxes, is avoided. Also, due to the increased structural integrity of the wet web, compared to earlier in the process, a higher vacuum can be applied. Hence, under favorable circumstances, solids levels in the range of 15 to 23% can be achieved (Räisänen 2000a).

Two key limitations on the feasibility of applying high vacuum at a couch roll are sheet marking and centrifugal acceleration. Couch marking occurs when the vacuum-induced forces are strong enough, relative to the structure of the wet web at that point, to shift material within the sheet, resulting in denser areas facing each suction hole in the couch. Such patterns can be highly undesirable, depending on the intended use of the paper product. In practice, sheet marking at the couch is avoided by maintaining a high enough solids after the vacuum flatboxes (Hansen 1987). In addition, centrifugal acceleration at the periphery of a rotating couch roll can make it increasingly difficult to remove water from the paper, even by high vacuum levels. The problem tends to become compounded in the case of fast, wide paper machines, where the couch roll must have a sufficiently large diameter to withstand the imposed bending stresses.

Wet-press (single-felted)

After leaving the couch roll of a conventional Fourdrinier paper machine, the next set of unit operations that has significant dewatering effect is the wet press. Reviews of wet-press operations include the following (MacGregor 1989; Paulapuro and Nordman 1991; Räisänen 1996; Paulapuro 2000, 2001; McDonald and Kerekes 2017b). It is important, before wet pressing, to reach a solids content of the web as high as possible. Wet pressing can be used only to a limited extent for fixing problems in sheet structure resulting from vacuum dewatering. Koponen et al. (2012) used a dynamic wet pressing simulator to show that differences in solids content after vacuum dewatering remained after wet pressing regardless of the press levels employed. Similar results were obtained in Koponen et al. (2015) at the pilot scale.

One of the most intriguing aspects of dewatering paper within a wet-press nip has become known as stratification (Campbell 1947; Schiel 1972, 1973; Chang 1978; MacGregor 1983a,b, 1989; Szikla 1986; Paulapuro 2000, 2001; McDonald 2020). The phenomenon is most evident when the paper web is dewatered in a single-felted nip. In such a nip, the water pressed from the sheet is constrained to move mainly in only one direction, from the paper into the felt. A dense layer develops adjacent to the boundary from which water is leaving the web. The dense layer persists when the paper is dried by evaporation (Szikla and Paulapuro 1989).

Further evidence that might be used to understand what is happening during wet-pressing can come from a little-known phenomenon that can be called “membrane formation”. As reported and discussed by MacGregor (2002), high-resolution micrographs of cross-sections of the surface of paper obtained after a wet-pressing operation sometimes show a very thin (1 to 2 µm) membrane that appears to be composed mainly of colloidal-sized cellulosic matter. This is present at, though often not fully attached to, the side of the paper from which the water had been removed during pressing. Though the evidence showing the existence of such a membrane seems quite strong, the phenomenon has not otherwise been reported, presumably due to experimental challenges in obtaining the needed micrographs. Also, there is no direct evidence that this membrane restricts water removal from the wet web of paper.

Early insights on what happens within a wet-press nip were explained by Bergström (1959). In his view, dewatering takes place mainly in the entering side of a wet press nip, where water is forced into the void spaces of the felt. Some of the expressed water then may return to the sheet (“rewetting”) in the expanding side of the nip (Bergström 1959; Sweet 1961; MacGregor 1989; McDonald and Kerekes 1995; McDonald et al. 2013; McDonald and Kerekes 2018).

There has been much discussion related to components of the pressure that resists the applied mechanical pressure within a wet-press nip (MacGregor 1989; Paulapuro 2000, 2001; Rogut 2009). According to Wahlström (1960, 1969), the resisting pressure can be described as the sum of structural pressure and hydraulic pressure. The concept appears to have been originated by Terzaghi (1943, 1960), who was modeling the flow of water through soil, which is often dominated by relatively incompressible matter such as sand particles. To apply such concepts to papermaking, by suitable experimental design, it has been possible to measure what appears to be the hydraulic component of pressure during simulated wet-pressing (Carlsson et al. 1977; Chang 1978; Carlsson 1984; Szikla and Paulapuro 1989). In general, higher components of hydraulic pressure have been observed or predicted in cases where the fibers had been refined, thus making them more resistant to dewatering.

