We present an optimization approach that allows various designs of membrane networks for gas separations to be evaluated simultaneously while choosing the optimal separation system. The model is based on mixed-integer nonlinear programming (MINLP) and is based on the concept of superstructures (all possible flowsheets put together from which one is picked). We present an optimization approach that allows various designs of membrane networks for gas separations to be evaluated simultaneously while choosing the optimal separation system. The model is based on mixed-integer nonlinear programming (MINLP) and is based on the concept of superstructures (all possible flowsheets put together from which one is picked). Abstract Background Natural gas processing consists of separating all of the various hydrocarbons and fluids from the pure natural gas, to produce what is known as 'pipeline quality' dry natural gas. Pipeline quality gas has a composition of 2-5% carbon dioxide in order to prevent corrosion due to impurities in the natural gas stream such as carbon dioxide and hydrogen sulfide. Membranes offer better environmental processing methods by cutting emissions. Hollow fiber membranes were used in the development of the mathematical model. Using the form of a membrane shown in Kookos [2] the component material balance was established assuming that the membrane is divided into K segments. The model is a countercurrent flow membrane. Component material balance for the shell and tube sides of the membrane using (j) components: The flux through the membrane is based on the partial pressure gradient between the tube and shell side. Components include carbon dioxide, methane, hydrogen sulfide, and heavier hydrocarbons. The superstructure is a model that is able to compare all competing, possible two membrane networks simultaneously instead of tediously comparing each network one by one. The objective function to minimize includes capital costs and operational costs for electricity to run the compressors that are involved in compressing recycle streams into the feed mixing points. The capital costs include:  cost of the housing of the membranes ($200/m2).  Compressor (efficiency =70%) costs ( $1000 per KWh)  27% of capital cost is paid back each year.  The objective function is normalized for one year  We compare the results the work by Qi and Henson (1998). The operating costs include  the cost of running the compressors  Maintenance costs are assumed to be 5% of the FCI per year.  The cost of replacing the membranes is normalized to $30/year. The cost of product losses is also taken into account and is proportional to the rate of product loss and the cost the fuel cost. Hollow fiber membranes were used in the development of the mathematical model. Using the form of a membrane shown in Kookos [2] the component material balance was established assuming that the membrane is divided into K segments. The model is a countercurrent flow membrane. Component material balance for the shell and tube sides of the membrane using (j) components: The flux through the membrane is based on the partial pressure gradient between the tube and shell side. Components include carbon dioxide, methane, hydrogen sulfide, and heavier hydrocarbons. The superstructure is a model that is able to compare all competing, possible two membrane networks simultaneously instead of tediously comparing each network one by one. The objective function to minimize includes capital costs and operational costs for electricity to run the compressors that are involved in compressing recycle streams into the feed mixing points. The capital costs include:  cost of the housing of the membranes ($200/m2).  Compressor (efficiency =70%) costs ( $1000 per KWh)  27% of capital cost is paid back each year.  The objective function is normalized for one year  We compare the results the work by Qi and Henson (1998). The operating costs include  the cost of running the compressors  Maintenance costs are assumed to be 5% of the FCI per year.  The cost of replacing the membranes is normalized to $30/year. The cost of product losses is also taken into account and is proportional to the rate of product loss and the cost the fuel cost. Membrane Model Development The model was tested on one membrane Our Model was extended to consider a superstructure of  Several Membranes  Several Compressors  Multiple mixing and splitting points. As a result, the model includes all possible flowsheets at once and is able to extract the optimal one The MINLP model we developed  Does not provide a fully rigorous optimum of the membrane network. It is  Preferentially chooses models with a parallel arrangement of the feed, which is the simplest model of a membrane network. We developed several methods to both assist the model in finding a feasible solution as well as to consider recycles between the membranes rather than running in parallel. These methods were somewhat successful, but the solutions may only be considered as local minimums in the cost function. We recommend working on more efficient solution procedures. The model was tested on one membrane Our Model was extended to consider a superstructure of  Several