Soil Science Society of America Journal 65:1045-1055 (2001)
© 2001 Soil Science Society of America
DIVISION S-1SOIL PHYSICS
Chemical Osmosis in Compacted Dredging Sludge
Th. J. S. Keijzer* and
J. P. G. Loch
Dep. of Geochemistry, Faculty of Earth Sciences, Utrecht Univ., P.O. Box 80021, NL3508 TA Utrecht, the Netherlands
* Corresponding author (keijzer{at}geo.uu.nl)
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ABSTRACT
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Sediments of high clay content are known to exhibit semipermeable properties when compaction is sufficiently high, resulting in osmotically induced water and solute transport. The semipermeability of these materials is quantified by the reflection coefficient,
. In the design of large dredging sludge depots in the Netherlands, osmotic transport is rarely taken into account. In a flexible wall permeameter, a bentonite and two dredging sludge samples were subjected to a chemical potential gradient to monitor water transport and to obtain values for
. Chemical osmosis was observed in the bentonite and one of the sludge samples (
56% clay), but was absent in the sludge with a relatively low clay content (
26%). The measured
are low in comparison with values obtained with the Fritz-Marine Membrane Model (FMMM) and a model presented by Bolt. The discrepancy between the theoretical and experimental values is explained by the assumptions made in both models. Several of these assumptions do not hold for the samples. If the observed semipermeability of the sludge is applied to an existing depot, chemical osmosis induces a water flux close to the maximum allowed advective flux laid down in Dutch legislation.
Abbreviations: AWy, Ankerpoort Wyoming bentonite BK, Beerkanaal BMR, Beneden Merwede River CEC, cation-exchange capacity FMMM, FritzMarine membrane model TMS, TeorellMeyerSiever model
, reflection coefficient
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INTRODUCTION
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IT IS WELL ESTABLISHED that clays can act as semipermeable membranes and are therefore capable of inducing osmotic water transport (e.g., Kemper, 1961; Hanshaw, 1962; Milne et al., 1964; Young and Low, 1965; Kharaka and Berry, 1973; Kharaka and Smalley, 1976; Graf, 1983; Fritz, 1986; Demir, 1988; Keijzer et al., 1999). Semipermeability is defined as the ability of a material to prevent the passage of a solute without affecting the passage of the solvent (e.g., Mitchell, 1993). The ability of a clay to act as a semipermeable membrane arises from the presence of diffuse double layers on the particle surfaces. Their share in the total pore solution increases by compaction of the clay, or the clayey material, under an overburden load. At very high loads, they may make up the whole pore solution and overlap. Compaction results in a higher concentration of cations and a lower concentration of anions in the double layer with respect to the equilibrium solution. At sufficient compaction, the water film present in the narrow pore between the clay layers is dominated by the double layers and the electrical restrictions they impose. Anions attempting to migrate through the narrow aqueous film are repelled by the negative charge of the clay platelets. This effect is known as negative adsorption or Donnan exclusion (Mitchell, 1993; Horseman et al., 1996). To maintain electrical neutrality in the external solution, cations will tend to remain with their co-ions. Thus, their movement across the clay will also be restricted (Fritz, 1986). Water and noncharged solutes are freely admitted to the membrane.
The above mechanism holds for charged membranes such as clays. However, there are also uncharged semipermeable membranes. In these uncharged membranes, rejection of a solute is on the basis of size or mobility. The result is that smaller components are less restricted during their passage through the membrane than larger ones. Semipermeable properties of clays with essentially no charge, like kaolinite, arise predominantly from their size-exclusion properties (e.g., Olsen, 1969, 1972). On the basis of pore-size distribution, Whitworth (1993) concluded that chalks may prove to be relatively efficient geological membanes.
