Published online 27 February 2007
Published in Vadose Zone J 6:175-185 (2007)
DOI: 10.2136/vzj2006.0033
© 2007 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
ORIGINAL RESEARCH
Conceptual Models and Simulations for Biological Clogging in Unsaturated Soils
M. Mostafa and
P. J. Van Geel*
Dep. of Civil and Environmental Engineering, Carleton Univ., Ottawa, ON, Canada K1S 5B6
* Corresponding author (paul_van_geel{at}carleton.ca)
Received 28 February 2006.
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ABSTRACT
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Biological clogging in unsaturated soils is an important concern in the design of biofilters that are used to treat wastewater in rural areas. Several conceptual models have been developed to simulate biological clogging in saturated flow systems but limited research has been performed to develop similar conceptual models in unsaturated soils. This study developed three conceptual models for biological clogging in unsaturated soils. The model formulations varied from microscale to macroscale and from analytically derived to empirical equations. They were all formulated based on the approaches proposed by Burdine and Mualem to estimate the relative permeability based on the effective water saturation and the soil moisture curve. A one-dimensional unsaturated flow and transport code was developed, which incorporates Monod kinetics to simulate the biodegradation of an organic substrate. The three conceptual models that were developed relate the relative permeability to the microbial growth term in the unsaturated flow equation. The models were implemented in a numerical model to illustrate the impact of microbial growth on the biological clogging of unsaturated soils. Also the effect of continuous loading versus pulse loading was simulated to illustrate the difference between the loading scenarios on the clogging process within biofilters.
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INTRODUCTION
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SEPTIC TANK SYSTEMS are considered the most feasible way to treat wastewater in residential areas not served with sewage facilities (Kennedy and Van Geel, 2001). Septic tanks and drainage fields are located in the unsaturated zone close to the ground surface. The soil in this zone will be responsible for treating the septic tank effluent and it may clog with time due to filtration and microbial growth. Hence, clogging of unsaturated soils and how this clogging will affect the conductivity of the soil has to be understood to minimize the clogging problems and to use the soil in this zone as an effective treatment system.
Researchers have looked at clogging from three aspects: chemical, physical, and biological. Chemical clogging is caused by chemical reactions between the dissolved salts in the water, which result in the formation of salt particles that precipitate between the soil particles and lower the permeability of the soil. Physical clogging is the result of suspended solids that physically block the pores and reduce the pore diameters, which will lower the permeability. Biological clogging is due to growth of bacteria that attach to the solid particles and block the flow paths, which lowers the permeability (Rice, 1974).
Biological clogging, which is the focus of this work, is an important clogging mechanism when we are dealing with septic tank effluent. Bacteria are already present in the soil and need a suitable environment to grow. This suitable environment can be summarized in two factors: physical and nutritional (biochemical). Physical factors include moisture, hydrostatic pressure, and osmotic pressure. Nutritional factors include availability of C, N, S, P, trace elements such as Cu, Fe, Zn, and Co, and in some cases vitamins (Black, 1999). Carbon and nutrient sources can include septic tank effluent, leachate from the land application of municipal wastes like biosolids, or leachate from sanitary landfills.
Practically, the impact of biological clogging can be seen in various biofilter applications. Biofilters such as peat filters are one important application in this field. Peat filters are used to treat wastewater streams and they are relatively inexpensive (Kennedy and Van Geel, 2001). Studies have been conducted to investigate the removal efficiencies (e.g., Brooks et al., 1984) and to investigate the hydraulics of peat filters (e.g., Kennedy and Van Geel, 2001).
Conceptual models for clogging of saturated soils have been proposed by many researchers (Taylor and Jaffé, 1990; Taylor et al., 1990; Vandevivere and Baveye, 1992; Vandevivere et al., 1995; Clement et al., 1996; Berkowitz and Ewing, 1998; Seki and Miyazaki, 2001; and others). These models were based on a conceptual model that assumed the pore volume of saturated soil could be represented by capillary tubes, ignoring the interconnection between them. Vandevivere et al. (1995) argued that using this assumption will lead to a model that is unable to accurately predict the reduction in hydraulic conductivity due to microbial growth. They suggested that a pore network model would more accurately estimate this reduction, as it will account for the interpore connections.
