Arsenic Retention on Technosols Prepared with Nanoparticles and Ferric Soil from Mine Drainage Water

Table 1

Variables used for the formulation of the model, including the equations, and the determination or estimation methods.

	Variables	Equation/determination or estimation method
Stocks	As free (mg·As)	= MAX (Water discharge − soil sorption − nanosorption, 0)^1
	As sorbed (mg·As)	= soil sorption + nanosorption
Flows	Water discharge (mg·As/h)	= discharge inflow · As concentration · PULSE TRAIN (INITIAL TIME, 72, 168, FINAL TIME)^2
	Soil sorption (mg·As/h)	^3
	Nano(particles) sorption (mg·As/h)	^3
Auxiliary	Time	Time of the simulation
	Initial time	0 h (initial time of the simulation)
	Final time	672 h (final time of the simulation)
	As concentration	4.5 mg/L (determination by AAS in real water discharge)
	Discharge inflow	3 L/h (field observation)
	Qmax soil/nano; Ksoil/nano^4	Estimated from laboratory sorption experiments with soil and nanoparticles
	Soil mass^5	5 kg (estimated from laboratory experiments)
	Nano(particles) mass^5	0.025 kg (estimated from laboratory experiments)
	Discharge time	72 h (field observation)

¹The function MAX of Vensim allows us to have a concentration of As free which is always positive or 0 (never negative). ²The function PULSE TRAIN returns 1 value (presence of contaminated water discharge), starting at “INITIAL TIME” and ending at “FINAL TIME,” for 72 h, each 168 h. The rest of the time, it returns a value of 0 (absence of contaminated water discharge). ³The function DELAY1 returns a first order exponential delay of the adsorption on soil and nanoparticles during the residence time. These equations correspond to the derivation of Langmuir equations with respect to time. The second fraction of the equation is used to adjust the units. ⁴Q_max and K of soil and nanoparticles where the parameters calculated using the experiments included in this work. ⁵The ratio of mass of soil and nanoparticles corresponded to that used in the laboratory experimentation used in this work.