NUMERICAL MODELING OF PHASE CHANGE DURING BIOVENTING: INFLUENCE OF INJECTION FLOW RATES AND THERMAL CONDUCTIVITY

NUMERICAL MODELING OF PHASE CHANGE DURING BIOVENTING: INFLUENCE OF INJECTION FLOW RATES AND THERMAL CONDUCTIVITY

LEE G. GLASCOE, STEVEN J. WRIGHT, and LINDA M. ABRIOLA

Department of Civil and Environmental Engineering

University of Michigan, Ann Arbor, MI 48109-2125

tel:(734)764-9426, fax:(734)763-2275, Email: glascoe@engin.umich.edu

ABSTRACT

This modeling investigation examines the influence of evaporative phase change on moisture content and temperature distributions during a bioventing gas injection operation for vadose zone remediation. Currently few soil vapor extraction or bioventing models incorporate non-isothermal effects when considering system performance. Laboratory and field measurements suggest, however, that even small changes in temperature and moisture content can enhance or impair biological activity and could thus affect the overall efficiency of a bioventing operation. The presented model is a one-dimensional simulator which describes mass and energy transport under steady, gaseous phase flow conditions. The coupled mass and energy equations are solved using a sequential iterative solver with matric potential and temperature as primary variables. A literature-derived relation is used to quantify the combined effect of moisture content and temperature change on biological growth rates. Radial flow simulations indicate that the injection of gas at temperatures and/or water vapor contents different from the initial ambient soil conditions can result in microbiologically significant changes in moisture content and local soil temperature. This investigation identifies that under typical gaseous flow conditions up to a 37% reduction in biological activity can occur at the injection well and a 20% reduction can occur up to a radius of 3.5 meters after one year of injection. Sensitivity to thermal parameters is explored, revealing that the representation of the thermal conductivity strongly influences model predictions.

Keywords: bioventing, subsurface remediation, phase change, bioremediation, multiphase flow, soil vapor extraction

INTRODUCTION

Bioventing (BV), a popular method of soil remediation, involves the induction of gas advection in unsaturated soil through the use of injection and/or extraction wells. The primary goal of BV is in situ bioremediation enhancement through oxygen delivery. Field BV data (e.g., Miller et al., 1994) and laboratory data (e.g., Potts, 1994; McMeekin et al., 1988; Stark and Firestone, 1995) suggest that even small changes in water content and temperature can affect biological activity. Lingineni et al. (1992) identified injection of warm gas as a possible remediation technique to enhance contaminant volatility. Walton and Anker (1996) developed a single compartment mathematical model and proposed that humidification could provide a low-cost enhancement to soil venting. A previous numerical study has identified the possible magnitude of microbiologically significant changes in temperature and moisture content induced by advection-driven phase change (Glascoe et al., 1998).

The modeling investigation presented herein was designed to assess the significance of injection flow rates and thermal conditions on advection-induced temperature and water content changes and the consequent effects on biological activity during a typical BV operation. The modeled scenario is gaseous injection into a homogeneous sandy soil beneath an impervious surface cap of wide extent. This scenario permits use of a one-dimensional radial model. Gas is forced through the system at a specified volumetric flux that is based on BV flow rates reported from field studies.

MODEL DEVELOPMENT

Equation Development

The one-dimensional simulator developed in this work is based upon mass and energy balance equations for non-isothermal multiphase flow and transport. Thermal and inter-phase mass partitioning equilibrium are assumed between the solid, aqueous and gaseous phases. Water vapor is transported in the gaseous phase under an imposed flux while liquid water flows in response to gradients in matric potential. The overall water balance equation can be written for radial coordinates as

EQ(1)

where the density terms r_v and r_w represent the density of water vapor and the density of liquid water, respectively; q_w is the volumetric aqueous content and q_g is the volumetric gaseous content which sum up to the porosity, n, of the medium. The flux terms, J_v and J_w, in EQ(1) can be expressed as

and

EQ(2)

where q_g is the forced volumetric gas flux, K(q_w) is the liquid water effective hydraulic conductivity, y is the matric potential, D_v,g is the effective coefficient of molecular diffusion of water vapor in gas, and a is the dispersivity. The one-dimensional equation for the conservation of energy assuming thermodynamic equilibrium between all phases, can be written as (Kaviany, 1991)