Recent studies show the effectiveness of having a pore network model in simulating biological clogging in saturated soil (Kildsgaard and Engesgaard, 2002; Thullner et al., 2002a, 2002b, 2004). Based on a pore network model presented earlier in Thullner et al. (2002b), Thullner et al. (2004) found realistic agreement between experimental data and numerical model prediction in the reduction in hydraulic conductivity of saturated soil caused by biomass growth. Thullner et al. (2002a) incorporated the biomass growth as a reduction in the porosity, which is directly related to hydraulic conductivity of the soil. Biomass, which mainly consists of extracellular polymers, was converted to a biovolume using an assumed density given by Characklis and Marshall (1990) and the biovolume was used to calculate the reduction in the porosity.
Despite the extensive research on bioclogging of saturated soils, limited research has been conducted to develop a conceptual model for clogging in unsaturated soils. The relation between the relative permeability and the microbial growth of the unsaturated zone is not well understood. Also, conceptual models for biological clogging in unsaturated soils have not been proposed or included in a numerical model to simulate clogging as proposed in this work. The objectives of this research work concentrated on developing conceptual models to simulate biological clogging in the unsaturated zone and show how microbial growth can affect the relative permeability of unsaturated soils from both theoretical and numerical points of view. The conceptual models vary from the microscopic to the macroscopic scale and from analytically derived to empirical equations. The microscopic-scale conceptual model was based on the assumption of a biofilm that covers the soil particles. The macroscopic-scale models relate the relative permeability to the growth of microbes and do not consider the distribution of the microbial growth at the microscopic scale. These conceptual models were implemented in a one-dimensional unsaturated flow and transport code to simulate the clogging of a one-dimensional peat column subjected to continuous and pulsed loading.
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MODEL DEVELOPMENT
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It is well known that the voids in unsaturated soil can be simulated as capillary tubes with different diameters; each diameter reflects a volume of void space that can be filled at a certain capillary pressure. The capillary pressure–saturation relationship used in this work was introduced by van Genuchten (1980) and the relationship is shown in Fig. 1
. This relationship expresses the relationship between the capillary pressure and the corresponding effective water saturation. At 100% saturation, all the pores are filled and as the capillary pressure increases, the larger pores drain. The schematic of the pores, provided in Fig. 1, is used below to illustrate the proposed conceptual models. Under a constant water flux or hydraulic load, the water content within the column will increase, causing larger pores to fill to increase the relative permeability of the soil. The proposed models all involve adjusting the relative permeability term to account for the microbial growth. The contaminant transport was modeled using a standard advection–dispersion model with a sink term to simulate the biological decay. Both the unsaturated flow and transport equations were verified against available analytical solutions and published model results.
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Fig. 1. Conceptual relationship between the pore size distribution and the van Genuchten relationship for the soil moisture curve.
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Model no. 1
In first model, which is macroscopic in nature, the bacterial growth will occur in the smaller pores since, for unsaturated soils, the larger pores drain first and the smaller pores are saturated and responsible for flow. Hence, the small-diameter pores will initially clog, and the flow will be displaced into the larger pores. As a result, the water content will shift to the larger pores to compensate for the presence of the microbial growth and to reestablish a sufficient relative permeability to conduct the same fluid flow. With time, microbial growth will continue and the flow will be displaced into the larger pores, until eventually the soil becomes fully clogged (Fig. 2
).
