Membrane Networks in Natural Gas Separation

Nina Wright, Ernest West, Debora Faria and Miguel Bagajewicz

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.

Topics

• Modern Natural Gas Processes• Membranes• Membrane Networks• Superstructures• Superstructure Model• Modeling Results • Questions

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 with Membrane Separation

Membranes could be used for:

• Wellhead dehydration

• Nitrogen Rejection

• Acid Gas Removal

• Dehydrator

• NGL fractionation

• Molecular sieves

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

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

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

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.

Membranes use in Industry Today

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.

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

What are membranes?

Why should we use them?

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

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

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,

PiFim

iii pp

l

DKN

iD

ii DK

iK

iP

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

B

B

A

A

xy

xy

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

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

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)

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.

Membrane Mathematical Models

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

Hollow Fiber Membrane Model

• Molar Component Material Balance

– Tube side Shell side

kjkt

jkt

jk AJff

NPkNCj

,,1,

),...,2,1,,...2,1 kjks

jks

jk AJff ,,1,

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

kmltk dzdNA ,tN

mld ,

ssjk

ttjk

m

jjk PxPx

QJ ,,,

jkJ ,

jQ

m

Hollow Fiber Model

• Mole fractions (source on nonlinearities) – Tube side mole fraction for component j

– Shell side mole fraction for component j

tlk

NCl

tjkt

jk f

fx

,1

,,

slk

NCl

sjks

jk f

fx

,1

,,

Modeling of Membrane Networks using Superstructures

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.

Superstructure Functionality Illustration

(a)

superstructure representation

Superstructure Functionality Illustration

(a)

Membrane network design (Qi, Henson, 2000)

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.

Ref: Qi., R., Henson, M.A., 1998

Generalized Superstructure used

Membrane network design (Kookos, 2002)

Ref: Kookos, I.K, 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.

Our Mathematical Model

Tube side

Shell side

K K+1 K+2

Feed Retentate

Permeate

GAMS Interface

ssjk

ttjk

m

jjk PxPx

QJ ,,,

kjks

jks

jk AJff ,,1,

kjkt

jkt

jk AJff

NPkNCj

,,1,

),...,2,1,,...2,1

Model Equations in GAMS Interface

GAMSSolution

Feasible One Membrane Model:

Mole Fractions

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Mole Fractions in Membrane Length

CO2 tubeCH4 tubeCO2 shellCH4 shell

Length

Mol

e F

racti

ons

Membrane Optimization

Length(m) 50CO2 Material Balance Tube

(Mol/s) 0.07CH4 Material Balance Tube

(Mol/s) 6.73CO2 Material Balance Shell

(Mol/s) 1.95CH4 Material Balance Shell

(Mol/s) 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) 0.07

Feasibility 8

One Membrane Optimization while Minimizing Area, and Flow of CO2 Tube side

• The Feasibility of the Membrane is discovered to be an eight.

• Eight is considered feasible

Complex Membrane Model

• Two membranes• Four components• Reasonable Values for Objective Function• Discretization of Continuous Model• Addition of Non-Linear Solver

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

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

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

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

Feasibility

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

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

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

-Two stage separation process -2% CO2 composition in final retentate-Spiral wound membranes vs. hollow fiber membranes-Four component system

Membrane System Design from Qi, and Henson

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

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

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

Questions ?

ReferencesQi., R., Henson, M.A., ‘Optimization-based design of spiral-wound membranes systems for CO2/CH4 separations’, Separation and Purification Technology, 13, 209-225, 1998

Qi., R., Henson, M.A., ‘Membrane system design for multicomponent gas mixtures via mixed-integer nonlinear programming’, Computers and Chemical Engineering, 24, 2719-2737, 2000

Kookos, I.K., ‘A targeting approach to the synthesis of membrane network for gas separations’, j. Membrane Science, 208, 193-202, 2002

Mark C. Porter, "Handbook of Industrial Membrane Technology", Westwood, New Jersey, Noyes Publications, 1990.

Seader, J. D., and Henley, E. J. "Separation Process Principles". New York: John Wiley & Sons, Inc., 1998.

Natural Gas Supply Association, http://www.naturalgas.org/index.asp

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.