4th International Conference on Engineering for Waste and Biomass Valorization

September 10-13, 2012 – Porto, Portugal

MULTICOMPONENT TRANSPORT PREDICTIONS OF 226RA IN SOIL
FOLLOWING THE USE OF PHOSPHOGYPSUM
M.S. BATALHA1*, C.R. BEZERRA1, D. JACQUES2, M.C. BARBOSA1,E.M. PONTEDEIRO3 and M.TH. VAN GENUCHTEN412

Program of Civil Engineering, COPPE, Federal Univ. of Rio de Janeiro, Brazil
Performance Assessment Unit, Belgian Nuclear Research Centre, SCK-CEN, Mol, Belgium
3Program of Nuclear Engineering, COPPE, Federal Univ. of Rio de Janeiro, Brazil4
Program of Mechanical Engineering, COPPE, Federal Univ. of Rio de Janeiro, Brazil*Corresponding author: marciabatalha.nunes@gmail.com

Keywords: contaminant transport, 226Ra, phosphogypsum, radionuclide transport, vadosezone, groundwater.

Abstract
In this study we provide an analysis of the subsurface transport of radionuclides released from
phosphogypsum (PG) when used as a fertilizer or amendment in agriculture. PG (dihydrated
calcium sulfate), a residue of the phosphate fertilizer industry, can contain relatively highamounts of impurities from the host rock, including heavy metals and radionuclides such as
238
U and especially 226Ra. It is important to assess the environmental risks caused by the longterm use of PG in agricultural operations. The natural uranium and thorium decay chains in
the phosphate host rock are in equilibrium. During the phosphate production process,however, this equilibrium is disrupted and radionuclides migrate to both the fertilizer(especially 238U and 234U) and phosphogypsum (226Ra and 210Pb). Our study focused on thetransport of 226Ra when PG is applied annually to a typical soil profile in the Brazilian
Cerrado. Expected water flow and solute transport processes were estimated first using theHYDRUS-1D software package assuming linear equilibrium transport, followed by similar
simulations using the HP1 multicomponent transport module of HYDRUS-1D. Analyses with
HP1 considered a range of geochemical and physical parameters affecting 226Ra transport inthe vadose zone. We investigated especially the effects of varying calcium concentrations on226
Ra transport, showing that this variable is relatively important when making predictions.
Several aspects related to the modeling approach, such as the use of daily versus monthly
weather data and the influence of assuming different transport regimes in the vadose zone
(e.g., transient versus long-term steady-state flow) are discussed also.

4th International Conference on Engineering for Waste and Biomass Valorization

September 10-13, 2012 – Porto, Portugal

1- INTRODUCTION
Human activities impact the environment in many ways. In attempts to minimize thegeneration of waste, much research is currently being carried out to find new applications forcertain classes of waste. One product often considered a waste is phosphogypsum (PG), a
residue of the phosphate fertilizer industry. PG in many areas is currently being stockpiled inlarge quantities. For each ton of phosphoric acid used to produce fertilizers, about 4.8 ton ofphosphogypsum is being created. At the same time, agricultural operations in many areas,including the Brazilian Cerrado region, could benefit from the use of phosphogypsum as afertilizer or soil amendment. For example, soils in the Cerrado typically are highly weathered,contain an abundance of kaolinite and iron and aluminum oxides, and are often acidic andgenerally low in organic matter as well as in such nutrients as P, Ca and Mg that are containedin PG. Hence, crop production would be improved by regularly using PG in the Cerrado.
Unfortunately, phosphate rock used for the production of phosphate fertilizers often containalso naturally several impurities such as heavy metals, fluoride and radionuclides from theuranium (238U) and thorium (232Th) decay chains. During phosphate production U and Th tend
to concentrate in the fertilizers (approximately 86% of 238U and 70% of 230Th), while radium
tend to concentrate in phosphogypsum (80% of 226Ra and its daughter products) [1]. Detailed
long-term analyses are needed of the environmental factors that influence the retention andtransport of these radionuclides in the subsurface. In this paper we study the transport of 226Ra
present in PG when applied once a year for 27 years to an agricultural soil in the Cerrado,after which its transport in the soil is followed for another 170 years. The HYDRUS-1D flow
and transport simulator [2] was used for this purpose to predict the long-term transport
through the vadose zone to underlying groundwater assuming linear equilibrium transport.
Recent studies [3] suggest that radionuclide transport is affected by a range of interactive
geochemical processes. Hence several simulations were also performed using the HP1
multicomponent module of HYDRUS-1D. This module was obtained by coupling HYDRUS1D with the PHREEQC biochemical code [4]. In this study we were especially concernedwith the possible effect of varying calcium concentrations on 226Ra transport.
2- MATERIALS AND METHODS
The behavior and transport of 226Ra in the subsurface was assessed assuming a finite
homogeneous soil profile (2 m) subject to transient precipitation and evaporation conditions.
Phosphogypsum was assumed to be applied one time annually to the soil surface in the formof a short pulse with known composition. The soil was assumed to be a rigid porous medium,physical and chemically uniform, with no preferential flow and no water and solute uptake byplant roots. Variably-saturated flow was described using the standard Richards equation [2,3]: (h)   h    K ( h)   1  tz  z(1)where z is distance (positive upward), t is time, h is the pressure head, θ is the volumetricwater content, and K(h) is the unsaturated hydraulic conductivity. Radionuclide transport wassimulated initially using the standard linear equilibrium advection-dispersion equation:
( RC )  C  D
 qC   C
tz z

