Analytical Equations of Storage Reservoir Water Quality

Analytical Solutions to Conservative and Non-Conservative Water Quality Constituents in Water Distribution System Storage Tanks

“…In this study, a three-compartment model for conservative material and a twocompartment model for non-conservative material were created using a conceptual picture of the internal reservoir mixing and flow patterns. Discrete volume compartments were used to illustrate these mixing features [16]. In addition, calibration was used to determine the capacity of each compartment.…”

“…For a given period, the inflow and outflow rates were constant. Even though this is not an actual occurrence in WDSs, it was assumed that the given duration corresponded to the time during which either the inflow or outflow was constant [15,16]. The flow rate between compartments was assumed to be constant.…”

“…Some scholars have proposed methods for simulating changes in water quality in pipe distribution networks, assuming that the storage facilities are continuously stirred tank reactors (CSTR) with complete and immediate mixing [13,14]. However, due to the complexity of the hydraulic patterns contained within these facilities, the assumptions may not be applicable in all storage configurations [11,15,16].…”

“…In the last two decades, a multi-compartment modeling approach has been used to assess water quality under the assumption that the interchange between compartments is the primary physical process inherent in storage reservoirs [15,16]. Explicit analytical or numerical solutions have been provided by formulating various configurations in terms of the number of compartments, the arrangement of inlet/outlet, the flow mechanism, or the decaying behavior of the substance [11,13,15,16]. Most simulation problems are solved using numerical methods that give an approximation result.…”

“…It characterizes mixing within storage tanks using four alternative models (full mixing, two-compartment mixing, first-in-first-out (FIFO) plug flow, and last-in-first-out (LIFO) plug flow) [17]. The developed models [15,16] take into consideration five different multi-compartment arrangements-a continuous flow stirred tank, a two-compartment tank, a three-compartment tank, a four-compartment tank, and a plug-flow tank. The turbulent flow patterns within the storage tanks significantly impact the mixing behavior and its implications on water quality.…”