1. Water Management in a Petroleum Refinery
by: Amy Frink, Timilehin Kehinde, and Brian Sellers

2. Background
In refineries, water is a crucial part in removal of contaminants from crude oil
Desalting
Steam cracking
Sweetening
Hydrotreating
Distillation
Crude fractionation unit

3. Background Water re-use as a practical way to reduce freshwater intake
Reduces wastewater treatment costs
Lessens need to comply with government standards for pollution levels
Relieves need to obtain larger amounts of freshwater (costly and limited)
Promotes a greener environment

4. Goals
Mathematical programming becoming main approach to solving water allocation problem
Optimize stream placement between water-using and wastewater treatment processes by performing mass and contaminant balances
Current methods rely on assumption of fixed outlet concentrations
However, outlet concentration has shown to be a function of pressure, temperature, Cin, etc.

5. Refinery Schematic Highlights water-using and regeneration processes
Red: Water-using units
Green: Conventional water regeneration processes (i.e. end-of-pipe treatment)

6. Water Treatment Units Regeneration processes* Regeneration process
Type of contaminant removed
Maximum outlet concentration (ppm)
API Separator
Organics 50
Activated Carbon Adsorption
Reverse Osmosis
Salts 20
Chevron Waste Water Treatment
H2S
NH3 5 30
Biological Treatment
230
*Typical refinery standards

7. API Separator API separator
Separates suspended solids and oil from wastewater streams based on differences in specific gravities between the oil and the wastewater
Particles settle based on Stokes Law

8. API Separator
Contaminant particles fall through the viscous fluid by their own weight
Upward drag of small particles (assumed to be spheres) combines with the buoyancy force balances the gravitational force and creates a settling velocity
Buoyancy force
Gravity
Drag force

9. Chevron Wastewater Treatment
Sour water containing H2S and NH3 enter into a hydrogen sulfide stripper
Steam absorbs H2S from passing liquid stream
Wastewater is sent to a distillation column where NH3 is stripped

10. Biological Treatment
Microorganisms present in wastewater will feed on the carbonaceous organic matter in the wastewater and repopulate in an aquatic aerobic environment
With a sufficient oxygen supply and an organic material food supply, the bugs (bacteria) will consume and metabolize the organic waste and transform it into cell mass, which settles in the bottom of a settling tank
Pseudomonas

11. Activated Sludge Air is pumped through the bottom of an aeration tank
Air rises and provides oxygen to the water
Effluent is sent through a secondary clarifier that separates the used cellular material from the treated wastewater
Activated Sludge schematic

12. Reverse Osmosis
Dissolved solutes are removed from a wastewater by a pressure- driven membrane
High pressure applied at the feed creates differential pressure between the permeate and feed sides of the membrane

13. Reverse Osmosis
Flux of water molecules through membrane: JW=kW (∆P - ∆π) Where: Jw=apparent volumetric flux of water (L/m2s) kw= mass transfer coefficient of water molecules (L/m2s.atm) ∆P= change in external pressure (atm) ∆π= change in osmotic pressure (atm)

14. Reverse Osmosis Flux of salt solute through the membrane is:
JS = ks (ΔC)
where: JS = mass flux of solute (kg/m2s)
kS = mass transfer coefficient of solute (L-S/m2)

15. Reverse Osmosis
Using van’t Hoff equation, the osmotic pressure is given as:
π=cRT
where:
c = concentration of solute in feed/permeate (mol/L)
R = gas constant ~ L.atm/(g-mol.K)
T = temperature of solution (K)

16. Reverse Osmosis The flow rate of water molecules in permeate
Flux of solutes is related to water flux by the equation
Mathcad was used to generate data points
Mathcad snapshot- Reverse Osmosis

17. Reverse Osmosis Accuracy <0.005% error For N membranes
Assume small membrane (negligible area/membrane)
Accuracy <0.005% error
CpN-1
CF0
CF2
CF1
CFN Cp
Cp1 ΔA
N=1
N=2 N

18. Activated Carbon Adsorption
A fixed bed of activated carbon adsorbs organics in wastewater
The bed of activated carbon is regenerated using
Pressure-swing desorption
Thermal-swing desorption

19. Activated Carbon Adsorption
Assumptions made
Isothermal and isobaric operation
Fixed bed adsorption
Langmuir isotherm for adsorption used
At equilibrium:
At saturation:
Mass transfer zone in column

20. Activated Carbon Adsorption
Klinkenberg approximate solution
Accuracy: <0.6% error
Dimensionless distance coordinate
Dimensionless time coordinate corrected for displacement
Excel sheet generated for ACA fixed bed

21. Simulation methods
PRO/II was used to model H2S stripper, NH3 stripper, and atmospheric distillation column
Inlet stream parameters and system properties were varied and outlet concentrations measured
MathCad generated points for input into GAMS for the API separator and reverse osmosis system
Snapshot of PRO/II crude oil distillation column
Atmospheric distillation
tower

22. Simulation methods Steady
Calculates a plant-wide mass balance and general dimensions of the unit processes involved
Snapshot of Steady program

23. Outlet Concentration Models
API Separator
Particles follow a normal distribution in size
Travel with a velocity that contains a horizontal and a vertical component
Furthermore, they are assumed to follow a uniform distribution along the height at which they enter
Equation 1. Horizontal and vertical time component
Equation 2. Mass fraction contaminants removed