The validity of applying the Tezaghi principle to paper webs has been questioned (McDonald et al. 2000; McDonald and Kerekes 2017b). Application of the Tezaghi principle to paper implicitly assumes that fibers support pressure in a manner that shields water from pressure. This is a misconception because the fibers are filled with a considerable amount of water, and the cell walls of the fibers are flexible and offer little mechanical resistance. Pressure applied in the press nip is exerted on both water between the fibers and water within the fibers. The rate of water removal is determined by the applied pressure and the average permeability of the fiber network. As dewatering proceeds, water is forced from smaller openings between and within fibers, making removal more difficult because of decreasing permeability, not diminishing hydraulic pressure. This concept is embodied in the Decreasing Permeability (DP) model (McDonald et al. 2000; Kerekes et al. 2013; McDonald and Kerekes 2017a,b). The applicability of Terzaghi’s principle for soft porous media was assessed experimentally for highly compressible fibrous media by Kirmanen et al. (1994). The authors presented results showing deviation from Terzaghi’s principle and proposed a phenomenological formula for a generalized effective stress under one‐dimensional static compression.

Carlsson et al. (1983a,b) suggested that the resisting pressure ought to be regarded as a “mixture” of hydraulic and structural pressure. Also it has been suggested that what may appear, based on experimental findings, to be evidence of structural pressure may at least partly be due to water that is at least momentarily entrapped within such spaces as fiber lumens, the mesopores within fiber cell walls, or maybe also in isolated places between fibers that have been blocked off from flow (Kerekes and McDonald 1991; Paulapuro 2001). The ultimate possible dryness is a function of the surface tension of water in the pores of the fibers (Kerekes and McDonald 2020).

There is evidence that when water is forced out of the cell wall of a refined kraft fiber by means of applied pressure, there can be a permanent loss of swelling ability, an effect that has been called hornification (Han 1969; Carlsson 1983; Carlsson et al. 1983a,b; Weise et al. 1996; Maloney et al. 1999).

Though clearly there is substantial flow of water from a wet web into the felt during wet-pressing, there also can be flow within the plane of the sheet. This results when high hydraulic pressure develops within the material when it is highly pressed. As a result of the buildup of pressure within the material, some of the water within the central part of the wet web is delayed in its entrance into the nip in comparison to the outer layers of the wet web (MacGregor 1983b; Kataja et al. 1992). When the phenomenon becomes unstable and is sufficient to cause recognizable damage to paper properties, it is called “crushing” (Wahlström 1969; Francik and Busker 1986; MacGregor 1989). Damage is expected in situations where the hydrodynamic forces exceed the structural integrity of the web, as in the case where the incoming moisture content is excessive relative to other parameters (Wahlström 1969).

Wet-press (double-felted)

One very promising way to overcome the two-sidedness problems often associated with wet-pressing is to employ a pair of felts, i.e. using a double-felted nip (Bergström and Kolseth 1989). In addition to providing symmetry, such practices can effectively double the capacity for accommodating the removed water within the voids of the felts. However, double-felting for lightweight paper can sometimes lead to a wetter web because of rewetting on both sides of the paper (McDonald and Kerekes 2017a).

Wet-press (extended nip)

Another approach to being able to remove more water from a paper web with less distortion of the structure is to employ a nip that is longer in the machine direction, i.e. an extended nip press. The development and implementation of extended-nip technology has been one of the most important contributions to paper machine speed and efficiency in recent decades (Paulapuro and Nordman 1991; Schlegel et al. 1997; Cedra 1999; McDonald et al. 2013; McDonald and Kerekes 2017a). In principle, by increasing the area of pressing, the force applied per unit area does not need to be as high and the water has more time to permeate outwards. In addition, the press impulse (the product of pressure and time) can be high enough to achieve higher levels of dewatering in comparison to conventional wet-presses.

RATE-LIMITING MECHANISMS AND SUPPORTING EVIDENCE

After having, in the previous section, reviewed aspects of unit operations that remove liquid water from paper during its manufacture, the present section will consider mechanistic aspects of those processes. The focus will be on factors and mechanisms that tend to impede dewatering.

Generalized Cause: Relative Motion among Solids

Table 2 in the Introduction to this article presented a series of working hypotheses, of which the first and most general was as follows: It is proposed that changes in the relative positions of solids in the wet web, in response to hydrodynamic and other forces, including changes in density vs. position, can play a major role with respect to dewatering rates in various unit operations of papermaking. Relative motion can take several forms. For instance, as noted in the previous section, densified layers can be expected to form within the wet web of paper adjacent to where water is passing into a forming fabric (in the case of a vacuum box) or felt (especially in the case of a single-felted wet-press (MacGregor 1989). The distribution of fine materials can shift as a result of dewatering operations (Tanaka et al. 1982; Räisänen et al. 1995b). And the pressing-together of conformable fibers at the surface of a forming fabric can create a sealing effect (Sjöstrand et al. 2019); such an effect was highly apparent when using highly swollen dialcohol cellulose fibers. So the general hypothesis motivating this discussion is that these mechanisms, each related to relative motion among solid components of the wet-web of paper, can contribute significantly to the slowing down of dewatering rates. The question at hand is to what degree there is evidence to support such mechanisms as playing an important role during ordinary papermaking.

