2.1. Fugacity approach

The Level III fugacity model (FUGIII) includes processes of evaporation or volatilization to atmosphere, leaching via percolating water into groundwater, advection, diffusion, and degradation (or loss). The model assumes first-order kinetics for all reactions, a linear function of all movements, and local equilibrium between compartments. FUGIII will estimate concentrations (C_i) of the substance (manure NH₃-N) in air, water, soil, and rice plant compartment systems as a function of fugacity f_i and fugacity capacity Z_i at the steady state condition of a mass balance equation given by C_i=f_iZ_i, where C_i is the concentration of chemical substance (mol/m³), fi is the fugacity (Pa), and Z_i is the capacity of fugacity or the proportionality constant (mol/m³·Pa). FUGIII deals with the distribution in a small quantity of a chemical substance between two compartments, i and j, under constant temperature and pressure, and non-equilibrium fugacity (f₁ ≠ f₂ ≠ f₃ ≠ …… ≠ f_n) in producing constant concentration ratio between two compartments, the partition coefficient k_ij defined as k_ij = C_i/C_j, where, C_i and C_j are the substance concentration in each compartment i and j respectively. The substance tends to accumulate in compartments depending upon the capacity of fugacity, which describes the affinity of the substance for the compartment. Thus, the fugacity capacity of each compartment has to be defined as considering the physicochemical properties of the substance for each compartment.

2.2. Governing equation

The rice-cropping system was modeled for air (i = a = 1), water (i = w = 2), soil (i = s = 3), and rice plant (i = r = 4) compartments. Since the model assumes the mass transfer of substance occurs from air to water and rice plants, from water to air and soil, from rice plants to air and soil and from soil to water and rice plants, governing equation for the mass balance of the substance is written by Eq.1. Table 1 presents a summary of mass balance equations in each compartment.

Considering the steady state condition,

where Input term I_i is emission E_i in each compartment i, mol/hr, Advection term N_i is mass flux by advection in compartment i, mol/hr, Diffusion term N_ij is mass flux by diffusion in compartment i, mol/hr, where D_ij is related to interfacial area A_ij, fugacity capacity Z_i and Z_j, and mass transfer coefficient k_i and k_j in Table 2. Loss term L_i is all mass fluxes by all removal processes such as reactions, deposition, runoff, leaching, uptake, litter fall, plant growth, and so on. However the removal process in this study is considered only leaching, uptake, litter fall, and plant growth, and a removal term with the approximate value, which is added instead of the deposition and runoff processes.

The advection term considers only vertical transport in this case. The mass flux by advection in the compartment i is regarded as the linear process with a constant speed and expressed by G_i(C_Bi-C_i), where G_i (m³/h) is the matter flow, C_Bi is the concentration entering compartment i and C_i is the concentration leaving the compartment. The advection inflow (G_AiC_Bi) is dealing with mass flow rate G_Ai and initial concentration in each compartment (C_Bi). Advection outflow (D_Ai) term is leaving from air and entering into water, leaving water and entering soil, and leaving from soil to groundwater. If i=2, dissolved components in water are leaving from water and entering into soil. The advection outflow (D_Ai) leaching from soil is expressed by vertical transport velocity U. The transfer coefficient by diffusion, D-value, (D_ij, mol/h·Pa) between two compartments i and j is estimated by the expressions as shown in Table 2. In Table 2, the substance in the compartments can be also transformed by chemical reaction, biological degradation, dilution of the rice plant growth, and water variation volume in rice fields (^{Hu et al., 2013}) and all reactions are assumed as first-order kinetics and reaction rate coefficients λ_i are determined by the half-life of the substance in compartment i, tⁱ_1/2; λ_i = ln(2)/tⁱ_1/2. The fugacity capacity and diffusivity for each one of these compartments and all removal processes are defined and summarized in Table 2. Further details for each term in Table 2 can be referred to literatures (^{Cousins and Mackay, 2000}; ^{Cousins and Mackay, 2001}; ^{MacKay, 1991}).

