1. Membrane Networks in Natural Gas Separation
Nina Wright, Ernest West, Debora Faria and Miguel Bagajewicz

2. Purpose
The purpose of this presentation is to show the importance of membranes in natural gas purification and their potential to be highly cost effective.

3. Topics Modern Natural Gas Processes Membranes Membrane Networks
Superstructures
Superstructure Model
Modeling Results
Questions

4. Natural Gas Processing System-Today
Major Components of Natural Gas Processing today include absortion, adsorption, molecular sieves and cryogenic processes
Absorption is used in:
Glycol Dehydration
Amine Treating
Cryogenics is used in:
NGL recovery
Natural Gas Process of today includes many stages, which I will discuss in subsequent slides.
The absorbed NGLs in the rich solvent from the bottom of the NGL absorber column are fractionated in the solvent regenerator column which separates NGLs overhead and lean solvent produced at the bottom.  After heat recuperation, the lean solvent is presaturated with absorber overhead gases.  The chilled solvent flows in the top of the absorber column.  The separated gas from the presaturator separator form the pipeline sales gas

5. Natural Gas with Membrane Separation
Membranes could be used for:
Wellhead dehydration
Nitrogen Rejection
Acid Gas Removal
Dehydrator
NGL fractionation
Molecular sieves

6. Glycol Dehydration
Triethylene glycol liquid absorbs water vapor from natural gas
Glycol water solution is then heated to remove water
Glycol solution is then reused for further dehydration use
Removing water levels to below 5lbs/MMscf
The Environmental Protection Agency (EPA) estimated that more than 38,000 glycol dehydration units are operating in the U.S., collectively emitting about 18.6 billion cubic feet of CH4 per year into the atmosphere
Wet gas enters a contacting tower at the bottom. Dry glycol flows down the tower from the top, from tray to tray, or through packing material. A bubble cap configuration maximizes gas/glycol contact, removing water to levels below 5 lbs/MMscf. Systems can be designed to achieve levels down to 1lb/MMscf. The dehydrated gas leaves the tower at the top and returns to the pipeline or goes to other processing units. The water rich glycol leaves the tower at the bottom, and goes to the reconcentration system. In the reconcentration system, the wet glycol is filtered of impurities and heated to 400°F. Water escapes as steam, and the purified glycol returns to the tower where it contacts wet gas again.

7. Sulfur Removal-Sweetening
Sour gas - H2S content exceeds 5.7 milligrams per cubic meter of natural gas
Sour gas is passed through contact tower containing amine solution
Amine solution absorbs H2S
Amine is recycled for further absorption
Currently Amine treating is used in 95% of U.S. gas sweetening operations

8. Methane Losses from Acid Gas Removal
There are 291 acid gas removal (AGR) units in gas processing plants
Emit 646 MMcf annually
6 McF/day emitted by average AGR unit
Most AGR units use diethanol amine (DEA) or Selexol process

9. Cryogenic Method for NGL removal
Expansion turbine is used to drop the temperature of the natural gas
Ethane and lighter hydrocarbons condense, methane remains in gaseous form
Allows for 90%-95% recovery of ethane from the original gas stream
In cryogenic processing, almost the entire volume of natural gas must be refrigerated, usually compressed, and then heated again. Accordingly, cryogenic processing is expensive to install and operate.
Cryogenic technology is believed only capable of cost effectively purifying reserves, which exceed 50,000,000 standard cubic feet of gas per day.

10. Membranes use in Industry Today

11. Largest membrane based natural gas plant
Natural Gas Processing Plant Qadirpur, Pakistan
In 1999: in the world (Dortmundt, UOP, 1999).
Design: 265 MMSCFD natural gas at 59 bar.
CO2 content is reduced from 6.5 % to less than 2 % using a cellulose acetate membrane.
Also designed for gas dehydration.
Plant processes all available gas.
Plans for expansion to 400 MMSCFD.

12. Natural Gas Processing with Membranes
Advantages
Less Environmental Impact
Less Maintenance Cost
Less Workspace Area
Ability to treat gas at wellhead
Disadvantages
Reduced flux capacity
High capitol cost
Thermal instability
More research is needed for widespread industrial sized usage
Why should we process natural gas with membranes?