The osmotic pressure difference induced by a chemical potential gradient across a semipermeable membrane can be calculated using Eq. [1]. The ability of the membrane to restrict solute transport is expressed as
. For ideal membranes which restrict the passage of all charged solutes,
is 1; for porous media without membrane properties (e.g., sand),
equals 0 (Katchalsky and Curran, 1965). The value of
depends on the type of clay, its surface charge and exchangeable cations (Kharaka and Berry, 1973; Kharaka and Smalley, 1976; Bolt, 1982b), porosity (Kharaka and Berry, 1973; Fritz, 1986), mean pore water concentration (Berry, 1969; Kharaka and Berry, 1973), and temperature (Haydon and Graf, 1986). The thickness of the membrane has no effect on the value of
(Benzel and Graf, 1984).
Laboratory experiments on compacted, monomineral clay membranes, mostly bentonite and kaolinite, have resulted in the description of water transport as the result of coupling of different driving forces, such as electro-osmosis (e.g., Mitchell, 1993; Grundl and Michalski, 1996), thermoosmosis (e.g., Dirksen, 1969), chemical osmosis (e.g., Kemper, 1961; Kemper and Rollins, 1966; Olsen, 1969; Fritz and Marine, 1983), and reverse osmosis (e.g., McKelvey and Milne, 1962; Kharaka and Berry, 1973; Kharaka and Smalley, 1976; Graf, 1983; Benzel and Graf, 1984). Experimental data on the semipermeable behavior of naturally occurring clayey materials are limited to shales and siltstones (Young and Low, 1965; Yearsley, 1989). Field evidence on these transport mechanisms is also limited. Marine and Fritz (1981) reported anomalously high pore water pressures as a result of different pore water compositions separated by a shale. Hanshaw and coworkers (Berry and Hanshaw, 1960; Hanshaw and Hill, 1969) also used chemical osmosis to explain abnormal pore water pressures in aquifers as a mechanism to induce faulting. Only recently, Neuzil (2000) reported on an in situ chemical osmotic experiment in the Pierre Shale of South Dakota (USA) presenting evidence of chemical osmosis on a field scale.
Based on the laboratory observations and the theoretical framework of the diffuse double layer, we postulated that in coastal regions, where large differences in salt concentrations may exist across clay layers or clay lenses, water and solute transport should be governed not only by hydraulic but also by osmotic pressure gradients (Loch and Keijzer, 1996). In the western parts of the Netherlands, aquifers containing either fresh or saline water are separated by layers of high clay content. The hydrology of this region may well be influenced by chemical osmosis (De Haven, 1982). In the predictions of water and contaminant fluxes from waste storage sites (e.g., dredging sludge depots in coastal regions as existing or planned in the Netherlands), these gradients are neglected. One of these depots, De Slufter (Fig. 1), is constructed in a salt water aquifer without a bottom liner. The clay rich dredging sludge itself is a low permeable layer restricting the advective transport of both inorganic and organic contaminants. However, the ability of the clay layer to act as a semipermeable membrane and its capability of inducing water transport and thus advective transport was not taken into account in the assessment of contaminant emissions.

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Fig. 1. Locations of the dredging sludge depot De Slufter near the Port of Rotterdam, the Netherlands, and the locations of the sampling sites in the Beerkanaal (BK) and Beneden Merwede river (BMR).
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The scope of this paper is to determine the capability of dredging sludge to act as a semipermeable membrane by measuring and to assess the magnitude of water transport induced by chemical osmosis. Therefore a laboratory instrument was designed in which a sample can be subjected to a chemical potential gradient and induced water transport, and hydraulic pressures can be measured. This system was tested using Wyoming bentonite (AWy) which is known to exhibit semipermeable properties. In addition, the capabilities of two models, the FMMM (e.g., Fritz, 1986) and a model based on the diffuse double layer by Bolt (1982b), were used to predict a
for natural clayey material are reviewed and discussed.