2.3. Model parameters

Nitrogen components in manure includes nitrogen gas (N₂), organic-nitrogen (Org-N), and inorganic-nitrogen such as ammoniacal nitrogen (NH₄⁺-N or NH₃-N), nitrite nitrogen (NO₂^--N), and nitrate nitrogen (NO₃^--N) with changing types in the nitrogen cycle process. To understand N-balance in liquid manure, N-balance model theory for Urea has been adopted from ^{Chowdary et al. (2004)} as shown in Fig. 1.

Fig. 1. Schematic representation of nitrogen balance model with reaction constants.

For the model simulation, NH₃-N among N components in manure is chosen and the mechanisms of NH₃-N in manure have been applied to simulate the fate of N components in environmental media (air, water, soil, and rice plants) during rice cropping as shown in Fig. 2. As shown in Fig. 2, crops imbibe lots of nutrients from the soil. Nitrogen, mainly inorganic-N such as NH₄⁺-N and NO₃^--N, is imbibed the most among those nutrients. Rice crops absorb NH₄⁺-N well. It is not that the rice crops don't imbibe NO₃^--N but that NO₃^--N has less chance to get the effect as the manure because it is denitrified mostly in the rice field. Rice cropping occurs with water in the rice field and it provides the best advantage, productive stability by the water supply. In a submerged condition, root environment of the rice plant becomes a reduced state of soil.

Fig. 2. Schematic representation of the N-transformations in flooded rice field.

Passing 1-2 weeks in the submerged condition, the water body in the rice field is divided into two layers, an oxidized layer or a floodwater zone with oxygen-rich water and a reduced layer or an aerobic zone with oxygen-poor water and the soil becomes an anaerobic zone saturated with water. Sometimes, the aerobic zone is thin enough to be ignored. In Fig.1, the reactions and reaction constants or their half-life in three zones are presented when applying quick-acting nitrogen liquid manure as basic manure in the rice field. In the floodwater zone and the aerobic zone, NH₃-N(aq) in manure are transformed by hydrolysis to produce NH₄⁺-N, volatilization to emit NH₃(g), and nitrification to generate NO₃^--N. The denitrification process is very important when the soil is saturated with water because the microorganisms of the denitrification process act only in waterlogged soil without oxygen in the anaerobic layer.

The reactions progressed in the saturated anaerobic zone with water include denitrifcation of NO₃^--N to produce N₂O and N₂(g) into atmosphere and leaching of NO₃^--N into groundwater, mineralization to covert Organic-N into NH₄⁺-N and immobilization to reduce NH₄⁺-N to form Organic-N in the soil. Also, uptake of NH₄⁺-N by rice plants roots is occurred around 30-40% of N. The losses of N are mainly caused by leaching into the groundwater and by release of N₂ gas into atmosphere by the denitrification process with frequent rainfall during late springtime and early summertime. The denitrification progresses regardless of the manure and fertilizer or source of NO₃^--N such as degradation. Also, other factors of the denitrification acceleration includes crop residue to be used as a carbon source, warm soil, pH (neutral to alkalinity), and so on.

Table 3 contains significant parameters to calculate terms in mass balance equations as shown in Table 1 and Table 2. Values of parameters are taken from references marked in Table 3.

2.4. Simulation condition

Physio-chemical properties of NH₃-N in manure are important to run FUGIII and they are indicated in Table 4. Ammonia is in its pure gaseous state and also commercially or commonly available in an aqueous solution about 28– 30% NH₃, which is almost saturated in water (^{Weast et al., 1988}). Liquid manure used in this study contains 0.19% total nitrogen (TN) and 29.8% aqueous NH₃-N of TN and 15.6% gaseous NH₃ of TN. The temperature for simulation was 25°C (298°K). Also Table 4 and Table 5 present important input parameters for the model simulation. Table 5 includes major parameters to run the simulation.