(2)where C is the solution concentration, D is the dispersion coefficient, q is the volumetric fluid
flux, μ is the radionuclide decay coefficient, and R is the retardation factor given by

4th International Conference on Engineering for Waste and Biomass Valorization

September 10-13, 2012 – Porto, Portugal Kd(3)in which b is the soil bulk density and Kd the distribution coefficient for linear sorption.
Multicomponent geochemical transport involving phosphogypsum was represented by asystem of Nm reaction equations for the primary (or master) species, in canonical form given
by Eq.( 4a), and correspondent mass action equations (Eq. 4b) assuming equilibrium:R  1

NmNmKi   i Ci    j C j  ji Aj  Ai ,j 1 ji(4a,b)j 1

where Nm the number of master aqueous species, Ns the number of secondary aqueous species,
Aj and Ai are the chemical equations for the master and secondary species, respectively, ji are
stoichiometric coefficients of the reaction, Ki is the equilibrium constant of a reaction, i is theactivity coefficient of the aqueous complex, and j is the activity coefficient for the jth masterspecies in solution. Transport of each species is represented in this manner by a set of Nm
multicomponent reactive transport equations of the form [3]:Ns
( C j )  C   D j  qC j   R0, j(5a,b)
C j  c j   ji citz zi 1where R0,j is the reaction term representing the sources/sinks for each aqueous component, Cj
is the total concentration of master species j, and ci is the concentration of secondary species i.
For 226Ra sorption we assumed a relatively simple equilibrium approach that lumps all of thesorption processes onto the solid phase into a single linear isotherm in which the distribution
coefficient is a nonlinear function of the calcium concentration:p(6)Kd  Kd 0CCain which Kd is the reference distribution coefficient for 226Ra when the calcium activity is 1,
CCa is the calcium activity in soil solution, and p is an empirical parameter whose value was
fixed at 0.4 as deduced from values presented in EPA Report [5].
Flow boundary conditions at the soil surface were defined by meteorological data (rainfalland temperature) obtained from a weather station in the western part of Minas Gerais state in
Brazil (latitude -17.2511, longitude -46.886) for the period 1982-2005. These values wererepeated many times for the long-term (200 y) simulations. Daily potential evapotranspiration
rates were calculated using the Hargreaves approach. Simulations of the cumulative flux
leaving the bottom of the 2-m soil profile over a 27 year period assuming transient water flow
were used to define the recharge rate (0.152 cm/d) used for the long-term simulations
assuming steady flow. Data of the rainwater composition were taken from Maier et al. [6] andadapted for use in HP1: pH 6.3; 5.59x10-5mol/L of Ca and 6.05x10-5mol/L of Mg. Physicaland chemical parameters of the soil used in our study are those of a typical latosol from
Brazil’s Cerrado. Most of the data were taken from Oliveira [7]. Table 1 lists pertinentchemical parameters. The soil bulk density was taken to be 1.50 g/cm3.

pHP
K+

Chemical Data
5.3
Ca2+
0.0810 mmol/L Mg2+
0.4100 mmol/L Al3+0.500 mmol/L
0.100 mmol/L
0.333 mmol/L

