Download Dynamic model for the disinfection process

Numerical prediction of the reaction rate constant of chlorine
disinfection process at a wastewater treatment plant.
Experimental model validation and simulation studies
Feridun DEMIR
Department of Chemical Engineering, Osmaniye Korkut Ata University,
Osmaniye 80000, Turkey
3rd World Congress on Petrochemistry and Chemical Engineering,
November 30 – December 2, 2015
Atlanta, USA
Outline
• Objectives
• Process description
• Water Reclamation Facility
• Kinetics of chlorine with ammonia and chlorine disinfection
• Modeling challenges
• Complex reactions with ammonia
• Too many partial differential equations (PDEs)
• Dynamic behavior of wastewater
• Dynamic model development
• Approach (Mathematical transformation techniques)
• Method of characteristics
• Odometric transformation
• Simulation results
• Model validation
Objectives
• Develop and validate a model for the entire chlorine
disinfection process of wastewater treatment plant
• Overcome PDEs of chlorine reactions that occur with
wastewater using the method of characteristics
• Overcome the highly variable flow rate using Odometric
transformation
• Overcome large and variable ˝ Time Delays ˝ that occur as a
result of the transport time required for the wastewater to
flow through contact basins
• Numerically determine the reaction rate constant for the
entire disinfection process
Process description
• Kanapaha Water Reclamation Facility is an advanced wastewater
treatment plant in Gainesville, Florida, and uses chlorine for
disinfection.
• Treats 14.9 million gallon wastewater to drinking water standards
per day, and then reuses the water for innovative irrigation.
• Performs the disinfection process in two chlorine contact basins that
are open to the atmosphere
Process description
• A schematic representation of the disinfection process
Sampling points for the chlorine measurements
Process description
Water parameters of the KWRF at the chlorine contact basin
Water parameters
pH
≈7
Water temperature (°C)
≈ 27
Conductivity (µmhos/cm)
≈ 500
Dissolved oxygen (mg/L O2)
≈ 3.5
Average Total suspended solids (mg/L)
= 0.367
Average total chlorine residual in the effluent (mg/L) = 2.8
Chlorine-ammonia breakpoint reactions
Chlorine chemistry
Cl2 + H2O→ HOCl + HCl
HOCl ↔ OClˉ + H+
Breakpoint reactions
pH dependent
Reaction kinetics
• Proposed kinetics equations at a wastewater reclamation
plant
rHOCL  k1 [NH 3 ][HOCl]  k2 [NH 2 Cl]  k3 [NH 2 Cl][HOCl]  k4 [NHCl2 ]
k5 [NHCl2 ][HOCl]  k6 [NCl3 ]  kDi sin fection [HOCl]
rNH3  k1 [NH3 ][HOCl]  k2 [NH 2Cl]  k7 [NH 2Cl] 2  k8 [NHCl2 ][NH3 ]
rNH2CI  k1 [NH 3 ][HOCl]  k2 [NH 2 Cl]  k3 [NH 2 Cl][HOCl]  k4 [NHCl2 ]  k7 [NH 2 Cl] 2
k8 [NHCl2 ][NH 3 ]
rNHCI2  k3 [NH 2 Cl][HOCl]  k4 [NHCl2 ]  k5 [NHCl2 ][HOCl]  k6 [NCl3 ]  k7 [NH 2 Cl] 2
k8 [NHCl2 ][NH 3 ]
rNCI3  k5 [NHCl2 ][HOCl]  k6 [NCl3 ]
•
represents the rate constant for the entire disinfection
process in the contact basin
kDisinfection
Modeling challenges
• Too long disinfection contact basin ( ≈ 200 m)
• Significant flow rate changes relative to daily water usage and
thereby large and variable ˝ Time Delays ˝
• Quality changes in wastewater
• Exposure of water to sunlight
• Complex reactions with ammonia
• Many partial differential equations and the difficulties of their
solution
• Difficulty to develop an appropriate dynamic model for the
process system
Development of simulation model
Disinfection contact basin
Dynamic model for the disinfection process
Assumptions: Plug flow reactor, no diffusion exists along the reactor
Influent
Effluent
ci
ci
 v(t)
 ri ct,z 
t
z
Transformation techniques
Overcome PDEs of chlorine reactions using the method of
characteristics
P
z
z
 Q  R(x, y)
x
y
Q
θ  tan 1  
P
x  r  s  cosθ 
y  s  sin  θ 
z x,y  z  x  y cot θ   
y cos ec θ 
0
Rx  y cot θ   s  cosθ ,s  sin θ 
ds 
P2  Q2
Transformation techniques
• Overcome the highly variable flow rate, and thereby ˝ Time Delays ˝
using Odometric Transformation ()
•  is the cumulative distance travelled by wastewater in the contact
basin
• This new variable replaces time with 
β
 v(t)
t
t
   0   v(t )dt
0
Applying transformation techniques
• First-order partial differential equations (PDEs) with variable Time
Delays
ci
ci
 v(t)
 ri ct,z 
t
z
• First-order ordinary differential equations (ODEs) with constant
Time delays