EQ(3)

The overall heat capacity is calculated as a volume-averaged sum of the heat capacities of all the phases, i.e., (rc_p)_m=(1-n)r_sc_ps + q_wrwc_pw + q_gr_gc_pg. The effective thermal conductivity of the matrix, k_m, is estimated using an empirical relation for partially-saturated sand (Somerton, 1992)

EQ(4)

where the k_s is the thermal conductivity of the soil solids. The soil is considered to be a spatially homogeneous rigid matrix. Matric potential is related to vapor density using a form of the Clausius-Clapeyron equation, i.e., r_v^sat=r_vexp(yg/R_vT), where R_v is the water vapor gas constant. The gas density, r_g, is determined using the ideal gas law while the saturated vapor density, r^sat_v, is expressed as a polynomial function of temperature.

Numerical Implementation

The two balance equations can be expanded using the chain rule and re-written in terms of the primary variables y and T in a manner similar to that of Milly (1982). For the modeled scenario, boundary conditions are defined by a 3rd-type flux boundary upstream (a constant total flux)and a 2nd-type fixed gradient condition downstream. The coupled equations are solved sequentially (EQ(1) for y and EQ(2) for T) with time derivatives approximated using a fully implicit backwards finite difference method. Non-linear coefficients are then updated and the process is repeated until acceptable convergence in primary variables is attained. The model components were verified through comparisons with available analytical solutions. In addition to these verifications, global mass and energy balances were computed for all simulations presented herein. Errors of less than 0.1% (relative to the incoming flux) were maintained for all cases.

Biological growth component

Ratkowsky et al. (1982) investigated the dependence of microbial growth rates (k_bio) on temperature and found that the Arrhenius equation poorly represented these observations. They proposed a temperature relation to better fit bacterial data called the square root model. McMeekin et al. (1988) noted that this relation can also be used to include changes in water activity, a. A complete form of this relation based can be written as

EQ(5)

where b_bio is the multiplier to normalize k_bio^1/2 to initial conditions. The parameters T_max and T_min are the limits of biological activity as determined from the regression analysis of the biological data. In this study, water activity is replaced by relative humidity, i.e., a=r_v/r_v^sat, which varies exponentially with water potential, y. The T-k_bio relation was taken from a bacteriological experimental study (McMeekin et al., 1988) while the y-k_bio relation was estimated from an experimental study investigating drying effects on bacteria (Stark and Firestone, 1995). Specifically the parameters used for the Pseudomonas sp. psychrophillic heterotrophs are T_max=37^oC, T_min=-10^oC, c_bio=0.223 and a growth limitation at y=-40m.

NUMERICAL SIMULATIONS

The focus of these simulations is the prediction of changes in soil temperature and water potential that occur under typical BV operational conditions due to the injection of gas of a different temperature and/or water vapor content than that of the in situ soil gas. Different flow rates are examined and a brief sensitivity study of the thermal parameters is discussed. Table 1 lists the parameters, boundary conditions, and initial conditions used for the simulations.

Initial Conditions 0<r<50m, t=0	T₀=283K, T_ref=273K y₀=-1000cm, a=0.1m
3^rd type Upstream conditions	r_v/r_v^sat\|_up=0.50, T_up=283K
for water balance	(q_gr_v)_up=J_v+J_w
for energy balance r=well, t>0	(q_gr_vhv+q_gr_gh_g)_up=qgr_gh_g+J_vh_v+J_wh_w +conductive term + dispersive term
2^nd type Downstream conditions r=50 m, t>0	dy/dr=0 and dT/dr=0
Parameters	q_w,sat=0.305
from Milly (1982) and Somerton (1992)	K_sat=2.15x10^-3 cm/s
	q_w=0.185(1+[log(-y)/1.27]^7.88)^-1 +0.027[7.0-log(-y)], y in cm
	ks=4.5W/m/K, cps=0.85 kJ/kg/K

TABLE 1. Initial and boundary conditions and soil parameters.