24. Outlet Concentration Models
Chevron Wastewater Treatment (H2S Stripper)
Modeled as a distillation column in PRO/II with a partial reboiler
Points 1-8: Varied Cin, NH3
Points 9-57: Varied T
Points : Varied η
Points : Varied Cin, H2S
Points : Varied N
R2 ≈ 0.99

25. Outlet Concentration Models
Chevron Wastewater Treatment (NH3 Stripper)
Modeled as a distillation column in PRO/II with a partial reboiler and a partial condenser
Points 1-8: Varied Cin, NH3
Points 10-58: Varied F
Points 59-65: Varied η
Points 66-71: Varied P
Points 72-76: Varied N
Points 77-83: Varied Cin, H2S
Points 84-89: Varied RFR
R2 ≈ 0.98

26. Outlet Concentration Models
Biological Treatment
Modeled as an activated sludge system in Steady involving 1 source stream and 2 effluents
Points 1-23: Varied Cin
Points 24-31: Varied biomass yield
Points 32-38: Varied kd
Points 39-45: Varied MCRT (mean cell residence time)
Points 46-52: Varied MLVSS/MLSS

27. Outlet Concentration Models
Crude oil distillation column
Modeled in PRO/II as a distillation column
Points 1-50: Varied crude feedrate, Fcrude
Points : Varied steam temperature, T
Points : Varied steam flowrate, Fsteam
Points : Varied efficiency, η
Points : Varied xin, organics

28. Outlet Concentration Models
Desalter (salts)
Points 1-7: Varied
Points 8-14: Varied
Points 15-21: Varied Cin
Points 22-27: Varied Voltage
Points 28-34: Varied
Points 35-41: Varied Voltage field gradient
Permittivity is a measure of the material’s ability to transmit or “permit” an electric field.

29. Outlet Concentration Models
Desalter (H2S)
Final equation:
Distribution coefficient is a measure of differential solubility of the compound between these two solvents:

30. Reliability of equations
Varied parameters for 15 points in simulation
Compared equation to simulation results
Any equations with ≤5% error were used to generate tables as input to GAMS
Figure 1. % error between simulation result and regressed equation
Figure 2. Linear regression between simulated results and developed equations

31. GAMS Model GAMS: General Algebraic Modeling System
Wastewater Model Solvers
MIP: Mixed Integer (Linear) Program
CPLEX Solver
rMIP: Relaxed Mixed Integer (Linear) Program
MINLP: Mixed Integer (Non-Linear) Program
DICOPT Solver

32. GAMS Model Objective Functions Cost Freshwater Usage
Cost = Annual Operation Cost + Annual Fixed Cost
Freshwater Usage
Consumption = Freshwater to water-using units +
Freshwater to regeneration units

33. GAMS Model Fixed Outlet Concentrations Fixed Outlet Efficiency
Cout, regeneration process = Cout, regeneration process
Fixed Outlet Efficiency
Cout, regeneration process = Cin, regeneration process * (1 – η)
Modeled Outlet Concentrations

34. GAMS Model 400,000+ Non-zero terms 1,200+ Non-linear, non-zero terms
1-5 hours to run
17,298 lines of code

35. Process Flow Diagram

36. Results Fixed Outlet Concentrations Modeled Outlet Concentrations
Cost: $1,220,000
Consumption: 33 tons/hour
Modeled Outlet Concentrations
Cost: $950,000
Consumption: 31 tons/hour
Model Constraints
Flow Rates: 250 tons/hour
Contaminant Outlet Concentrations (Salts, Organics, H2S, Ammonia): (100, 100, 10, 100) ppm

37. Conclusions
Water re-use can provide a means to save on operating costs while positively impacting the environment
Non-linear models of the outlet concentration of contaminants provides a more accurate model to represent refinery waste water regeneration
Equipment costs of the water-using units are a function of inlet concentrations and flow rates, as well as design parameters

38. Further Studies
Enter outlet concentration models for the water- using units
Define more specific concentrations limits in and out of the units, as well as flow rates ranges
Define better investment and operating costs
Compare actual data from a petroleum refinery with theoretical model results

39. Questions?

40. Derivation of osmotic pressure
The blue line acts as a membrane which is permeable to water but blocks gas passage
The green line acts as a membrane which allows the passage of gas

41. Derivation of osmotic pressure
Van’t Hoff constructed a closed, isothermal, reversible process
If the blue membrane moves up, the static membrane moves down to equilibrate system
cg dVg = cs dVs     Cg Cs

42. Derivation of osmotic pressure
Gibb’s free energy of the system
G(T, p, Ni) = U + p V - T S  
U= internal energy
S=entropy
T=temperature Cg Cs

43. Derivation of osmotic pressure
In a reversible process at constant temperature and pressure
DG = Si(∂G / ∂Ni) dNi = 0
   where:  ∂G / ∂Ni is the energy used to remove component (i) from the system studied Cg Cs

44. Derivation of osmotic pressure
W=pdVg
For two components in a reversible process
p dVg = п dVs  
From the previous equation:
      cg dVg = cs dVs
The equation for pressure is
  p (cs / cg ) dVs = p dVs   Cg Cs
W=пdVs

45. Derivation of osmotic pressure
W=pdVg
Then
p (cs / cg ) = п
By ideal gas law;
p = cg R T
Also,
п = cg R T Cg Cs
W=пdVs