In this model, the relative permeability equations proposed by Burdine (1953) and Mualem (1976) are used in a similar approach to that proposed by Lenhard and Parker (1987) for multiphase flow. In this case, a microbial-phase saturation is introduced to account for the volume occupied by the microbial mass. In addition, as in the approach to multiphase flow, a total saturation term is introduced. The total saturation is equal to the microbial saturation and the water saturation. The equations for the effective microbial saturation (Sem), effective water saturation (Sew), and effective total saturation (Set) follow and are illustrated in Fig. 3
. The effective microbial saturation reflects the volume of pore space occupied by the microbial growth, effective water saturation reflects the volume of pore space occupied by mobile water, and the effective total saturation represents the summation of the effective microbial and water saturations. It is assumed that the microbial growth is attached to the soil particles and the effective total saturation reflects the location of the water–air interface, which governs unsaturated flow. This is analogous to a multiphase flow system in which effective total saturation consists of the water and immiscible fluid saturations.
 | [1] |
where Pc is capillary pressure, and 
, m, and n are van Genuchten parameters,
 | [2] |
where Sam is actual microbial saturation and Swr is irreducible water saturation, and
 | [3] |
The integral form from Burdine (1953) or Mualem (1976) can be altered to reflect the presence of a microbial saturation as follows:
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Fig. 3. Capillary pressure (Pc)–saturation (Se) relationship for Model no. 1 that shows effective total saturation (Set) at a certain point as the sum of effective water (Sew) and microbial saturation (Sem).
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For Burdine:
 | [4] |
where kr is the relative permeability, Se is effective saturation, and 
is soil suction.
For Mualem:
 | [5] |
Equation [4] using Burdine's theory and Eq. [5] using Mualem's theory express the relation between the relative permeability and the saturation, taking into account the microbial growth. The additional term, 
0Sem dSe/2 for Burdine and 0Sem dSe/ for Mualem, acts to reduce the permeability due to the presence of the microbial mass.
The closed forms of the integrals Eq. [4] and [5] are given as
For Burdine:
 | [6] |
For Mualem:
 | [7] |
Hence, as the microbial growth continues, the microbial saturation increases and the relative permeability to the water phase decreases. To compensate and to conduct the same water flow, the effective total saturation increases, displacing water into larger pores.
Model no. 2
In the second model, which is also based on a macroscopic approach, the original relative permeability terms developed by Burdine and Mualem are multiplied by a new term, (1 – Sem), to reduce the relative permeability term by a factor to take into account the impact of microbial growth on relative permeability.
The equations used for Model no. 2 based on Burdine and Mualem are as follows:
For Burdine:
 | [8] |
For Mualem:
 | [9] |
There is no experimental proof or theoretical derivation for this formulation. The model provides an estimation of the relative permeability term by reducing the relative permeability as the microbial saturation increases. Further experimental work needs to be done to confirm whether this second conceptual model is appropriate or not.
Model no. 3
The third model is based on a microscopic conceptual model. In this model, a flow reduction factor due to microbial growth is developed and the unsaturated relative permeability equations of Burdine and Mualem are multiplied by this flow reduction term. In the development of the flow reduction term, the pore size distribution was determined or inferred from the soil moisture curve and the microbial growth was assumed to form a biofilm that covers the walls of the capillary tubes. The biofilm was assumed to form in all the pores since all the pores contain an irreducible water saturation in which the bacteria can grow. The reduction in the radii of the capillary tubes will increase the resistance to flow and reduce the permeability of those pores. Based on these assumptions, the flow reduction factor was developed. A conceptual schematic of the model is provided in Fig. 4
. It is important to note that the unsaturated flow is still based on the macroscopic relative permeability terms, which reflect a porous medium with interconnected pore bodies and pore throats. These relative permeability models have been simulated using a microscopic interconnected pore body–pore throat model. The flow reduction factor developed here attempts to reduce the flow within the interconnected pores based on a conceptual model of a biofilm lining the pore bodies and pore throats.