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THEORY
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Nonhydraulically driven fluid flow is generally denoted as osmosis. Chemical osmosis refers to the flow of water induced by a chemical potential difference across a semipermeable membrane (e.g., a compacted clay layer). Chemical osmosis will occur until a counteracting hydraulic pressure difference is established equal to the osmotic pressure difference between the two solutions. The osmotic pressure difference, 
0 in kPa, between two solutions seperated by a membrane can be calculated using:
 | (1) |
in which R is the gas constant (8.31451 J mol-1K-1), T is the absolute temperature,
w is the partial molar volume of water (m3 mol-1), and aw is the activity of the water at the low (aloww) and high (ahighw) concentration side of the membrane. Thus, the actual driving force is not the concentration difference of the salt across the membrane but the activity gradient of the water across the membrane. The activity of water at different concentrations below 1 mol L-1 can be found using (Alexander, 1990):
 | (2) |
here
is an integer representing the number of ions into which the electrolyte dissociates (e.g., for NaCl,
equals 2), and m is the molality of the solution in mol kg-1.
As discussed above, natural semipermeable membranes are seldom ideal. Their ideality is expressed as
, which is formally defined as the ratio between the osmotic pressure and the hydraulic pressure (
P) after equilibrium (i.e., at zero water flux):
 | (3) |
Its value determines the maximum expected osmotic water flux induced by a chemical potential gradient (Staverman, 1952).
Two models readily available in the earth and soil science literature were used to predict the theoretical
of the studied materials: (i) the FMMM (Marine and Fritz, 1981; Fritz and Marine, 1983; Fritz, 1986) based on the Donnan concept of the ionic equilibrium distribution adjecent to a clay particle surface (Mitchell, 1993); and (ii) a model by Bolt based on the GouyChapman concept of the diffuse double layer, modified for an immobile part in the double layer adjacent to the clay particle surface (Groenevelt and Bolt, 1969, 1972; Bolt, 1982b).
The FMMM is the most accessible model for the prediction of for natural materials exhibiting semipermeable properties. It is proven to be applicable to deep sedimentary basins where semipermeability of geological formations like shales is expected (Marine and Fritz, 1981; Alexander, 1990; Horseman et al., 1996; Osborne and Swarbrick, 1997). The FMMM is a refinement of the TeorellMeyerSiever model (TMS) for a diffusion potential across a charged membrane (Hanshaw, 1962; Kharaka and Berry, 1973). The FMMM is modified for the mineralogy and porosity found under geological conditions (Fritz, 1986). The expression derived for
in this model is:
 | (4) |
Ks is a measure for the salt exclusion of the semipermeable membrane given by the ratio of the anion concentration in the membrane pores (
a) to the average concentration of solute external to the membrane (Cs).
c is the cation concentration in the membrane pores given by (Hanshaw, 1962; Marine and Fritz, 1981; Fritz, 1986):
 | (5) |
where
a is:
 | (6) |
CEC is the cation-exchange capacity in molc g-1,
p is the particle density of the membrane material in g cm-3, and
w is the volumetric water content or the porosity of the membrane.
Equation [4] contains three friction ratio coefficients, R. Firstly, Rm is the ratio of the friction coefficient (f) of the cations (c) and anions (a) with the solid membrane structure (m); thus Rm equals fcm/fam. It relates the tendencies of the charged species to be retarded by frictional resistance by the membrane walls. A value of Rm between 1.2 and 1.8 for the NaCl + H2O system can be used (Kharaka and Berry, 1973; Fritz, 1986; Marcus, 1997). Secondly, Rwm is the ratio of the friction coefficients of the anions with the matrix of the membrane and with the water (w) in the membrane, Rwm equals fam/faw. In the FMMM, it is assumed that for a highly compact membrane, Rwm > 1, whereas Rwm is taken to be 0 when there is little frictional resistance as in loosely compacted membranes. For geological membranes with a porosity above 40%, it is assumed that the value for Rwm is equal to 0 (Fritz and Marine, 1983). Finally, Rw is the ratio of the friction coefficients for the ions with the water in the membrane, Rw equals fcw/faw. If it is assumed that the frictional resistance of the cation and anion with the water in the membrane structure is equivalent to that in the free solution, the reciprocal of the transport number (t0) of the cation equals Rw + 1 (Fritz and Marine, 1983). The transport number is a measure for the percentage of charge that is transported by the cation or anion when the mobilities of the ions in solution differ. For the NaCl + H2O system, the value for tNa0 equals 0.38 throughout the concentration range of 0 to 3 mol L-1, thus Rw is approximately 1.63.