Different Injection Rates

A survey of field applications of BV identified flows per unit depth ranging from 10 to 1,000 m³/m/day (e.g., van Eyk, 1994). For the following simulations a low flow rate of 20 m³/m/day and a higher flow rate of 200 m³/m/day were chosen to illustrate the effect of differing lower-end flow rates on advection-induced phase change during BV. Both simulations assumed a 50% relative humidity for the injected air. The 30-cm diameter injection well is screened over a unit (meter) depth. Figure 1 illustrates the evaporative temperature decrease induced by the two different flow rates. The higher the flow rate, the faster the decrease in temperature. The temperature drop is ultimately limited to the wet-bulb temperature. Similarly, the higher the flow rate, the greater the decrease in water content at the well. The combined effect of a drop in temperature and a drop in moisture content will have negative implications for biological growth near the well. Figure 2 illustrates the influence of temperature and moisture changes on biological activity as predicted by the square-root equation, EQ(6). Less than a 10% reduction in microbial activity occurs at the well for the low flow rate, while at the higher flow rate a 10% reduction occurs at a radius of 4.5m after 180 days and 6m after 360 days. A 20% reduction in biological activity occurs at a radius of about 2 meters for the high flow rate at 180 days and at 3.5m for 360 days. At the well a reduction of nearly 37% occurs for the higher flow rate.

Figure 1. Temperature profiles for low (20m³/m/day, solid line) and for high (200m³/m/day, dashed line) injection flows.

Lines (a) are for t=180 days while lines (b) are for t=360 days.

Figure 2. Profile of relative biological rate for low (20m³/m/day, solid line) and for high (200m³/m/day, dashed line) injection flows.

Lines (a) are for t=180 days while lines (b) are for t=360 days.

Parameter sensitivity

A sensitivity study was conducted to explore the influence of thermal parameters on model predictions for a typical range in c_ps (0.65 to 0.98 kJ/kg) and a (0.01 to 1.0 meter).The most sensitive parameter, however, was found to be the selected estimation approach for the effective thermal conductivity term, k_m. The use of a volumetrically weighted effective thermal conductivity, i.e., k_m=(1-n)k_s+q_wk_w, has been proposed by previous researchers investigating non-isothermal soil vapor extraction (Lingineni et al., 1991; Kaluarachchi and Islam, 1995). Using a volumetric weighted form in place of an empirical form for k_m, such as EQ(4), can result in dramatically different estimated conductivities for unsaturated systems. These values have been shown to be incorrect for partially-saturated sands (Somerton, 1992). EQ(4) estimates k_m at 1.15W/m/K for the presented simulations. When using a volumetrically weighted k_m based on combining conductivities of dry sand (0.595W/m/K) with water (0.598W/m/K) the overall k_m is 0.61W/m/K. Conversely, if a volumetrically weighted k_m at the same water content is based on combining conductivities of sandstone (4.5 W/m/K) with water the overall k_m is 3.21W/m/K. Plotted in Figure 3 are the different model predictions at the higher flow after 360 days. The higher value of k_m results in a greater smearing of temperature while the lower value of k_m predicts a sharper temperature front, resulting in a greater degree of reduction in biological activity near the well.

Figure 3. Temperature profiles for high (200m³/m/day) injection flow and differing representation of effective thermal conductivity, k_m.

CONCLUSIONS

The non-isothermal bioventing (BV) simulations presented suggest that, depending upon the injected gaseous flow rate, microbiologically significant changes in temperature and moisture content may occur. At flow rates on the very low end of the BV spectrum significant changes are not anticipated. However, at higher flow rates, reduction in biological activity due to advection-induced phase change is potentially significant and of wide radial extent. These simulations indicate that evaporative phase change for BV operations should not be neglected. Note that,

condensation effects created by injection of warm, humid air could serve to raise local soil temperatures and water contents, thus enhancing BV operations.

The sensitivity study indicates that the non-isothermal simulations of BV are very sensitive to the methods of estimation of k_m. A commonly used volumetric weighting approach for estimating effective thermal conductivity leads to dramatically different values for k_m than an empirical approach. These differences are particularly important when dealing with BV injection, due to the relative importance of conduction at low gas fluxes.

ACKNOWLEDGMENTS

Funding was provided by GLMAC for Hazardous Waste Substance Research under Grant R-819605 from the Office of Research and Development, US EPA. Partial funding was also provided by the State of Michigan Department of Environmental Quality. The contents of this publication does not necessarily represent the views of either agency.

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