In developing this conceptual model, the capillary pressure–saturation relationship will be used to determine pore size distribution. The van Genuchten relationship can be rearranged to solve for capillary pressure. The resulting equation is as follows:
 | [10] |
To determine the distribution of radii for the bundle of capillary tubes representing the soil, the saturation is divided into a user-specified number of equal divisions. The average saturation at the midpoint of each division is then used to determine the corresponding capillary pressure. The capillary pressure is used to calculate the radius of the capillary tube.
The number of capillary tubes per unit cross-section area of soil within each division can be calculated by dividing the total void volume of each division (represented as a cross-sectional area) by the cross-sectional area of one capillary tube.
Once the distribution of capillary tubes is known, the microbial volume (Vm, expressed as an area per unit cross-sectional area) can then be distributed as a biofilm of uniform thickness, th, within the capillary tubes using the following equation:
 | [11] |
Based on Hagen Poiseuille's derivation for laminar flow in a pipe and summing the flows within all the capillary tubes, a total flow Q can be estimated using the following equation:
 | [12] |
where r is the radius of the capillary tube, 
is the density of the liquid, g is the gravitational acceleration, µ is the dynamic viscosity, and 
h/L is the hydraulic gradient.
The presence of a biofilm will impact this flow and Eq. [12] could be modified as follows:
 | [13] |
In Eq. [13], the pore radii are reduced by the thickness of the biofilm, hence reducing the flow through each pore.
To adjust the unsaturated permeability of the soil to account for the impact of the biofilm, a flow factor, U, was introduced and the ratio of the flow factors with and without the biofilm were used to estimate the flow reduction factor, which is used to reduce the relative permeability. The flow factor without the biofilm is expressed as
 | [14] |
and the flow factor with the biofilm is expressed as
 | [15] |
where Uo|0Porosity represents the initial flow without a biofilm for all the pores and Ur|0Porosity represents the reduced flow with a biofilm present in all the pores. The flow reduction factor is equal to Ur|0Porosity over Uo|0Porosity and is used to reduce the relative permeability term to account for the presence of the microbial growth.
Finally, the relative permeability saturation relationships that can be used to simulate this scenario for Burdine and Mualem are as follows:
For Burdine:
 | [16] |
For Mualem:
 | [17] |
Note that, at each time step as the biofilm grows, the biofilm thickness increases. At a certain point, as shown in Fig. 4, some radii will be filled by the bacteria and will no longer contribute to the flow. As a result, Eq. [11] is modified with time to account for the capillary tubes that are filled. Likewise, the filled capillary tubes are not included in the calculation of the flow factor with biofilm, Eq. [15].
A fourth conceptual model, similar to Model no. 3, was developed in which the flow reduction factor assumed that the biomass was distributed as a biofilm in only the water-filled pores. Convergence problems were encountered, however. As the water saturation increased and water was displaced into the next pore size, the biomass was redistributed and the biofilm thickness recalculated. Since the total surface area of the capillary tubes contributing to flow increased, the biofilm thickness and flow reduction factor decreased. This caused the flow reduction factor to oscillate as water was displaced into the next pore size, which in turn caused convergence problems. The convergence problem may be overcome by increasing the number of divisions used to establish the radii of the capillary tubes—20 divisions were used for the model results presented here—or by simulating the microbial growth in each capillary tube as clogging progressed. The latter option requires even more knowledge of the biomass distribution at the pore scale and adds greater complexity to the conceptual model. Although this approach warrants further consideration, it was beyond the scope of this research effort, as there is a greater need for accurate data to validate the proposed models.
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MODEL RESULTS AND DATA ANALYSIS
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The three conceptual models were implemented in a one-dimensional unsaturated flow and transport code. The code was used to simulate biological clogging in two soil types (i.e., peat and sand) to simulate biofilters and sand filters. Also, different loading conditions (i.e., continuous vs. pulse) were simulated to study the effect of the loading conditions on the clogging process. Both Burdine's and Mualem's formulations were implemented in the code, but only the results using Mualem's formulation are presented here. It is important to note that the model results are for a generic or hypothetical clogging scenario and are a function of the input parameters such as the microbial growth kinetics and the assumed microbial density to convert the microbial mass to a microbial saturation. Further experimental work is needed to better assess these parameters. The model results presented here are intended to highlight the differences between the three proposed models and to illustrate the models' ability to assess continuous vs. pulse loading and its impact on the clogging process.