The dependency of on the porosity for various clay minerals with different cation-exchange capacities is clearly illustrated by the FMMM (Fig. 2). The model also shows the change in ideality for a membrane with decreasing average solute concentration across the membrane as was experimentally found by several investigators (e.g., Berry, 1969; Kharaka and Berry, 1973; Kharaka and Smalley, 1976).
Using the framework supplied by the thermodynamics of irreversible processes, Groenevelt and Bolt also derived a relation for
. They assumed that the distribution of the ions in the double layers follows the corrected GouyChapman theory (Bolt, 1955; Van Olphen, 1963) of the planar diffuse double layer (Groenevelt and Bolt, 1969, 1972; Bolt, 1982b). The salt exclusion properties of clays originate from the diffuse double layers on the particles and are dependent on the clay mineralogy and the ionic composition. They assume a monomineral, mono-ionic system where the clay is completely dispersed. Anion exclusion is assumed to take place within a mobile water layer extending from the shear planeat distance xs from the clay particle surfaceto the truncation plane, at a distance xt (Fig. 3). If no truncation of the double layer occurs, anion exclusion extends from xs to dl. The shear plane is defined as the location where the viscosity of the water changes from very high values directly adjacent to the clay platelet to the value of bulk pore water (Groenevelt and Bolt, 1972). Truncation of the double layer occurs when removal of water forces both counterions and co-ions into a liquid layer of decreased thickness (Bolt, 1982a), e.g., as the result of compaction or decrease in water content by evaporation. Thus, the mobile water layer between shear plane and truncation plane is taken as an approximation of the thickness of the diffuse double layer. The immobile water layer between the surface of the platelet and the distance xs does not participate in the salt exclusion. This results in a relation between and the diffuse double layer properties according to:
 | (7) |
for which the analytical solution can be derived (Bolt, 1982b):
 | (8) |
in which
0 is the Debije-Hckel reciprocal thickness of a diffuse double layer in m-1 for a given equilibrium solution and dl is the thickness in m of the nontruncated double layer on a charged surface (Fig. 3). The value for
0 is given by (ßI0)1/2 where ß is 10.80 x 1015 mmol-1 at 25°C, and I0 is the ionic strength of the equilibrium solution in mol m-3 (Bolt, 1982b). Furthermore, t represents the mathematical expression (u1/2 - 1)/(u1/2 + 1), in which u is the Boltzmann accumulation factor for monovalent counterions in the diffuse double layer. At x equals xs and x equals xt; the values, ts and td, are given by:
 | (9) |
 | (10) |

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Fig. 3. Schematic representation of the distribution of the ions in a normal (dotted lines) and truncated (solid lines) double layer. The position of the immobile and mobile water adjacent to the clay platelet for the truncated double layer according to the model by Bolt is also indicated.
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where
is the absolute distance of an imaginary plane of infinite charge and potential behind the surface of the clay particle in m (Mitchell, 1993; see also Fig. 3). For a 1:1 electrolyte, like NaCl, it can be calculated by
= 4/ß
for solutions up to 1 mol L-1, where
is the counter charge per unit surface area in molc m-2. For a given sample,
can be plotted against
0dl, which is the normalized double layer thickness corrected for the presence of the immobile layer, from x equals 0 to x equals xs, directly adjacent to the particle surface. Equation [8] is valid for values of
0dl
1 (Bolt, 1982b).
