CONCEPTUAL MODEL AND MODEL GRID
A loamy sand tillage plot typically in arid regions of northwest China is considered for the present study. The irrigation rate from each nozzle is assumed to be 6.94×10-4kg/s·m2 for the base case (C0; cf. Table 1) and the infiltration presumably occurs with the same rate, given that the soil is mostly dry in arid environment. The irrigation is delivered using a sprinkling irrigation system, with the nozzles having spraying radius of 0.1 m and horizontal spacing of 0.3 m. The irrigation water is assumed to be uniformly applied to the surface of the entire circular area. Although there is supposed to be 38 nozzles in a length of 11.2 m in reality, only 3 nozzles are considered in the model domain for simplicity, as illustrated in Fig. 1. The VWCs for each depth interval of 0.1 m inside the block of interest (BOI) are calculated for analysis based on the numerical simulations.
The numerical code TOUGH2/EOS3 was chosen to simulate the processes of soil imbibitions under infiltration induced by irrigation, as well as of water redistribution due to drainage in the irrigation intermittence. The lateral range and the depth of the model geometry are 11.2 m and 2.1 m, respectively (Fig. 1). The grid size ranges in horizontal from 0.1 m close to the nozzle gradually up to 0.4 m at the periphery. The grid refining interval is roughly between 480 and 660 cm of the X coordinate, particularly in the vicinity of 0.3 m of the nozzles. The resulting mesh has 800 elements and 2170 connections.
Since TOUGH2/EOS3 uses phase saturation as output, liquid saturation, approximately equal to water saturation Sw , is converted in some cases to VWC using the following formulation:
VWC = Sw ·ϕ (4)
The intrinsic permeability required for the current simulator is calculated with the following formulation, since only the measurement of saturated hydraulic conductivity ks is available in the previous studies (Wang, 2013; Li, 2014).
\(K_{h}=\frac{\mu k_{s}}{\text{ρg}}\) (5)
Here, Kh denotes horizontal intrinsic permeability [m2], μ is dynamic viscosity [Pa·s], and the others are found in the above text.
Figure1. Grid design of the model.