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 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

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 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.

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 Why should we process natural gas with membranes?

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,

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

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) How does a substance travel through the membrane? this depends on the solubility of the gas component, and the diffusivity of the gas component.

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

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

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

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 superstructure representation

Superstructure Functionality Illustration

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 1970-1979 I found 7 articles when I searched for the words optimisation + membranes (in title, keywords and abstract). From 1980-1989 there were 23 and from 1990-2000 there were 695 and from 2000-2004 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

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

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

GAMS Interface

Model Equations in GAMS Interface

GAMS Solution Feasible One Membrane Model:

Mole Fractions

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

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

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

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 ?

References Qi., 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.