Table 1. Selected soil chemical parameters of the latosol used in this study

4th International Conference on Engineering for Waste and Biomass Valorization

September 10-13, 2012 – Porto, Portugal

Values for the soil hydraulic parameters were estimated from available soil textural data using
pedotransfer functions, which correlate the hydraulic properties with soil texture. The
granulometric composition of the soil was 16% sand, 63% fine sand, 5% silt and 16% clay.
For the pedotransfer functions we used the Rosetta neural network functions of Schaap et al.
[8] as implemented in HYDRUS-1D. For solute transport we used a diffusion coefficient infree water (Dd) of 1.0 cm2/d, while dispersivity (DL) of 20 cm was used for the simulations
involving transient water flow and 30 cm for the steady-state flow regime.
Measurements of 226Ra present in the phosphogypsum were carried out at the Poços de Caldas
Laboratory of the Brazilian Nuclear Energy Commission (CNEN). Results indicated anactivity of 252±26 Bq per kg of PG. For the calculations we assumed an annual PG
application of 1000 kg/ha, applied once a year in the wet season (November). Calculations
produced the following values: 73.45mmol/L of CaSO4 and 3.04x10-13mol/L of 226Ra whenapplied in 1 cm of rainwater for the transient simulations; and 483.22 mmol/L of CaSO4 and20x10-10 mmol/L of 226Ra when considering the constant flow regime with an averaged fluxof 0.152 cm/day. Finally, as initial condition we assumed an unsaturated soil profile having apressure head of -100 cm, and a distribution coefficient (Kd) of 2000 cm3/g. The latter value
was calculated based on data provided by ISAM as described elsewhere [9].
3- RESULTS AND DISCUSSION
Calculated fluxes (evaporation minus precipitation) across the soil surface during the firstnine years of simulation are shown in Figure 1. The plot clearly indicates two main seasons(dry and wet) during the year. The simulations revealed no run-off during the transient
ActualSurface
simulations using daily
weatherdata. Flux
20-2-4-6-8-10-12-140365

730 1095 1460 1825 2190 2555 2920 3285

Time [days]

Figure 1: Calculated net fluxes across the soil surface during the first 9 years of thesimulations (negative fluxes are downwards into the soil profile).

Figures 2 shows calculated cumulative drainage fluxes from the soil profile assuming
transient flow using daily precipitation and evaporation data (left) and monthly averaged
precipitation and evaporation data (right). Slopes of the two plots indicate an average recharge
rate of 0.152 cm/day when using daily weather data, and a nearly 50% lower value of 0.079
cm/d when monthly values are used. This result is important in that it shows that timeaveraging weather data (especially precipitation) can lead to significantly lower estimates of
the recharge rate.

4th International Conference on Engineering for Waste and Biomass Valorization

Cum. BottomFluxSeptember 10-13, 2012 – Porto, Portugal

Cum. BottomFlux

00-100-200-200-400-300

-600

-400

-800-500-1000-600-1200-700

-1400

-800
03285

6570

-16009855

03285

Time [days]

65709855

Time [days]

Figure 2: Calculated cumulative drainage from the soil profile during 27 years using daily weather data (left)\and monthly averaged weather data (right).

Figure 3 compares 226Ra transport assuming transient (Fig. 3a) and steady-state (Fig. 3b)
water flow conditions. Calculations for transient flow were obtained using observed daily
weather data, while the results for steady-state flow assumed a constant long-time average
recharge rate of 0.152 cm/d as deduced from the transient simulations (Fig. 2, left). The twoapproaches agree very well. Since the transient regime produced a slightly more dispersed
contaminant front, we used a higher dispersivity (DL=30 cm) for the steady flux scenario.
These results indicate that long-term simulations can be performed equally well assuming
steady-state water flow rather than transient flow.
Figure 4 presents calculated 226Ra distributions in the soil profile after 27, 100 and 200 years.
Notice the very slow transport rate, with the radionuclide not even reaching a depth of 1 m
after 200 years. The very slow transport is also evident from Figure 5, which shows theamount of 226Ra passing a depth of 40 cm depth. After 27 years of PG application, only
2.35x10-16 mmol/cm2 of 226Ra had passed this depth. Cumulative amounts that leachedbeyond 40 cm depth after 100 and 200 years were 3.58x10-13 and 1.85x10-12 mmol/cm2.
The influence of the calcium concentration on 226Ra transport after 9, 18 and 27 years of PG
application is shown in Figure 6. Results are for a constant distribution coefficient, Kd (left)
and for a Kd that varies as a function of Ca2+ activity (right). Clearly, Ca2+ stemming from thePG application has a major effect on both the transport rate of 226Ra and its solution
concentration. However, this trend is only present initially. Once the PG is no longer applied(after 27 years), calculated 226Ra curves as shown in Figure 6a,b slowly converge to the pointthat after 100 or 200 years they become very similar.
Profile Information: 226Ra Concentr

Profile Information: 226Ra Concentr

Profile Information: 226Ra Concentr

000-5-5-20-10-10-40-15-15-60-20-20-80-25-25-100-30-30-120-35-35-140-40-40-160-45-45-180-50-5003e-006

6e-0069e-006

1.2e-005 1.5e-005-200
03e-006

T1T29e-006

1.2e-005 1.5e-005

03e-006

Conc [1E -10mmol/cm3]

Conc [1E -10mmol/cm3]
T06e-006

T0T3

226

T1T26e-006

9e-006

1.2e-005 1.5e-005

Conc [1E -10mmol/cm3]
T0T3

226

Figure 3a: Calculated Ra
Figure 3b: Calculated Ra
distributions after T0= 0, T1=9, T2=18 distributions after T0= 0, T1=9, T2=18and T3=27 years (transient regime).
and T3=27 years (steady flow).