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MATERIALS AND METHODS
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Samples
A Wyoming bentonite, (AWy), or Na-montmorillonite commercially available as Ankerpoort Colclay A90 was used (AWy; Table 1). This bentonite is used in the Netherlands in both sand-bentonite and cement-bentonite liners as a low permeable barrier to prevent the transport of water and contaminants from landfill sites.
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Table 1. Sample properties of the bentonite (AWy) and dredging sludges from the Beerkanaal (BK) and the Benede Merwede River (BMR).
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The dredging sludge samples were retrieved from the Beerkanaal (BK) and the Beneden Merwede River (BMR) in the Port of Rotterdam, the Netherlands (Fig. 1). The BK sediment was deposited in a brackish environment influenced by the tidal regime of the North Sea resulting in a sediment of high clay content. The BMR sediment is from a fresh water environment and is of lower clay content. The two sludges are typical examples of dredging sludge, highly contaminated with either organic or inorganic compounds, which according to Dutch legislation have to be permanently stored in a depot as De Slufter (Fig. 1). Sample properties of the dredging sludges are also given in Table 1.
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Experimental Design and Procedures
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An instrument was designed to study the semipermeable properties of compacted clay rich samples under near surface conditions by directly measuring the water transport induced by a chemical potential gradient. This resulted in an instrument based on a triaxial cell (Daniel et al., 1984) where two stainless steel solution reservoirs are connected to a flexible wall clay permeameter (Fig. 4). In the permeameter, a sample of 50-mm diameter and 100-mm maximum thickness can be fitted, and is placed in a cylindrical cell. The cell can be filled with deaired water and pressurized to ensure the contact between the flexible wall and sample. The bottom end of the sample is connected to a reservoir containing a low concentration solution, referred to as the fresh water reservoir. The top end of the sample is connected to a reservoir containing a saline solution, referred to as the salt water reservoir. The reservoirs each contain a magnetically coupled gear pump, a manifold which connects each reservoir to calibrated glass standpipes, and pressure transducers (Fig. 4). Each reservoir also contains an electrical conductivity cell. The whole assembly is placed in a temperature controlled bench top chamber at 25.0 ± 0.2°C. A more detailed instrumental description can be found in Keijzer (2000).

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Fig. 4. Schematic drawing of the experimental instrument showing the cell in which the flexible wall permeameter is located and both water reservoirs. The close-up shows the location of the sample between the porous stones and the latex membrane within the cell.
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A sample with a thickness of
2 mm was prepared by weighing 5 g of air-dried bentonite or dredging sludge into a stainless steel mold with an internal diameter of 50 mm. The only preparation of the samples prior to the usage was the removal of the larger aggregates by gently grinding. After compaction, the sample was mounted in the cell and saturated with deaired tap water at atmospheric pressure. A pressure of
500 kPa was applied to the water in the cell.
The hydraulic conductivity of the sample was measured prior to the osmotic experiment using a falling head permeability test (Daniel et al., 1984; Benson and Daniel, 1990). Under identical conditions but without a hydraulic gradient present, the sample was subjected to a chemical gradient. The fresh water reservoir was filled with a 0.01 M NaCl solution and the salt water reservoir with a 0.10 M NaCl solution, corresponding to an osmotic pressure difference of 421 kPa or 43 m H2O at 25°C (Eq. [1]). The solutions were deaired prior to the filling of the reservoirs. The flux of water was measured using the calibrated standpipes and the induced hydraulic head was monitored using the pressure transducers. Diffusion or convection of salt was monitored using the electrical conductivity in the fresh water reservoir.
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RESULTS AND DISCUSSION
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Sample Preparation and Hydraulic Conductivity
The samples obtained after saturation had a porosity generally around 0.5 (Table 2). This porosity is representative for naturally occurring clays under near surface conditions. Porosities are not as low as can be expected under geological conditions where they are generally below 0.3.
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Table 2. Properties and experimental conditions for the bentonite (AWy) and dredging sludges during the chemical osmosis experiment.