13. What are membranes?
Why should we use them?

14. Membrane Definition
A membrane-a physical barrier from semi-permeable material that allows some component to pass through while others are held back. Usually, the driving force is pressure difference
Feed
Retentate
Permeate
Membrane module

15. Permeability of a Non-Porous Membrane
The rate of gas permeation through a membrane is determined permeability.
Permeability = solubility (k) x diffusivity (D)
This comes from the fact that the gas needs to dissolve first in the matrix and then diffuse.
Solubility indicates how much gas can be taken up by the membrane and diffusivity measures of the mobility of the molecules in the membrane

16. Membrane-Diffusion
Mass transport through membranes described by Fick’s Law
is the diffusivity of the solute in the membrane
accounts for the solubility of the solute
is the permeability,

17. Membrane Characteristics
Selectivity
Ideal Membranes incorporate high permeability with high selectivity
This is accomplished usually with a highly selective membrane and making it as thin as possible to increase the permeability

18. Membrane Modules
Membrane modules divided into Flat sheets and Tubular form
Two membranes commonly used are spiral bound and hollow tube
Spiral bound are an example of Flat sheet modules- essentially a flat sheet module rolled into a spiral form
Spiral shape accommodates more surface area then a regular flat sheet
Insert caption

19. Hollow Fiber Membranes
Tubular membranes are divided into
Tubular >5mm
Capillary 0.5 > 5mm
Hollow fiber < 0.5 mm
Low operation cost
More Area per unit vs. Spiral wound
Susceptible to fouling
WINNER!!
Cross Section of Hollow Fiber

20. Cellulose Acetate
Cellulose acetate membrane-most commonly used in gas separation industry (especially CO2 removal)
Drawbacks-sensitivity to water and plasticizing gases
Limited temperature and pressure resistance
Advantages-increased selectivity towards CO2 over methane (CO2 with a selectivity of 10-20)
How does a substance travel through the membrane?
this depends on the solubility of the gas component, and the diffusivity of the gas component.

21. New membrane technology
Recently, (Oct. 2007) information published about “thermally rearranged” plastic membrane from University of Texas shows great promise:
Membrane pores modeled on ion channels in cells
Selectivity 4 times higher than Cellulose Acetate
CO2 100 times more permeable
Highly thermally stable, can operate over 600°F.
500 times less space taken up by process compared to current conventional CO2 removal.

22. Membrane Mathematical Models

23. Hollow Fiber Modeling Assumptions: Uniform properties at each element
Ideal gas behavior
Steady-state isothermal operation
Constant ambient pressure at the shell side
Constant permeabilities (independent of composition)
Negligible axial diffusion and pressure drop
Negligible deformation of the fibers under pressure

24. Hollow Fiber Membrane Model
Molar Component Material Balance
Tube side Shell side

25. Hollow Fiber Membrane Model
Active Area of membrane element
is the number of membrane tubes
is the logarithmic mean diameter
is the rate of transport of pure component
per unit area of the membrane
is the permeability of component j
is the thickness of the membrane

26. Hollow Fiber Model Mole fractions (source on nonlinearities)
Tube side mole fraction for component j
Shell side mole fraction for component j

27. Modeling of Membrane Networks using Superstructures

28. Superstructure
(a)
(b)
(c)
(d)
A superstructure is a flowsheet that contains all possible flowsheets simultaneously. Optimization determines the oprtimal configuration
Mathematical programming is needed.

29. Superstructure Functionality Illustration
superstructure representation

30. Superstructure Functionality Illustration

31. Membrane network design (Qi, Henson, 2000)
Generalized Superstructure used
Model
Spiral-Wound module
Multi-component gas mixtures
MINLP
Case study: CO2 and H2S separation from natural gas.
Simultaneous optimization of flow in terms of total annual process costs.
Using optimisation for membranes seems to be a growing field. From I found 7 articles when I searched for the words optimisation + membranes (in title, keywords and abstract). From there were 23 and from there were 695 and from there were 714.
Some of the interesting new articles I have found uses optimisation with a superstructure approach.
A superstructure is used to represent all the possible process configurations that is possible. For the membrane problem this means that all different membrane units, possible compressors, recycle streams, mixing and splitting of streams have been represented. When this is optimised, usually in terms of some capital and operating costs, the solution will give the best operating structure for the given problem. All the alternatives are then “tested” and the most economical one is found.
This example is a mixed integer nonlinear programming solution to a CO2/methane separation using spiral wound modules. The optimisation of the flowsheet was done in terms of total annual costs.
Ref: Qi., R., Henson, M.A., 1998

32. Membrane network design (Kookos, 2002)
Model
Hollow-fibre membrane system
Multi-component gas mixtures
Limit study to two membranes network
NLP
Case study: O2 and N2 separation from air
Find the optimal membrane permeability, selectivity and the optimum structure.
Configuration and membrane properties are optimized together.
Ref: Kookos, I.K, 2002