T1

T2

T3

Figure 4: Calculated 226Ra
distributions after T0= 0, T1=27,
T2=100 and T3=200 years.

4th International Conference on Engineering for Waste and Biomass Valorization
Profile Information: 226Ra Concentr

Cumulative BottomSolute Flux
0.000
(9855;-2.3509e-006)-0.002September 10-13, 2012 – Porto, Portugal
Profile Information: 226Ra Concentr

00-5-5-10-10-0.006-15-15-0.008-20-20-25-25-30-30-35-35-40-40(36500;-0.0038133)-0.004-0.010-0.012-0.014-0.016-45-45-0.018(73000;-0.018469)-0.020018250

36500

54750

73000

Time [days]

226

Figure 5: Total Ra passing a depthof 40 cm after 27, 100 and 200 years

-50

-50
0

1e-0052e-005 3e-005

4e-0055e-005 6e-005

01e-005

2e-005

T1

226

T2T3

Figure 6a: Ra concentrations after
T1= 9, T2=18 and T3=27 years(no influence of Ca+ activity

3e-0054e-0055e-0056e-005

Conc [mol/cm3]

Conc [1E -10mol/cm3]
T1

T2

T3226

Figure 6b: Ra concentrations after
T1= 9, T2=18 and T3=27 years(with influence of Ca+ activity)

4- CONCLUSIONS
Our results indicate that for the assumed long-term transport scenario (200 years and having
relatively low 226Ra activities), steady-state flow conditions can be assumed without
significantly affecting the predictions. Most of the 226Ra remained in the upper 40 cm of thesoil profile. The effect of PG derived calcium was important by decreasing the effective
distribution coefficient of 226Ra, and hence increasing the transport rate. All of the simulationsin this study assumed equilibrium flow and transport. Not considered here are preferential
flow and other non-ideal transport processes (such as colloid-facilitated transport) which
could lead to much higher transport rates. Still, we believe that modeling efforts such as thosein this study using HYDRUS-1D and HP1 are essential for detailed environmental assessmentof the long-term use of phosphogypsum or other naturally occurring radioactive materials(NORMs). They are especially needed for scenarios that cannot be easily monitored overrelatively long time periods.
REFERENCES[1] Mazzili, B., Palmiro, V., Saueia, C., Nisti, M.B.: Radiochemical characterization of Brazilian
phosphogypsum, J. Environ. Radioactivity 40, 113-122 (2000)[2] Šimůnek, J., Šejna, M., Saito, H., Sakai, M., van Genuchten, M.Th.: The HYDRUS-1D Software
Package for Simulating the Movement of Water, Heat, and Multiple Solutes in Variably Saturated
Media, Version 4.0, HYDRUS Software Series 3, Department of Environmental Sciences, Univ. ofCalifornia, Riverside, CA (2008)[3] Jacques, D., Simunek, J., Mallants, D., van Genuchten, M.Th,: Modeling coupled hydrologic
and chemical processes: Long-term uranium transport following phosphorus fertilization,
Vadose Zone J., 7(2), 698-711 (2008)[4] Parkhurst, D.L., Appelo, C.A.J.: User's guide to PHREEQC (Version 2), A computer programfor speciation, batch-reaction, one-dimensional transport, and inverse geochemical
calculations, Water Resources Investigations Report 99-4259, Denver, CO (1999)[5] U.S. Environmental Protection Agency: Understanding Variation in Partition Coefficient, Kd,Values. Vol III, EPA 402-R-04_002C, EPA, Washington,DC (2004)[6] Maier, M.H., Takino, M., Miyamaru, L.L.: Alguns aspectos da composição da água da chuva,
Acta Limnol.Brasil., IV, 247-254, Brazil (1992)[7] Oliveira, K.A.P.: Aplicação do fosfogesso na agricultura do Cerrado e suas implicaçõesradiológicas, Dissertação de Mestrado, CDTN/CNEN, Belo Horizonte, MG, Brazil (2008)[8] Schaap, M.G., Leij, F.J., van Genuchten, M.Th.: Neural network analysis for hierarchicalprediction of soil hydraulic properties, Soil Sci. Soc. Am. J., 62, 847-855 (1998)[9] Batalha, M.S.: Transporte Multicomponente dos Contaminantes Liberados no Ambiente pela
Aplicação de Fosfogesso, Dissertação de Mestrado em Engenharia Mecânica, COPPE/UFRJ,
Rio de Janeiro, RJ, Brazil (2011)