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The hydraulic conductivity measured for the samples (Table 2) is between 10-11 and 10-12 m s-1, and is representative for compacted clays (Benson and Trast, 1995).
Model Predictions
The two previously described models were used to predict
of the bentonite and the dredging sludge in the experimental setting.
The
as a function of porosity for the samples, is shown in Fig. 5. The
is calculated over the whole porosity range using Eq. [4] for the sample properties (Table 1) and the experimental conditions during the chemical osmosis experiment (Table 2). The porosity of a sample during the experiment being known,
can be easily derived from these curves (Table 3).
To obtain values for
using the model by Bolt,
is plotted against
0dl, for the
0
value of the sample, using Eq. [8] (Fig. 6). The value for
0dl can be calculated from the properties listed in Tables 1 and 2. All necessary additional values needed for Eq. [8], such as
, ts and td can be found with the formula provided. We found that Eq. [8] converges at n
60 for the summation terms. Subsequently, knowing
0dl of the samples,
can be derived from the curves (Table 3).
Chemical Osmosis
As expected the AWy showed semipermeable properties when it was subjected to the chemical potential gradient. The induced water flux resulted in an increase in differential hydraulic pressure, defined as
P equals Pfresh subtracted from Psalt, between the two reservoirs (Fig. 7). The differential pressure as defined yields positive values as water flows from the fresh water reservoir into the salt water reservoir. During the first few days, the pressure across the AWy sample increases rapidly until it reaches a maximum value between five and ten d. After this period, the value of
P slowly decreases. This behavior can be explained by the nonideality of the AWy as a semipermeable membrane. In the period up to Day 10, water is mainly transported by chemical osmosis causing
P to increase. However, during the same period, diffusion of ions across the sample occurs as the clay is not an ideal membrane and thus not capable of completely restricting the diffusion of salt. As a result, the salt concentration in the fresh water reservoir increases (Fig. 8), decreasing the osmotic gradient and thus reducing the osmotic water flux. In addition, the diffusion also causes the double layer of the clay platelets to shrink because of the increased ionic strength of the pore water which results in flocculation and consequently a more permeable clay. The second period in the experiment, after Day 10, is characterized by the slow dissipation of the induced pressure difference by water transport.

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Fig. 8. The increase in conductivity during the first 72 h as the result of diffusion of salt across the samples.
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In Fig. 8, the increase in the conductivity is shown for the AWy and dredging sludges. As with AWy, the salt concentration in the fresh water reservoir increases for the dredging sludges. However, the rate in which the salt concentration increases is larger for both dredging sludges. Although the dredging sludges were not capable of restricting the passage of solutes, the BK sample did show semipermeability which resulted in an elevated hydraulic pressure in the salt water reservoir (Fig. 9) as a result of the induced water transport (Fig. 10). This is in contrast with the BMR sample where no pressure increase or water transport was observed. The BK sludge in the experiments never reached an equilibrium state as observed for AWy. This is because after 72 h the water level in the standpipe in the fresh water reservoir dropped below the readout and the experiment had to be stopped. The
for this sample is calculated for a lower than maximum
P value.

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Fig. 10. The transport of water during the first 12 h for the Beerkanaal (BK) dredging sludge showing the flow of water from the fresh to the salt water reservoir.
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The
for AWy and BK can be calculated from the experimental data in two different ways. Firstly, by applying Eq. [3] and using the maximum observed pressure at equilibrium. And secondly, by using the average measured water flux during the first 48 h of the experiment, and applying an analogue of Darcy's law when hydraulic pressure differences are still negligible (Barbour and Fredlund, 1989; Keijzer et al., 1999; Keijzer, 2000):
 | (11) |
in which Jw is the measured water flux in m3 s-1, Kh is the hydraulic conductivity in m s-1, A is the area of the sample in m2 and 
0 is the absolute osmotic pressure difference in m H2O across the sample with thickness, x in m.