3.1. Fugacity Capacity

The model simulation estimated capacity of fugacity Z_i, fugacity F_i for non-equilibrium each other (i.e., F₁ ≠ F₂ ≠ F₃ ≠ F₄), and concentration C_i in each compartment i (i = 1 ~ 4 for air, water, soil, and rice plants). Capacity of fugacity in each compartment, Z_i, was calculated as a function of partition coefficient between compartments i and j, and physicochemical property of the substance NH₃ and compartments (air, water, soil and rice plants). Z_i is not time dependent so Z_i of NH₃ for each compartment is constant with time changes. Z₁ is valued as 4.04 × 10^-4 mol/m³·Pa for air, Z₂ is 1.04 × 10^-1 mol/m³·Pa for water, Z₃ is 1.894 × 10^-2 mol/m³·Pa for soil, and Z₄ is 9.19 × 10^-2 mol/m³·Pa for rice plants. As shown in Fig. 3, water compartment (Z₂) took 48.3%, next was the rice plant compartment (Z₄) with 42.7%, soil compartment had little about 8.8% (Z₃), and the minimum value was found in the air compartment (Z₁) less than 0.2%.

Fig. 3. Content of fugacity capacityZiin each compartment resulted from the model simulation. The values ofZiare 0.2% for air Z1, 48.3% for water Z2, 8.8% for soil Z3 and 42.7% for rice plant Z4.

3.2. Variation of Fugacity and Concentration

During all simulations, the same amount of emission was used but emission rates were different depending upon different detention times. Fugacity and concentration for all compartments except the rice plant compartment were decreased linearly with the detention time change in the log-log graph but those for the rice plant compartment were performed nonlinearly in the log-log graph. Fig. 4 and Fig. 5 present the log-log graph between fugacity and different detention times in (a) and between concentration and different detention times in (b). The detention times were applied from 1 hour to 20 days with one time emission of manure initially. Fig. 4 is the case that the value of other removal term is same as that of uptake from soil, R_others = RSF, and Fig. 5 is the case that the removal term for the rice plant compartment is ignored, R_others = 0. In Fig. 4(a) and Fig. 5(a), fugacity values from the highest to the lowest were found in air, water, soil, and rice plant compartment orderly until 2 days and 1 day respectively. After that day, fugacity in soil (F3) was lower than fugacity in rice plant (F4).

Fig. 4. Changes of Fugacity and concentration in each compartment for different detention times from 1hour to 20 days.

Fig. 5. Changes of Fugacity and concentration in each compartment for different detention times from 1hour to 20 days when the removal process in the rice plants was ignored.

Unlike the fugacity, the highest concentration was determined in water, next was in soil and rice plant, and air detected the lowest values in Fig. 4(b) and Fig. 5(b). Concentrations between soil and rice plants were exchanged after 0.15 days and the concentration in rice plants was greater than the concentration in the soil and closed to the concentration of water with time increase, and the most concentration of NH₃ was remained in the water compartment in Fig. 4(b) but in Fig. 5(b) the rice plants took NH₃-N mostly after 7 days. As shown in Fig. 4 and Fig. 5, changes of fugacity and concentration in the rice plants were depending on the removal term considerably.

3.3. Mass Balance

Fig. 6 shows the mass balance with values for all processes of the model equation graphically. Units of all values in Fig. 6 were [mol/hr] and the values between gain and loss for each compartment were matched well. In the compartment of air, the gain was from emission and diffusion from water to air, and the loss was caused by the diffusion from air to water and transformation in the compartment. The water compartment was mostly affected by emission and diffusion from air to water for the gain and by transformation and diffusion from water to air for the loss. The mass in the soil compartment was balanced with the gain from diffusion from water to soil and the loss from transformation and diffusion from soil to water. The rice plants were gained by uptake of NH₃-N from the soil and lost by diffusion from rice plants to air and by removal processes. The removal processes in the rice plants were not described in details but assumed the same value of uptake from soil.

Fig. 6. Graphical representation of mass balance (mol/hr) in and between compartments.

The analysis of mass balance using Level III shown in Figure 6 can yield considerably realistic results. It can scientifically identify, quantify, and diagnose the fate of nutrients in agricultural land, the description of fate mechanism, and the analysis of mass balance, thereby preventing the excessive use of liquid manure, and inducing natural-friendly agriculture. Based on the model studying, the fate of nutrients in liquid manure in the environmental media can be understood. It can be applied to create accurate inventory for liquid manure, to control total amount of nutrients for plant growth, to quantify and minimize the nonpoint pollutants, and to quantify the pollution load affected on water quality adversely.