Simulation of a Peat Soil with Continuous Loading
A simulation was conducted on a 100-cm vertical peat column. The input parameters for the soil properties and degradation kinetics are given in Table 1. Initially, the soil column was assumed to reflect a clean soil with an initial static moisture profile based on the initial or fixed head at the base of the column. A continuous flux of 20 cm/d with a substrate concentration of 2000 mg/L was simulated at the top of the column starting from time zero until the column was clogged. Clogging was defined to occur when the total saturation reached one that corresponds to a condition where the microbial growth will start to cause ponding at the top of the column. The boundary condition at the base of the column was a prescribed head boundary such that the head was fixed at –9.9 cm. The cumulative flow and substrate mass balance errors were found to be 0.058 and 0.59% for Model no. 1, 0.034 and 0.19% for Model no. 2, and 0.035 and 0.22% for Model no. 3, respectively. The low mass balance errors indicate that the developed code was conserving fluid and substrate mass reasonably well. It should be noted that the number of divisions used in Model no. 3 for the flow reduction factor was 20 divisions.
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Table 1. Soil and Monod kinetics parameters used in the clogging simulation for the peat soil with continuous loading. The Monod equation used in this study is:
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Figure 5
illustrates the concentration profile with time for the peat using Model no. 1. Similar profiles were generated for Models 2 and 3. At early times, 1 to 4 d (t1–t4), the contaminant front advances in the column with limited decay since the microbial mass is establishing itself. The initial microbial mass in the column was 1500 mg/L and is specified by the user. With time, the microbial mass established at the top of the column and at later times, 40 to 62 d (t8–t10), there is sufficient microbial mass present in the top 2 to 3 cm to degrade the specified organic load.
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Fig. 5. Substrate concentration profiles with time for peat soil using Model no. 1 (initial concentration C0 = 2000 mg/L).
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To illustrate how the three different models approached clogged conditions, Fig. 6
, 7
, and 8
illustrate the water, microbial, and total saturation profiles with time for Models 1, 2, and 3, respectively. The clogging times were found to be close for all three model scenarios: 62, 58, and 60 d for Models 1, 2, and 3, respectively. Each model, however, predicted a slightly different saturation path to clogging.
As mentioned above, Model no. 1 assumed that the smaller pores will fill first with microbial mass. Since these smaller pores contribute the least to the flow, Model no. 1 should predict the lowest reduction in relative permeability at early times and the least impact on the actual total saturation at early times (Fig. 6). For example, after 40 d, the actual microbial saturation increased to 20% with little change in actual total saturation and hence a corresponding decrease in actual water saturation of 20%. Little change in the actual total saturation indicates that the 20% microbial saturation present in the smallest pores had minimal impact on the relative permeability. Even after 60 d and a microbial saturation of 0.55, there is minimal impact on the total saturation profile. Once the microbial saturation was large enough to significantly impact the relative permeability term and the total saturation profile, however, the clogging occurred rapidly.
Models 2 and 3 are macroscopic and microscopic models, respectively, but with different reduction factors (i.e., 1 – Sem for Model no. 2 and the ratio of flow factors for Model no. 3). Due to the form of the reduction factors, the impact of an increase in microbial saturation on the relative permeability term is more significant at earlier times. In comparison with the results of Model no. 1, after 40 d the microbial saturation predicted using Models 2 and 3 also increased to 20%. The total saturation, however, also increased by approximately 10% to account for the reduction in relative permeability caused by the microbial growth. In addition, the simulated increase in the total saturation with time at the top of the column was more gradual for Models 2 and 3 than for Model no. 1. Clogging still occurred, however, after approximately 60 d for all three clogging models.