The experimental values for
obtained by the two different methods yield values which are in good agreement (Table 4). They are, however, considerably lower than the theoretical values for predicted by the two models (Table 3). The only exception is
calculated for the BK sludge by the Bolt model. For this sample, the measured value is of the same order of magnitude as predicted. The most striking contrast between theory and practice is observed for the BMR sludge which, in this experiment, did not show any semipermeable properties whereas high values of
were predicted.
Discrepancies Between Modeled and Measured Reflection Coefficients
The discrepancy between the theoretical and measured values for
result from the assumptions made in either of the two models. These assumptions result in a model which enables the description of a highly idealized system, but is unsuitable for the prediction of the semipermeability of natural occurring material.
The FMMM was supported by both laboratory experiments on bentonite (Fritz and Marine, 1983) using hyperfiltration or reverse osmosis and field observations in the Dunbarton Triassic Basin, USA (Marine and Fritz, 1981). The authors found a good correspondence with their experimental work even for porosities of the bentonite around 0.5. However, there is a fundamental difference between their experiments with reverse osmosis and the direct measurement of osmotic water transport as used in this study. In a typical reverse osmosis experiment, the salt solution is forced through the clay membrane against the osmotic gradient; and the osmotic pressure difference between the two solutions has to be overcome. Subsequently, the semipermeability of the sample can be derived. In these experiments, the sample is generally confined in a rigid wall permeameter and subjected to an axially applied overburden pressure to ensure a good wallsample contact. The experiment is rapid which made it popular in research of osmotic phenomena (e.g., Kharaka and Berry, 1973; Kharaka and Smalley, 1976; Fritz and Marine, 1981; Benzel and Graf, 1984; Demir, 1988). But because reverse osmosis normally is applied in a short period of time it reduces the effects of salt diffusion into the sample. Therefore, the
produced is a maximum value. As the clay is not an ideal membrane, salt will diffuse causing the overlap between adjacent double layers to reduce, and the clay to flocculate, making the membrane more permeable for the salt. As the experiment progresses in time, the diffusion front extends further into the clay, reducing the overall
of the sample. Thus, the
will decrease with time in the experiment (Fig. 11). In reverse osmosis experiments, this deterioration of the samples as a semipermeable membrane has been overlooked and not incorporated into the theoretical framework for the prediction of
. The fact that
is not an intrinsic value for a given sample or geological membrane was also observed by Whitworth and Fritz (1994).
The two models are based on other assumptions that may not be valid for the experimental conditions during our experiments. Both models were developed for completely dispersed, monomineral samples. The exchange complex is assumed to be occupied with only one monovalent cation. They also assume complete occupation by Na, as is evident from the frictional coefficients being calculated for the NaCl + H2O system only (Fritz, 1986). The influence of other cations on double layer thickness and the salt sieving capability of the samples is neglected. As our samples, with the exception of AWy, are a complex mixture of several clay minerals, and have not only Na+ but also other counterions on the exchange complex (Table 1), both models fail to predict a realistic value for
. The AWy and the sludges have substantial amounts of Ca2+ on the complex, reducing the double layer as this divalent cation is attracted stronger to the particle surface (Bolt, 1982a), thus making the samples less ideal membranes.
Complete dispersion of the clay platelets also does not hold in our samples. The specific surface area (As) needed to calculate the
should be the total area (Bolt, 1982b) as can be determined with the EGMEmethod (Churchman et al., 1991). When using the total As for the samples (Table 1), Bolt's model results in a
for AWy of 0.95, for BK of 0.69 and for BMR of 0.92. These values correspond closely with those found with the FMMM listed in Table 3. However, the values calculated in Table 3 with the Bolt model were obtained using the external area determined with the N2BET method (Aylmore et al., 1970; Feller et al., 1992). This is the surface area of assemblies or aggregates of particles. The external area is a more realistic value to use as the samples. Especially the sludge samples are not completely dispersed, and most certainly contain assemblies of clay-sand minerals. For the AWy and the BK, the clay content was high enough to result in semipermeable properties but the clay content of BMR (approximately 26%) was too low for a working membrane. Additionally, the clay minerals present in the BMR sludge, mainly illite and kaolinite, are less favorable than those present in the BK sludge, which include smectite (Table 1). Clays of low CECs are inherently less ideal semipermeable membranes than those with of high CEC (Kharaka and Berry, 1973; Fritz, 1986). Furthermore, both models seem to overestimate the influence of the porosity on the value of
as can be concluded from the discrepancy between the model values for the BMR sludge. It was, however, this sample which did not show any semipermeable properties.