σ σ 
ci  β 
,

 
1
1
σ σ 
2 2


ri  c β 
,
 
σ
σ   
2 
2 2 
v β 

2

• Use of the transformation techniques produced efficient ODEs for
numerical integration
Simulation of the model
• The model was coded in Matlab programing language
• A step change in the chlorine dosing was performed at the
chlorine injection point, and its effect was observed along the
entire contact basin
• The chlorine concentrations used for the simulation and model
validation were measured online at the chlorine injection point
and at the effluent, and recorded approximately for 8 hours
• The flow rate of the wastewater was obtained online, and
recorded during the investigation
• To fit the simulation results to the experimental data, various
trial values of kDisinfection were used in the simulation model
changing from 0.006 to 0.0085 h-1
Comparison of results
Comparison of the simulation results with experimental measurements
10
Conc. of HOCl (ppm)
8
6
4
2
200
300
400
Time (minutes)
Chlorine concentration at
•
•
•
the chlorine injection point (red dashed line)
the effluent (blue solid line)
the simulated results (black circles)
500
600
Model validation
• To determine the kDisinfection more precisely, model validation was
performed
• The model was validated by the comparison of the simulated
responses with the experimentally measured chlorine concentrations
using Matlab software packages (2013b)
• The Matlab codes:
Experimental_Results = iddata(y,[ ],Ts)
Simulation_Results = iddata(sys,[ ],Ts)
Ts = 120
compare(Experimental_Results,Simulation_Results)
compare(Experimental_results, k_006,'--b', k_0065,'--g', k_007,'-r', k_0071, '--c')
Model validation
Comparison of the simulated responses with the experimental measurements
k Disinfection = 0.006 h-1, k Disinfection = 0.0065 h-1, k Disinfection = 0.007 h-1, k Disinfection = 0.0071 h-1
Model validation
Comparison of the simulated responses with the experimental measurements
k Disinfection = 0.0072 h-1, k Disinfection = 0.0073 h-1, k Disinfection = 0.0074 h-1, k Disinfection = 0.0075 h-1
Model validation
Comparison of the simulated responses with the experimental measurements
k Disinfection = 0.0076 h-1, k Disinfection = 0.0077 h-1, k Disinfection = 0.0078 h-1, k Disinfection = 0.008 h-1
Fit (%) for the various reaction rate constants
Reaction rate constant , k Disinfection (h-1)
Fit, (%)
6x10-3
-56.5
6.5x10-3
-14.68
7x10-3
15.46
7.1x10-3
19.25
7.2x10-3
22.06
7.3x10-3
23.83
7.4x10-3
24.52
7.5x10-3
24.13
7.6x10-3
22.7
7.7x10-3
20.33
7.8x10-3
17.12
8x10-3
8.665
The results suggest that the value of 0.0074 h-1 yields the highest fit (%)
Conclusions
• The joint application of the transformation techniques
• successfully transformed the dynamics of the system into the ODE
models with constant time delay
• made the solution of the resulting equations numerically feasible
• The numerical solutions of the resulting equations
• were validated using Matlab software packages
• provided the highest fit (%) value for different trial values of reaction
rate constant
• According to the simulation results;
• kDisinfection was found to be 0.0074 h-1 , and confirmed by the
experimental data
• first-order kinetic model is able to describe chlorine consumption by
microorganisms in the ammonia-free part of the contact basin.