Clogging was faster for Model no. 2 vs. Model no. 3 as the 1 – Sem factor for Model no. 2 generated a greater reduction in the relative permeability values vs. the flow reduction factor in Model no. 3. This can be seen in Fig. 9
, as the minimum value of the flow reduction factor for Model no. 3 was approximately 0.95 in comparison to 0.47 for Model no. 2.
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Fig. 9. Comparison between the (1 – Sem [effective microbial saturation]) factor from Model no. 2 and the flow reduction factor using a van Genuchten n value of 1.3 for Model no. 3.
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To illustrate the impact of the shape of the soil moisture curve on the clogging process, the van Genuchten n value was increased from 1.3 to 3.0. The value of n in the van Genuchten relationship impacts the slope of the soil moisture curve and hence a larger value of n reflects a more uniform pore size distribution and a sharper change in saturation for a small change in capillary pressure (i.e., uniform sand). Figure 10
shows a comparison between the 1 – Sem factor for Model no. 2 and the flow reduction factor for Model no. 3 for the higher n value. Using a higher value resulted in a sharper decrease in the flow reduction factor as the microbial saturation increased. The same simulations were conducted as those using Models 2 and 3 and a van Genuchten n value of 3.0. The minimum value of the flow reduction factor at clogging was approximately 0.13 for Model no. 2 and 0.17 for Model no. 3 in comparison to 0.47 and 0.95 for Models 2 and 3 with n equal to1.3. The clogging times for Models 2 and 3 were found to be very close: 47.88 and 47.90 d, respectively. Increasing the value of n caused the soils to clog more quickly, which indicates that a uniform sand with the same saturated hydraulic conductivity as a well-graded sand is predicted to clog more quickly for the conceptual models proposed in this research. Intuitively, one expects a uniform sand with fewer fines to take longer to clog; however, fewer fines also increases the hydraulic conductivity, which is not adjusted accordingly in this comparison. Additional experimental work is ongoing to validate the proposed models for uniform vs. well-graded sands.
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Fig. 10. Comparison between the (1 – Sem [effective microbial saturation]) factor for Model no. 2 and the flow reduction factor using a van Genuchten n value of 3.0 for Model no. 3.
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Clogging was simulated to occur faster with Models 2 and 3 vs. Model no. 1. As stated above, for Model no. 1 the effect of microbial growth will not be significant at earlier times and only when the actual microbial saturation is significant will the relative permeability be impacted. Figure 11
supports this conceptual idea, as a significant reduction in the relative permeability started at about 37 d when the effective microbial saturation was approximately 0.18 (i.e., 0.16 actual microbial saturation). The actual total saturation increased at later times (i.e., 60 d) as shown in Fig. 6 and Fig. 11 and it reached 100% in the last 2 d of the simulation. It should be noted that there is a slight increase in Set at earlier times. This slight increase is not obvious in Fig. 11 due to the scale of this figure. The fact that Model no. 1 simulated a larger time before clogging is also supported by the actual microbial saturation at clogging, which was approximately 90% for Model no. 1 and approximately 50% for Models 2 and 3.
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Fig. 11. Relative permeability (kr) and effective total, water, and microbial saturations vs. time for the top 0.5 cm of the peat column using Model no. 1 with a van Genuchten n value of 1.3.
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In Models 2 and 3, the impact on the relative permeability was different. A significant impact occurred at earlier times (Fig. 12
for Model no. 2 and Fig. 13
for Model no. 3). The relative permeability started to decrease when the effective microbial saturation was approximately 0.006 (i.e., 0.005 actual microbial saturation) at 12 d for Model no. 2 and at approximately the same saturation for Model no. 3. The effective total saturation increased to compensate for the reduced permeability and it reached 100%, while the effective microbial saturation reached was approximately 54% for Model no. 2 and approximately 57% for Model no. 3.