To begin the discussion, Fig. 4 provides simplified illustrations of several of the hypothesized mechanisms that have been proposed as being important in at least some cases in significantly impeding dewatering on a paper machine.

Fig. 4. Simplified schematics for six reported phenomena that appear to underlie various aspects of resistance to the dewatering of paper webs

Briefly stated, some of the factors associated with slow dewatering or resistance to vacuum or pressing can be described as involving dense layers, the plugging of drainage channels in the wet web by cellulosic fines, various sealing effects associated with the conformability of fibers, especially well-refined kraft fibers, inefficient response to vacuum due to flocculation, repairing of thin areas of paper by a healing mechanism, and finally the rarely-reported phenomenon of a thin membrane that may form on the surface of paper facing a wet-press felt. These and other phenomena will be considered later in this section, along with discussion of supporting evidence.

Typical Composition of Headbox Stock

The intent of this subsection is to provide sufficient background to facilitate discussion of mechanistic discussions that come later. This is intended especially for readers who don’t have extensive experience with the composition and behavior of the fibers and other materials used in papermaking. This subsection might be skipped by other readers.

The amount of water that needs to be removed from solid matter during the preparation of a paper sheet cannot be overemphasized. Figure 5 illustrates the proportions of water, compared to solid matter, at various points of typical paper machine systems that produce a variety of paper products. Background information related to these unit operations, including discussion of hydrodynamic aspects, has been provided by Zhao and Kerekes (2017).

Fig. 5. Simplified schematic of a typical paper machine system, indicating the ranges of water content in the paper web, compared to solid matter, at different points in the process

The filtrate collected during formation of a paper sheet, i.e. the “white water,” also will contain some solid matter. Those solids are together known by the term “fines”. Depending on the paper grade, much of that material is likely to consist of parenchyma cells, as well as fibrillar material separated from fibers during refining, i.e. cellulosic fines. According to TAPPI standard T 261 cm-94, cellulosic fines are expected to be able to pass through a circular opening of 76 µm. The cellulosic fines that are generated during mechanical refining of pulp fibers tend to have high aspect ratios and high surfaces areas (Brecht and Klemm 1953; Marton 1980a,b, 1982). They are especially of interest in this paper, since high levels of such fines, especially when making paper products of relatively high basis weight, have been shown to slow down rates of dewatering in laboratory tests (Hubbe 2002; Cole et al. 2008; Hubbe et al. 2008; Chen et al. 2009).

In addition to cellulosic fines, again depending on the grade of paper and local practices, there may be a substantial amount of mineral fillers, including calcium carbonate, clay, or other inorganic particles. During commercial-scale papermaking, depending on chemical additives and many other factors, a substantial proportion of the fines will be retained in the paper during each pass through the paper machine process.

Upwards of 70% of the solid matter contained in the jet of furnish coming from the headbox of typical paper machine systems will consist of cellulosic fibers. The nature of such fibers, as well as how they are processed, can have a large effect on dewatering rates. Most of the paper in the world is produced with fibers from trees. Softwood (conifer) trees that are used commonly for papermaking yield tracheids (fibers) that have lengths of about 3 to 4 mm and widths generally in the range of 30 to 50 µm (Nanko et al. 2004). Such fibers are especially used in fabrication of containerboard, fluff pulp for absorbent products, paper bags, and as reinforcement to achieve the needed tear strength in other paper products. Hardwood (deciduous) trees have lengths typically near to 1 mm and widths of 15 to 30 µm. In temperate zones a large contrast in cell-wall thickness can be expected when comparing fibers formed in the springtime (earlywood) and those formed in the summer and autumn (latewood). The earlywood fibers have much thinner walls and larger void spaces (lumens) in their centers. This difference means that the earlywood fibers tend to be much more collapsible, especially after kraft pulping and mechanical refining. Another contribution to nonuniformity of fiber properties comes from the age of the tree when different fibers were formed (Burdon et al. 2004). Juvenile wood, which is produced by trees when then are young (often less than ten to 20 years) has fibers that are shorter and thinner than mature wood, which constitutes the outer wood of an older tree.

