. 2024 Mar 22;12:1380213. doi: 10.3389/fbioe.2024.1380213

TABLE 4.

Setting of boundary conditions for numerical simulation.

Stage	Bacterial solution	Retention	Cementation solution
Upper boundary of sand column
q ^w	$q_{i n 1}^{w}$		$q_{i n 2}^{w}$
P _l		P _atm
C ^bacl	C0_{_} bact	$(D \cdot n \nabla C) \cdot n = 0$	$(D \cdot n \nabla C) \cdot n = 0$
C ^urea	$(D \cdot n \nabla C) \cdot n = 0$	$(D \cdot n \nabla C) \cdot n = 0$	$C_{0}^{u r e a}$
$C^{{C a}^{2 +}}$	$(D \cdot n \nabla C) \cdot n = 0$	$(D \cdot n \nabla C) \cdot n = 0$	$C_{0}^{{C a}^{2 +}}$
$C^{{N H}_{4}^{+}}$	$(D \cdot n \nabla C) \cdot n = 0$	$(D \cdot n \nabla C) \cdot n = 0$	$C_{0}^{{N H}_{4}^{+}}$
Lower boundary of sand column
q ^w
P _l	P _atm		P _atm
C ^bacl	$(D \cdot n \nabla C) \cdot n = 0$	$(D \cdot n \nabla C) \cdot n = 0$	$(D \cdot n \nabla C) \cdot n = 0$
C ^urea	$(D \cdot n \nabla C) \cdot n = 0$	$(D \cdot n \nabla C) \cdot n = 0$	$(D \cdot n \nabla C) \cdot n = 0$
$C^{{C a}^{2 +}}$	$(D \cdot n \nabla C) \cdot n = 0$	$(D \cdot n \nabla C) \cdot n = 0$	$(D \cdot n \nabla C) \cdot n = 0$
$C^{{N H}_{4}^{+}}$	$(D \cdot n \nabla C) \cdot n = 0$	$(D \cdot n \nabla C) \cdot n = 0$	$(D \cdot n \nabla C) \cdot n = 0$