33. Our Mathematical Model
Tube side Shell side
Feed
Retentate K
K+1
K+2
Permeate

34. GAMS Interface

35. Model Equations in GAMS Interface

36. GAMS Solution
Feasible One Membrane Model:

37. Mole Fractions

38. Membrane Optimization
One Membrane Optimization while Minimizing Area, and Flow of CO2 Tube side
Length(m) 50
CO2 Material Balance Tube (Mol/s)
0.07
CH4 Material Balance Tube
(Mol/s)
6.73
CO2 Material Balance Shell (Mol/s)
1.95
CH4 Material Balance Shell
0.15
Area(m2 )
2.09
Mole fraction CO2 (tube side)
0.01
Mole fraction CH4 (tube side)
0.99
Mole fraction CO2 (shell side)
0.93
Mole fraction CH4 (shell side)
Feasibility 8
The Feasibility of the Membrane is discovered to be an eight.
Eight is considered feasible

39. Complex Membrane Model
Two membranes
Four components
Reasonable Values for Objective Function
Discretization of Continuous Model
Addition of Non-Linear Solver

40. Objective Function Capital Costs $1000 per kWh per compressor
$200 per m2 of membrane area for housing
Stainless Steel compressors
Working capital = 10% of FCI
27% of TCI paid each year

41. Objective Function Operating Costs
Power costs = fuel cost*working days per year*compressor power / heat content of fuel / efficiency
$30/yr/m2 cost of membrane replacement
Labor cost is assumed to be 5% of FCI/year
Product losses = fuel cost * working days per year * rate of loss of product

42. Additional Information
Efficiency of compressors is 70%
Stainless steel compressors
Feed available at 3.5MPa
Permeate pressure at .105MPa (~1bar)
10mol/s total feed
19% CO2, 73% CH4, 7%C2+, 1%H2S
Membrane Area available in 40m2 increments
Operates 300 days/year

43. Mathematical Model
Model uses a combination of mixed integer linear programming (MILP) and mixed integer non-linear programming (MINLP).
The MILP solves a initial linear problem to obtain initial guesses and provides a lower bound
The MINLP then solves the non-linear problem to obtain a feasible solution

44. Feasibility

45. Difficulty in Finding Optimum
Model is highly non-linear, so obtaining solutions is difficult
Most simple model involves no recycle, model preferentially chooses parallel configuration
MILP solution generates a lower bound that is too low and does not provide good enough initial guesses on its own
When forcing the model to recycle, much lower objective function occurs

46. Increasing Maxcycles and Including Infeasder
Added infeasder option and increased maxcycles from 20 to 100.
Infeasder unable to be used because there were too many non-linear sub-problems in the model
Increasing maxcycles occasionally causes the model to obtain a feasible solution if model cannot converge with 20 cycles
Does not improve model enough

47. Addition of Loop Function
Model cannot obtain optimum solution without initial guesses or bounds
Loop generates initial guess for recycle flows and feed flows
Successfully is able to obtain much lower minimums than original model run on high max cycles

48. Membrane System Design from Qi, and Henson
-Two stage separation process -2% CO2 composition in final retentate -Spiral wound membranes vs. hollow fiber membranes -Four component system

49. Two Membrane Network Two Membrane Network
Partial Recycle of the Permeate of the Second Membrane
Fraction of the Retentate from Membrane 1 to Membrane 2
Comparable compressor results
Comparable Cost of Processing

50. Two Membrane Network P=5MPa
Total Area = 80m2
Cost of treating = $8.14/km3
P (tube side) =5 Mpa
Complete Recycle of Permeate of Membrane 1

51. Conclusions
Successfully modeled two component, counter current flow membrane
Several computational problems were highlighted
Parallel configurations
Less Total Membrane Area
Two Membrane Networks modeled from Superstructure

52. Questions ?

53. References
Qi., R., Henson, M.A., ‘Optimization-based design of spiral-wound membranes systems for CO2/CH4 separations’, Separation and Purification Technology, 13, , 1998 Qi., R., Henson, M.A., ‘Membrane system design for multicomponent gas mixtures via mixed-integer nonlinear programming’, Computers and Chemical Engineering, 24, , 2000 Kookos, I.K., ‘A targeting approach to the synthesis of membrane network for gas separations’, j. Membrane Science, 208, , 2002 Mark C. Porter, "Handbook of Industrial Membrane Technology", Westwood, New Jersey, Noyes Publications, Seader, J. D., and Henley, E. J. "Separation Process Principles". New York: John Wiley & Sons, Inc., Natural Gas Supply Association, John A. Howell, The Watt Committee on Energy, "The Membrane Alternative, London, Elsevier Science, 1990.
Polymeric Gas Separation Membranes by Donald R. Paul, Yuri P. Yampolskii, 1996.