The kraft pulping process is the most dominant method of converting wood to pulp fibers (Gullichsen and Fogelholm 1999). By breaking down and solubilizing much of the lignin, which functions as a binder between the fibrillar cellulosic domains in the fiber, the kraft process leaves mesopore spaces. Subsequent refining of the pulp tends to delaminate the fibers, including within the dominant S2 sublayer of the fibers. As has been demonstrated by suitable tests, such refining renders the fibers more conformable (Tam Doo and Kerekes 1982; Paavilainen 1993). Conformability of the fibers tends to increase with increased completion of delignification, i.e. with decreasing yield (Tam Doo and Kerekes 1982). Thus, high-yield pulps, such as those obtained by thermomechanical pulping (Wang et al. 1998; He et al. 2011) or with relatively high-yield kraft pulping tend to be stiffer and less conformable (Broderick et al. 1996; Nordström 2014). It also has been reported that higher-yield pulps of the same type tend to give higher dryness after pressing (Opherden and Rudolph 1980). Also, fibers that have been dried during a previous cycle of papermaking, and thereby hornified, tend to be less conformable, thus contributing to lower relative bonded area and lower strength of the resulting paper (Jayme 1944; Paavilainen 1993; Weise and Paulapuro 1999; Somwang et al. 2001; Zhang et al. 2002). Kerekes and Tam Doo (1985) have provided a chart of fiber stiffness, showing how fiber stiffness differences can be estimated based on species, yield, chemical treatment, and refining.

The mechanical refining of pulp fibers, which usually happens by means of shearing and compression of 4 to 6% consistency pulp between a rotor and stator with raised land areas (bars), has a profound effect on all aspects of removal of liquid water from paper. The basics of the procedure and its effects have been reviewed (Gharehkhani et al. 2015). Evidence of such effects includes the fact that the extent of refining is almost universally monitored by standard tests of the drainage rates of the refined fiber suspensions (e.g. TAPPI Method T 227 om-94). Such a practice is counterintuitive, since the most usual goal of papermakers is to increase strength properties of paper, whereas decreasing the freeness of pulp typically is associated with lower rates of production on drainage-limited paper machines (Ingmanson and Andrews 1959; d’A Clark 1970; Attwood and Jopson 1998b) and in wet-pressing operations (Carlsson 1983; Carlsson et al. 1983a; Paulapuro 2000).

Especially when one considers removal of water in a wet-pressing operation, the water located within the cell walls of fibers appears to play an important role (Wahlström 1990; Maloney et al. 1999). The amount of such water present in a wet pulp specimen is the water retention value (WRV), which can be determined by a centrifugation test (e.g. TAPPI Useful Method UM 256 or SCAN-C 60:00). In such tests, the pulp slurry consistency is first adjusted to an initial range, usually near to 10% solids. Then the material is subjected to a standard acceleration and time. The mass of the material after the centrifugation is compared with that of the same specimen after it has been fully dried in an oven. The difference in mass, divided by the dry mass, is reported. The SCAN test is sometimes preferred over the TAPPI test because it employs a higher acceleration (3000 rather than 900 gravities) and hence can be expected to remove more of the excess water located between the fibers and at their surfaces. For precise, theoretical work, some researchers prefer the employ results of fiber saturation point tests (Scallan and Carles 1972; Maloney et al. 1999), which are based on measuring the concentration of very-high-mass dextran molecules, which are generally too large to enter the mesopores within a typical pulp fiber. The amount of water within the cell walls of kraft fibers is expected to increase with increasing extent of mechanical refining. Cell-wall water is believed not to be removed from a wet web to a significant extent in the forming section of the paper machine (Gruber et al. 1997). On the other hand, strong correlations have been observed between water retention value and the moisture still in remaining in paper after high-vacuum dewatering (Sjöstrand et al. 2019) and after wet-pressing (Rousu et al. 2010). As noted by Carlsson (1983), though the cell-wall water may be difficult to remove from fibers during the very brief exposures of the wet web to pressure within a press nip, some of it is removed. This hard-to-remove water in the fiber wall ultimately limits the amount of water that can be removed by pressing (Kerekes and McDonald 2020). A certain portion of the water in the cell wall appears to be sufficiently strongly associated with the cellulosic material that its properties differ from those of bulk water, e.g. such as not having a freezing point or being more difficult to remove (Weise et al. 1996; Maloney and Paulapuro 1999; Park et al. 2006, 2007). In line with some of these findings, Jönsson and Jönsson (1992a) developed a model of the dewatering process for incompressible media in which 0.3 parts of water per mass of cellulosic matter was assumed not to move at all relative to the solids.