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Fig. 12. Relative permeability (kr) and effective total, water, and microbial saturations vs. time for the top 0.5 cm of the peat column using Model no. 2 with a van Genuchten n value of 1.3.
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Fig. 13. Relative permeability (kr) and effective total, water and microbial saturations vs. time for the top 0.5 cm of the peat column using Model no. 3 with a van Genuchten n value of 1.3.
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It was also noted in the literature that clogging occurred in the top 1 to 2 cm of a soil column when continuously loaded with an organic source. The simulation results presented here indicate the same trend. For Models 1, 2, and 3, >95% of the microbial growth occurred within the top 1.5 cm of the soil column.
Simulation of a Sand Soil with Continuous Loading
Another simulation was conducted for a 100-cm sand column using Models 1 and 2. Table 2 provides the soil parameters used in this simulation. The saturation profiles for Models 1 and 2 are given in Fig. 14
and 15
, respectively.
For a porosity of 0.3 for the sand soil, clogging will occur faster than for the peat soil. The microbial mass can only occupy this smaller porosity vs. the greater porosity in the peat. Using Model no. 1, clogging occurs after 44 d with a cumulative flow mass balance error of 0.053% and a cumulative substrate mass balance error of 1.03%, while clogging occurs after 43 d using Model no. 2 with a flow mass balance error of 0.045% and a substrate mass balance error of 0.38%.
It is also worth noting the distribution of the microbial growth in the sand vs. peat simulations. As discussed above, Fig. 6, 7, and 8 indicate that >95% of the microbial mass is located in the top 1.5 cm of the peat column. In comparison, Fig. 14 and 15 indicate that the microbial mass is distributed throughout a greater depth of 4 to 5 cm due to the lower porosity.
As the porosity decreases, the seepage velocity increases, which allows the substrate to penetrate faster and further into the column. As the microbial mass increases, the degradation rate also increases; however, it never reaches the degradation rate in the peat column since the sand column clogs more rapidly. The slower degradation rate at the time of clogging and the higher seepage velocity allow the contaminant to advance further into the column to establish the larger zone of microbial growth. Also, the trends in the relative permeability for the simulation with sand are similar to the simulation results for peat (i.e., Fig. 11, 12, and 13; data not shown).
Pulse Simulation
As discussed above, septic systems are one of the most important applications where clogging can be seen. Peat filters designed to treat larger volumes of septic tank effluent at schools (Kennedy and Van Geel, 2001), for example, or small commercial systems designed to treat smaller volumes at a home generally pulse the system to decrease the chances of the formation of a thin biomat at the surface.
As seen in the previous simulations, a low continuous flux results in a very shallow biomat, which clogs a column very quickly. If the same hydraulic and organic loading is applied in two to three pulses rather than continuously throughout a period of a day, the organic source can advance farther into the column before degrading and hence the microbial mass needed to degrade the organic load will distribute itself throughout a greater depth.
To simulate a pulsed loading scenario, a column was pulsed daily with a total flux equivalent to 10 cm in the first 15 min of the simulation, followed by no flux for 11.75 h. After 12 h, the column was pulsed again with 10 cm for another 15 min, followed by no flux until the end of the day. Hence, the hydraulic loading remained at 20 cm/d.
The simulated (Model no. 1) microbial, water, and total saturation profiles after 180 d for a pulsed peat column with the same daily hydraulic and organic loading are presented in Fig. 16
. It is evident from the microbial saturation profile that the microbial mass has distributed itself throughout a greater depth, 25 vs. 1.5 cm for the continuous flow simulation, and the total saturation profile remained unchanged during the 180-d simulation. The continuous flow system clogged after 62 d in comparison to the pulsed system, which indicated very little impact due to microbial growth after 180 d or approximately 6 mo.