Despite all assumptions that do not hold for the samples tested, the experimental
values, especially for the BK sludge, correspond closely with predicted values found with the model by Bolt. This is the result of the possibilities it offers to adjust the input values, e.g., the As, needed to calculate a
. The FMMM offers less possibilities to do so, and is too specifically derived for geological membranes. Finally, it should be noted that it can be shown that the friction coefficients in the FMMM vary only slightly for membranes at low and medium porosities and therefore have only a limited effect on the predicted value of the
(Keijzer, 2000).
Implications for Dredging Sludge Depots
As dredging sludge is capable to act as a semipermeable membrane, it is possible to determine the possible osmotically induced water flux through a depot and compare these values with other driving forces.
As it is customary to reduce the hydraulic gradient across the sludge, the hydraulic induced water flux is generally in the order of 2 mm yr-1. As a result, the maximum allowed advective water flux from a sludge in depot laid down in Dutch legislation should not exceed 2 mm yr-1 (VROM, 1993).
Assuming that the hydraulic conductivity of the sludge in the Slufter depot is higher than under the experimental conditions as a result of the lower consolidation grade, a Kh-value of 10-9 m s-1 is taken. Using the
found for the BK sludge (Table 4) and an approximated thickness of the sludge layer currently present in the depot of 20 m, a water flux of
1.5 mm yr-1 is calculated. Thus, the osmotically induced water flux is of the same order of magnitude as the maximum allowed water flux from a sludge in depot.
Therefore, a minimization of the hydraulic gradient only will not automatically lead to a minimization of the water flux and of transport of contaminants. As a consequence, the design criteria laid down in Dutch legislation will be exceeded.
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CONCLUSIONS
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To study osmotic transport in materials high in clay content, AWy and two dredging sludges from the Rotterdam harbor were subjected to a salt concentration gradient in the laboratory. Chemical osmosis was observed in the AWy and in one of the dredging sludge samples, quantified by
of 0.015 to 0.030, and 0.019 to 0.022, respectively. No chemical osmosis was observed in a second dredging sludge sample of low clay content. The s were found to be significantly lower than predicted by the FMMM (Fritz, 1986), and by a model based on the diffuse double layer theory presented by Bolt (1982b). The discrepancy between the theoretical and experimental values can be explained by the assumptions made in both models, which do not apply to the samples used in this study. Neither model is suitable for the complex mineralogical and ionic composition of the studied materials. The two models also seem to overestimate the influence of the porosity on the value of
. It is therefore essential that before applying one of the models for the prediction of the semipermeability of natural materials of high clay content, a thorough analysis is made of the applicability of their underlying assumptions.
The implications for dredging sludge as a semipermeable membrane in the transport of water and solutes are relevant when hydraulic gradients are eliminated. The semipermeability found for the BK sludge should be treated as a minimum value, but is still capable to induce a substantial water flux at salt concentrations present in coastal systems.
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ACKNOWLEDGMENTS
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The authors thank Dr. G. Kamerling at the Directorate General for Public Works and Water Management (Rijkswaterstaat) for partly supporting this work. The experimental setup benefited from the comments and adjustments made by Pieter Kleingeld, Tony van de Gon Netscher and Hans Bliek. The manuscript was improved by the comments of Prof. Dr. C.H. van der Weijden. This is contribution 20010103 of the Netherlands Research School of Sedimentary Geology.
Received for publication March 20, 2000.
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