Near the end of this article, in the context of strategies to increase rates of water removal, some attention will be paid to chemical effects. Since some of the effects may be related to mechanisms of dewatering, some brief background will be provided here. First it is worth noting that the extent of swelling, including the WRV levels of pulp fibers, will be affected by anything that changes the charge properties of the furnish. Such issues are covered in more detail in an earlier review (Hubbe and Heitmann 2007).

As shown by Lindström and Carlsson (1982), much of the tendency of kraft fibers to swell with water can be attributed to the negatively charged ionic groups within them, especially the carboxylate groups associated with hemicellulose. The osmotic pressure promoting swelling of the fibers with water is suppressed to an increasing extent with increasing ionic strength (salt content) in the water phase. In addition, swelling can be decreased either by lowering the pH (in the range of about 6 to about 3) or by adding multivalent positive ions. In addition, it is well known that dewatering rates, especially early drainage, can be promoted by the addition of cationic polymers (Britt and Unbehend 1980, 1985; Stratton 1982; Wegner et al. 1984; Allen and Yaraskavitch 1991; Räisänen et al. 1995a; Hubbe et al. 2008).

Models to Estimate Resistance to Flow

For a concise overview of mathematical models related to rates of the release of water from paper, readers are referred to a review article by McDonald and Kerekes (2017b). The article covers the most important historical developments in such models, as well as emphasizing some visco-elastic effects that are highly relevant here. To start off, Table 4 provides a summary of some key publications related to the modeling of dewatering rates of paper in various unit operations.

Table 4. Advances in Mathematical Models to Predict Rates of Release from Wet Webs of Paper Subjected to Vacuum or Pressure

Darcy’s law

Other sources give a fuller explanation of hydrodynamic principles and factors acting to resist flow (Hubbe and Heitmann 2007; Guyon et al. 2015). Some topics, however, need to be summarized here, since they will be mentioned repeatedly in discussions that follow. One such topic is called Darcy’s law (Darcy 1856). This relationship can be expressed as in Eq. 1,

 (1)

where V is the superficial velocity (i.e. the porosity times the real velocity within the pores), k is the permeability coefficient, P is the pressure difference across a uniform bed, µ is the viscosity, and L is the height of the bed. The relationship can be expressed equivalently in terms of the volume of flow as,

 (2)

where Q is the volumetric flow and A is the area of the face of the bed or pipe within which the material is packed. Notice that for Darcy’s law to provide reasonable predictions, the particles and packing within the bed need to be sufficiently uniform (McDonald and Kerekes 2017b). For fiber networks, a classical review on permeability models and measurements can be found in Jackson and James (1986).

For practical purposes Darcy’s law is sometimes written in the form,

 (3)

where b is the mass of the sheet per unit area (i.e. basis weight) and K is the specific filtration resistance or the resistivity of the filtered sheet. This form is useful when the sample thickness is not known, as is the case in many practical cases. Note that there is the following relation between the sheet permeability and resistivity, where is the density of the porous material:

 (4)

Though Darcy’s law deals only with flow through rather than from a porous medium (the latter of which is the interest of papermakers), it has provided a reference point or a starting point for many modeling efforts by papermakers (Campbell 1947; Meyer 1962; Luey 1979; Jackson and James 1986; Ethier 1991; Jönsson and Jönsson 1992a; Kataja et al. 1992; McDonald and Kerekes 1995; Funkquist and Danielsson 1998; Martinez 1998). An obvious problem that needs to addressed is that during water removal, the permeability k in Darcy’s law is not a constant but decreases as water is removed from the web and the web is compressed (Kerekes and McDonald, 1991; McDonald et al. 2000; McDonald and Kerekes 2017b).

The most important advance to build upon Darcy’s contribution was achieved by Kozeny and Carman (Kozeny 1927; Carman 1937, 1938). These authors figured out a way to estimate the value of the permeability coefficient k in Darcy’s equation. The most useful form of the Kozeny-Carman equation is as follows (Carrier 2002),

 (5)

where is the fractional void volume (or porosity) of the packed bed, kc is essentially a correction factor, which includes e.g. the effect of tortuosity, and S is the specific surface area of the solids. Kozeny-Carman law has been a starting point or a comparison point for many analyses of the flow resistance during dewatering of paper webs (e.g. Campbell 1947; Ingmanson 1952, 1953; Carlsson et al. 1983a; Kerekes and McDonald 1991). Notice that for dilute fiber networks the Kozeny-Carman equation does not work well and one should use correlations developed specifically for dilute systems, such as that of Jackson and James (1986),

 (6)

where d is the diameter of fibres.