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CONCLUSIONS
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Several researchers have developed conceptual models for biological clogging in saturated flow systems. Limited research has been completed, however, to understand and develop similar conceptual models for biological clogging in unsaturated soils. This research proposed three new conceptual models that relate the relative permeability to the microbial growth of the soil based on the relative permeability relationships put forward by Burdine (1953) and Mualem (1976).
Model no. 1 is a macroscopic model analog to multiphase flow in which the relative permeability terms proposed by Burdine and Mualem are adjusted to account for a microbial mass. Since this model assumes that the smaller pores are filled first with microbial mass and these pores contribute the least to the flow, no significant impact was noticed on the relative permeability term using this model until a sufficient microbial mass was generated to significantly affect the flow path.
Model no. 2 is a macroscopic model based on the same equations presented by Burdine and Mualem, and microbial growth was taken into account by reducing the relative permeability by a factor of (1 – Sem). Any slight increase in the microbial mass will result in a reduction in the relative permeability and a corresponding increase in the actual total saturation to conduct the flow.
Model no. 3 introduced a flow reduction factor, which is based on a capillary tube–biofilm model. This model uses the same equations presented by Burdine and Mualem multiplied by a flow reduction factor based on laminar flow (Hagen Poisseuille) in the capillary tubes with and without a biofilm. An increase in microbial mass increases the thickness of the biofilm, which in turn reduces the relative permeability.
A one-dimensional, unsaturated flow and transport code was developed as a part of this work to study the effect of the different conceptual models on the clogging of unsaturated soil. Microbial growth was simulated using Monod kinetics. Two different soil types, sand and peat, were simulated to illustrate the functionality of the code. Sand soil was chosen as it is often used as a filter medium and peat was selected because it has become a common filter medium used with septic systems. In addition, these two soils have different porosities, which helps to illustrate the impact of porosity on the clogging processes within a filter.
Continuous and pulsed load scenarios were simulated to illustrate the effect of continuous and pulsed loading conditions on clogging. It was clearly demonstrated that for the same daily hydraulic and organic loading, continuous loading, due to the formation of a thin biomat at the influent surface, resulted in clogging much sooner than pulsed loading.
Further research is needed to validate the conceptual models proposed here. Detailed experimental studies under controlled hydraulic and organic loading are needed to evaluate the impacts of soil type (e.g., uniform vs. well-graded sands, alternative media like peat, etc.) and the impacts of continuous vs. pulsed loading. The proposed models are dependent on the microbial saturation, which is a function of the microbial mass, simulated using the Monod equations, and the assumed density of the microbial mass. Hence, additional research is needed to evaluate the form and distribution of the microbial mass at the pore scale to further development and improve the conceptual models proposed here and to better estimate the density of the microbial mass.
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APPENDIX
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- b
- cell decay coefficient
- g
- gravitational acceleration
- kr(Sew)
- relative permeability as a function of effective water saturation
- Ks
- half velocity constant
- Ksat
- saturated hydraulic conductivity
- K(
) - saturated hydraulic conductivity as a function of moisture content
- MT
- microbial concentration
- m, n, and
- van Genuchten parameters
- Pc
- capillary pressure
- Q
- total flow
- qm
- maximum specific rate of substrate utilization
- r
- radius of capillary tubes
- Se
- effective saturation
- Sam
- actual microbial saturation
- Sem
- effective microbial saturation
- Set
- effective total saturation
- Sew
- effective water saturation
- Swr
- irreducible water saturation
- th
- thickness of biofilm layer
- Uo|0Porosity
- flow factor represents the initial flow without a biofilm for all the pores
- Ui|0Porosity
- flow factor represents the reduced flow with a biofilm present in all the pores
- Vm
- volume of biofilm
- Y
- cell yield coefficient
- porosity
- µ
- dynamic viscosity
- r
- irreducible moisture content
- density of liquid
- bacteria
- density of bacteria
- h/L
- hydraulic gradient
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ABSTRACT
INTRODUCTION
