Clean Technologies and Environmental Policy

, Volume 19, Issue 3, pp 823–844 | Cite as

An optimization approach for the sustainable water management at macroscopic level accounting for the surrounding watershed

  • Esbeydi Villicaña-García
  • José María Ponce-Ortega
Article

Abstract

Water is one of the most important resources in the world because it is essential for the life. Recently, several strategies for the proper use of water in different sectors (industrial, agricultural and domestic) have been ported, which involve options such as recycling, reusing and regeneration. However, the overall water management in a macroscopic level has received lower attention. In the macroscopic level, numerous water uses are involved and several sources of freshwater can interact to satisfy the freshwater demands, where also recycling, reusing and regeneration strategies can be implemented. Therefore, in this paper is proposed a new optimization formulation for the proper use of water in a macroscopic level involving water recycling, reusing and regeneration as well as accounting for the impact in the surrounding watershed. A case study from the central-west part of Mexico was analyzed, and the results show that is possible to reduce the freshwater consumption by 21 % with an investment of US $686,510,000/year.

Keywords

Water management Rainwater harvesting Optimization Recycling Reuse 

Abbreviations

Acronyms (superscripts)

A, agri

Agriculture

bw

Black water

cap

Capacity

D

Direct discharges

G, gar

Gardening

GW

Greywater

H

Residential discharges

I

Industrial

In

Inlet

L

Loses

Out

Outlet

p

Precipitation

R, res

Residential

t

Treated flowrate

tbw

Treated black water

tgw

Treated greywater

tww

Treated wastewater

U

Uses

ww

Wastewater

Variables

\(A^{{}}\)

Conditioned area for rainwater harvesting

\({\text{BW}}^{\text{res}}\)

Flowrate for treated black water from the residential sector

Cost

Cost

fcap

Capacity for piping

F, f

Flowrate

GW

Flowrate for the treating greywater

Qr,t

Outlet water from the reach r over the time period t

TAC

Total annual cost

TotFresh

Total freshwater flowrate

S

Flowrate for the stored water

\({\text{TBW}}_{t}^{\text{discharge}}\)

Flowrate for treated black water that is sent to discharge into different reaches of a river over the time period t

\({\text{tbw}}_{{{\text{r}},t}}^{\text{discharge-reach}}\)

Flowrate for treated black water that is distributed to any reach r over the time period t

tgw

Flowrate from treated greywater for residential sector that is reclaimed

\({\text{TGW}}_{t}^{\text{discharge}}\)

Flowrate for treated greywater that is discharged into different reaches of a river over the time period t

\({\text{tww}}_{{{\text{r}},t}}^{\text{discharge-reach}}\)

Flowrate for treated industrial wastewater that is distributed to any reach r over the time period t

\({\text{TWW}}_{t}^{\text{industry}}\)

Flowrate for treated wastewater for the industrial sector that is available for a further use over the time period t

\(V_{{{\text{r}},t}}\)

Uses of any reach r over the time period t

\(U_{{{\text{r}},{\text{trib}},t}}\)

Flowrate discharged from tributary uses trib to the reach r over the time period t

WWind

Flowrate for the treating wastewater from the industrial sector

\(X_{{c,{\text{r}},t}}^{\text{reach}}\)

Composition of the outlet water of a pollutant c of any reach r over the time period t

\(k_{c} (X_{{c,{\text{r}},t}}^{\text{reach}} )^{{\sigma_{c} }}\)

Reactive term to account for the chemical and biochemical reactions that take place in the reach

Parameters

\(a^{\text{A}}\)

Unit fixed cost for area to rainwater harvesting

\(A^{\text{MAX}}\)

Maximum available area

\(a^{\text{t}}\)

Unit fixed cost for treating water

\(a^{\text{S}}\)

Unit fixed cost for storing to rainwater harvesting

\({\text{ap}}\)

Unit fixed cost for piping from a source to a sink

\(b^{\text{A}}\)

Unit variable cost for area for rainwater harvesting

\(b^{\text{t}}\)

Unit variable cost for treating wastewater

\(b^{\text{S}}\)

Unit variable cost for storing harvested rainwater

\({\text{BW}}^{\text{MAX}}\)

Maximum capacity available for the treatment unit for black water

\({\text{bp}}\)

Unit variable cost for piping from a source to a sink

\(C\)

Exponent to take into account the economies of scale

\(D_{{{\text{r,}}t}}\)

Direct discharges of any reach r over the time period t

\(F\)

Flowrate needed for different purposes

\(f^{\text{MAX}}\)

Maximum capacity available for the pipe segment from a source to a sink

\({\text{FT}}_{{{\text{r,trib,}}t}}\)

Flowrate of discharges from tributaries trib of any reach r over the time period t

\({\text{GW}}^{\text{MAX}}\)

Maximum capacity available for treatment units for greywater

\(H_{{{\text{r,}}t}}\)

Residential discharges to any reach r over the time period t

\(I_{{{\text{r,trib,}}t}}\)

Flowrate discharged from industries to tributary trib of the reach r over the time period t

\(k_{\text{F}}\)

Factor used to annualize the inversion

\(L_{{{\text{r,}}t}}\)

Loses to any reach r over the time period t

\(P_{{{\text{r}},t}}\)

Precipitation from the reach r over the time period t

\(R_{t}\)

Factor of precipitation over the time period t

\(S^{\text{S-MAX}}\)

Maximum available capacity for the storage device

\(S\)

Flowrate discharged

\(UC\)

Cost of water from a fresh source

\(UPC\)

Operating cost for piping from a pond to a sink

\(URC\)

Operating cost for piping from rainwater harvesting to a sink

\({\text{UTBWC}}_{{{\text{r,}}t}}^{\text{discharge-reach}}\)

Operating cost for piping from treated black water to discharge at any reach r over the time period t

\(UTGWC\)

Operating cost for piping from treated greywater to a sink

\(UTWWC\)

Operating cost for piping from treated industrial wastewater to a sink

\(UWC\)

Operating cost for piping from well w to a sink

\({\text{VC}}^{\text{t}}\)

Operating cost for treating water

\({\text{WW}}^{\text{MAX}}\)

Maximum capacity available for treatment units for industrial wastewater

\(X\)

Composition of the pollutant

\({\text{X}}_{c}^{\text{reach-mx}}\)

Maximum composition of the outlet water of a pollutant c

\({\text{X}}_{{c , {\text{r,trib,}}t}}^{{S^{u} }}\)

Composition of the pollutant c in untreated flowrate for any tributary trib, for any reach r over the time period t

Binary variables

y

Binary variable to activate the existence for a harvesting rainwater area (A), treatment units (t), pipe section (p) and storage units (S)

Greek symbols

\(\alpha\)

Fraction that is associated with water lost through a sector

\(\beta\)

Fraction of water that can be treated for a future use

Sets

C

Set for different pollutants in the river (c|c = 1, …, C)

P

Set for available ponds (p|p = 1, …, P)

R

Set for available reaches (r|r = 1, …, R)

T

Set for time periods in years (t|t = 1, …, T)

TRIB

Set for the tributaries in the river (trib|trib = 1, …, TRIB)

W

Set for available wells (w|w = 1, …, W)

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Chemical Engineering DepartmentUniversidad Michoacana de San Nicolás de HidalgoMoreliaMexico

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