While permeability models, such as Eq. 5 (Kozeny-Carman), can be used for general description of the permeable behavior of fiber networks, the irregular shape of the fibers and effects related to their compressibility usually prevent accurate prediction of permeability a priorii.e. without supporting experiments. Such experiments are technically rather straight-forward to perform, and there are numerous papers on them in different porosity regions (Carlsson et al. 1983a; Chan et al. 1996; Lindsay and Brady 1993a,b). Recently, the developments of X-ray tomographic imaging and computational fluid dynamics have enabled quantitative determination of the permeability of pulp fiber networks also without explicit flow measurements (Koivu et al. 2009a,b). This approach has made it possible to develop more accurate permeability models for fiber networks that take into account the real structural details, such as local thickness distribution, of the network (Koponen et al. 2017).

An important implication of the models considered up to this point is that the permeability of a paper mat can be expected to decrease as the mat becomes more densified. With less void volume and with smaller channels of water between fibers or particles of solid material, there is higher frictional resistance to flow. Notably, this conclusion can be reached even without considering effects due to non-uniform densification or any details of packing of the solids within a paper mat.

Simple linear model for the sheet flow resistivity

According to Sayegh and Gonzalez (1995) and Koponen et al. (2016) the dependence of the water flow resistance through pulp fiber sheets was studied as a function of pressure. It was found that the resistivity of the fibre sheet could be described in the pressure range of 5 to 70 kPa with a good accuracy by a linear model,

 (7)

where I is impulse density (integral of pressure over time), and , , and are pulp-dependent material parameters. In most practical cases dewatering takes place so quickly that the term αI in Eq. 7 can be eliminated. Equation 7 suggests that the effect of increased pressure is mostly lost due to simultaneously increasing flow resistance. So, in addition to leading to potential sheet sealing, high pressure levels may lead to a waste of energy without giving major benefits in the initial dewatering.

A widely used application of the Kozeny-Carman equation has been in the characterization of the hydrodynamic surface area of particulate or fiber materials (Sullivan and Hertel 1940, 1942; Ingmanson and Andrews 1959; Kumar and Ramarao 1995). Such approaches, as well as the results from such analyses, need to be viewed with caution in the case of compressible and deformable materials such as papermaking fibers. According to the initial assumptions, the particulate material in a Kozeny-Carman analysis ought to have no dependency of the shape or the spaces between particles as a function of applied pressure. Also, the representation of the packed bed as being uniform needs to be justifiable.

Binary mixtures

It is well known that a higher density of loosely packed material generally can be achieved if a fraction of the particles have a smaller size (Santiso and Müller 2002; Brouwers 2006). Accordingly, it has been shown, with application of the Kozeny-Carman analysis, that bimodal mixtures of particles present greater resistance to flow (Carman 1937; Ethier 1991; MacDonald et al. 1991; Andrade et al. 1992). As pointed out by Andrade et al. (1992), the details of topology can be expected to play a significant role, which tends to place limits on the precision of predictions based on uniform packed bed models. These considerations are highly relevant to papermaking systems, in which there can be a range of sizes of fibers, cellulosic fines, and other particles. For example, Görres et al. (1996) described how different placement of fines within a paper sheet formed from mechanical pulp fibers and fines can achieve a range of densities, depending on whether the fines are engaged in bridging, blocking, or the filling of places within the structure. Likewise, Sampson and Kropholler (1995) found a strong correlation between the packing ability of solids in the furnish and both drainage resistance and mat density.

Lucas-Washburn analysis

The Lucas-Washburn analysis of rates of wetting of porous materials is relevant to the dewatering of paper for two reasons. First, it presents an alternative, and possibly equivalent way to estimate the viscous resistance to flow through porous material. Second, it provides a way to predict certain contributions to resistance to flow imposed by the presence of an air-water meniscus within or at the entrance to an individual pore. In the Lucas-Washburn analysis, the viscous resistance to flow is estimated based on the model of a single, uniform, cylindrical pore, using the Hagen-Poiseuille equation (Sutera and Skalak 1993). The viscous force was envisioned as providing the main resistance against flow of liquid into a porous solid. Lucas (1918) and Washburn (1921) proposed that the force motivating the liquid to enter a porous solid is provided by interfacial tension. The physical situation can be modeled as shown in Fig. 6, where the porous material is represented as a single cylindrical pore of uniform cross-section.

Fig. 6. Representation of model envisioned by Lucas and Washburn for estimating the rates of penetration of liquids into porous solids based on capillary forces and viscous resistance to flow

The most important result from the analysis of Lucan and Washburn is a prediction that the amount of liquid adsorbed ought to be dependent on the square-root of time that has passed after the moment of wetting (see Eq. 11). This relationship has been found to be applicable to wetting of paper by non-aqueous fluids, but there can be large deviations in the case of water (Bristow 1967; Aspler et al. 1987). The following four equations show, in turn, the anticipated meniscus force, the viscous force that is expected to resist penetration, and the expressions that result when the opposing forces are set equal to each other. In these equations, P is a change in pressure, LV is the interfacial tension between water and its vapor phase, is the angle of contact (drawn through the liquid phase), r is the effective radius of a capillary (modeled as being cylindrical), is the fluid viscosity, v is the velocity of fluid entering the pore, and L is the wetted length of the pore at time equal to t.

Capillary force equation

Pcapillary = 2LV cos / r (8)

Viscous retarding force, Poiseuille’s equation

Pviscous = 8vL r2 (9)

Lucas-Washburn equation in differential form

dl/dt = LV r cos / (4 ) (10)

Lucas-Washburn equation in integrated form

= [(2LV cos t) /(4)]1/2 (11)

In the context of water removal from paper, the Lucas-Washburn approach points to the possibility of using the Poiseuille equation as a relatively simple way to estimate resistance to flow in a porous material, replacing the complication of a packed bed structure with simple equivalent cylindrical pores. But it also provides a way to begin to account for effects of an air-water meniscus at the entrance to a pore or at other places within a porous structure. Related approaches have been used to some extent to understand and predict aspects of the dewatering of paper, especially when considering the vacuum flatbox or when predicting flow through compressed beds (Sullivan and Hertel 1942; Carlsson et al. 1983a; Brundrett and Baines 1996). Notably, in the context of water removal from paper, a meniscus generally will act to completely prevent flow at the phase boundary until such point that the difference in pressure exceeds the capillary pressure, which depends on the radius of the pore, the contact angle, and the interfacial tension.

Non-laminar flow resistance

The predictions of the Darcy’s law can be expected to show deviations when flow rates are sufficiently high to induce significant inertial contributions to flow resistance (Carman 1937; Sullilvan and Hertel 1942; Ergun 1952; Ingmanson and Andrews 1959; Kyan et al. 1970; Kufereth 1982a,b; Norman 1989; Polat et al. 1989; Sjöstrand et al. 2017). Especially during initial dewatering, when the filtered fiber network is still dilute, flow resistance is low and the flow rate inside the network is high. Ergun (1952) proposed the idea of including a term from Burke and Plummer (1928) to Darcy’s law to account for the inertial component of resistance to flow through a packed bed:

 (12)

The second term in Eq. 12 is also called the Forchheimer term. The quantity ρ is the density of the fluid and

 (13)

is a parameter that depends on the medium geometry (here is the effective diameter of the particles and parameter α is 1.8 for smooth-walled particles and 4.0 for rough-walled particles). Notice that the formula for parameter has some similarity with the Kozeny-Carman equation.

Usually the effect of turbulence is omitted in the analysis of initial dewatering. When this simplification is justified is currently unclear. The flow coming from the headbox is fully turbulent, which could affect the filtration resistance if the Kolmogorov scale of the turbulence is smaller than the pore size of the filtered sheet. Moreover, the flow rates during early initial dewatering could sometimes be high enough to generate turbulent eddies inside the fiber network.

Compressibility incorporated into models

As already mentioned in passing, effects related to compressibility and deformability of the solids are not accounted for in the models provided by Darcy and Kozeny-Carman. Work to incorporate compressibility effects into experimentation and analysis suitable for paper dewatering system has been undertaken by several researchers (Ingmanson 1953; Nordman 1954; Ingmanson and Andrews 1959; Jones 1963; Chang 1978; Kerekes and McDonald 1991; Roux and Vincent 1991; Jönsson and Jönsson 1992a,b; Nordén and Kauppinen 1994; Zhu et al. 1995; Vomhoff and Schmidt 1997; McDonald et al 2000). In general, compression of a fiber mat can be expected to increase the resistance to flow through the compressed layer (Gruber et al. 1997; Kerekes and McDonald 1991; Jönsson and Jönsson 1992a,b; McDonald et al 2000). In response to applied pressure, fibers can be expected to bend, slide relative to each other, and to be individually compressed (Gurnham and Masson 1946; Jones 1963; Han 1969; Zhu et al. 1995).

After a mat of fibers is compressed and the pressure is released, it may not immediately snap back to its expanded state. Jones (1963) suggested that such behavior can be regarded as a form of viscous creep, i.e. a gradual change in shape when an elastic force of recovery is applied over time. There are hydrodynamic factors too, which can be considered in accounting for delayed re-expansion. The compared mat initially is likely to be saturated with water, and the necessity of flow through the narrow channels among compressed fibers will require time. As just discussed, there also may be significant capillary resistance due to an air-water meniscus at openings of pores leading into the fiber mat.

Separation of pressure components

When pressure is being applied to a wet web of paper, it makes sense to expect that at least some of the applied pressure will be borne directly by the strength of the solid material, as can be predicted from its elastic modulus and detailed structure. In other words, one assumes that there will be a structural component of resistance to the applied pressure. Wahlström (1960, 1969), who based his analysis on principles set forth by Terzaghi (1943) for soil mechanics, proposed that the resistance to compression during wet-pressing of paper can be divided into two parallel components, of which the other consists of hydraulic pressure.

There are reasons, however, to suspect that the actual contribution of mechanical structural forces may be relatively small. The first reason is the relatively high proportion of water that is present, especially when considering the parts of the dewatering process prior to wet-pressing. In addition, pressing on a water-swollen kraft fiber might be compared to squeezing a leaky water balloon; what appears to be structure could just be the effect of water that is slow to escape from a fully or partially blocked area (Paulapuro 2000, 2001). Accordingly, Campbell (1947) predicted that at no time during the papermaking process would the structure of the paper web carry the full load of the applied pressure during in dewatering. Kataja et al. (1995) set out to determine whether there is justification to distinguish between hydraulic and structural forces in a wet-press nip. They concluded that such a model cannot be justified in the case of deformable materials, which tend to form finite areas of contact when pressed together. In an early version of their decreasing permeability model, Kerekes and McDonald proposed that at least during the initial stages, the pressure is dominated by hydrodynamics, i.e. rate-dominated pressures resisting the applied pressure. Based on that they developed a more comprehensive mathematical model, which shows promise for accounting for results of wet-pressing over a range of conditions (McDonald and Kerekes 1991; McDonald et al. 2000; Kerekes and McDonald 2013). Jaavidaan et al. (1988) reported that the hydraulic pressure component usually followed the applied pressure quite closely.

Viscoelastic elements in modeling

If pressure is applied to paper for a longer time, more water generally will be released, even if very short impulses of pressure appear to be opposed by forces that resemble solid-like elasticity. This contrast between short-term solid-like behavior and long-term ability to flow means that the wet web is acting like a visco-elastic material (Carlsson 1983). The validity of this statement is evident in the wide-spread commercial success of extended-nip wet-presses, which can greatly exceed the dewatering capacity of conventional wet-press equipment, despite the fact that they generally apply lower peak levels of pressure (Wicks 1983; Paulapuro and Nordman 1991; Pikulik 1999; Lange and Meitner 2006). In light of such practical evidence, it makes sense to employ visco-elastic models in modeling of what happens in a wet-press nip. Accordingly, Carlsson et al. (1983b) and Springer et al. (1989) employed a simple Kelvin model (a parallel spring and dashpot) in their model of wet-pressing. Davis et al. (1983) explicitly evaluated the viscoelastic response of paper during simulated wet-pressing. Dimic-Misic et al. (2013) found evidence that shear-thinning behavior of highly fibrillated cellulose affects its dewatering behavior when it is present in a wet web of paper.

Although shoe presses may apply a lower peak pressure than roll presses, they apply a higher line load, which gives a greater press impulse (line load/speed or dwell time multiplies by pressure). Press impulse has been shown to be the dominant factor in press section water removal (Busker and Cronin 1984; Kerekes and McDonald 1991; McDonald et al 2005). The fact that the Kelvin model only predicts this at vanishing small dwell times, indicates that the spring and dashpot concept is flawed.

Advances in Experimental Devices

The tests that enabled many of the advances in models of water-removal operations, as just described, were obtained when using laboratory equipment, such as drainage jars and wet-press simulators. Equipment for evaluation of dewatering by gravity and vacuum was described in an earlier review article (Hubbe 2007). Some of these devices were compared in a series of tests carried out by TAPPI (Kerekes and Harvey 1980). Some notable advances in such technology are listed in Table 5. Likewise, Table 6 lists some of the wet-press simulation devices that have been reported.

Table 5. Dewatering Devices based on Gravity or Vacuum

Table 6. Wet-press Simulation Devices