Membranes  Several Compressors  Multiple mixing and splitting points. As a result, the model includes all possible flowsheets at once and is able to extract the optimal one The MINLP model we developed  Does not provide a fully rigorous optimum of the membrane network. It is  Preferentially chooses models with a parallel arrangement of the feed, which is the simplest model of a membrane network. We developed several methods to both assist the model in finding a feasible solution as well as to consider recycles between the membranes rather than running in parallel. These methods were somewhat successful, but the solutions may only be considered as local minimums in the cost function. We recommend working on more efficient solution procedures. Constraints:  The composition of the final retentate must be less than 2% CO 2.  The membrane network is operated isothermally at steady state.  The total feed to the process is 10 mol/s and the composition of the feed is 19% CO 2, 73% CH 4, 1% H 2 S, and 7% C2+.  The feed is available at 3.5MPa and the shell side of the membranes is assumed to be ambient pressure (.105MPa).  The plant is assumed to operate 300 days out of the year.  Finally, the membrane is purchasable in 40m 2 increments. We ran models for various configurations of membrane networks. The models that we ran included a 2 membrane, 3.5MPa tube side pressure membrane network optimization which resulted in the configuration shown below..  The membrane network has the feed going to each membrane and has recycle from the permeate of the second membrane to the feed of membrane 1.  Additionally, it has a small amount of recycle from the retentate of membrane 1 to the feed of membrane 2.  Some agreement with the results by Datta and Qi (xxxx) are found.  The total amount of work necessary is comparable, and the recovery of CH 4 is higher in our model. The overall cost of the process is also comparable. The cost of the membrane network is very similar to that of the network obtained by Qi and Henson.  The overall cost of the operation amounts to $11.05/km 3 of feed processed. This compares favorably with the model presented by Qi and Henson which shows $11.11/km 3 of gas processed. The lower cost of our model is due to the lower membrane area and the superior recovery of methane. Constraints:  The composition of the final retentate must be less than 2% CO 2.  The membrane network is operated isothermally at steady state.  The total feed to the process is 10 mol/s and the composition of the feed is 19% CO 2, 73% CH 4, 1% H 2 S, and 7% C2+.  The feed is available at 3.5MPa and the shell side of the membranes is assumed to be ambient pressure (.105MPa).  The plant is assumed to operate 300 days out of the year.  Finally, the membrane is purchasable in 40m 2 increments. We ran models for various configurations of membrane networks. The models that we ran included a 2 membrane, 3.5MPa tube side pressure membrane network optimization which resulted in the configuration shown below..  The membrane network has the feed going to each membrane and has recycle from the permeate of the second membrane to the feed of membrane 1.  Additionally, it has a small amount of recycle from the retentate of membrane 1 to the feed of membrane 2.  Some agreement with the results by Datta and Qi (xxxx) are found.  The total amount of work necessary is comparable, and the recovery of CH 4 is higher in our model. The overall cost of the process is also comparable. The cost of the membrane network is very similar to that of the network obtained by Qi and Henson.  The overall cost of the operation amounts to $11.05/km 3 of feed processed. This compares favorably with the model presented by Qi and Henson which shows $11.11/km 3 of gas processed. The lower cost of our model is due to the lower membrane area and the superior recovery of methane. Membrane Model-ResultsMembrane Model Natural Gas Processing Steps Hollow Fiber Model (*) This work was done as part of the capstone Chemical Engineering class at the University of Oklahoma (**) Capstone Undergraduate students Membrane Model-Results Results obtained for three membranes  Membranes network modeling is capable of discovering new structures.  The MINLP models offer several difficulties and they often find local minima far from better solutions. I Results obtained for three membranes  Membranes network modeling is capable of discovering new structures.  The MINLP models offer several difficulties and they often find local minima far from better solutions. I Future Work References 1. Qi., R., Henson, M.A., ‘Optimization-based design of spiral-wound membranes systems for CO2/CH4 separations’, Separation and Purification Technology, 13, , Kookos, I.K., ‘A targeting approach to the synthesis of membrane network for gas separations’, j. Membrane Science, 208, , Datta and QI????  New strategies with better solving capabilities are needed.  Membranes are limited due to low flux capacity and susceptibility to fouling, and plasticizing gases. The new research in membranes are starting to produce results that may counter act this effect. A family of rubbery materials based on cross-linked poly(ethylene oxide) shows promise for overcoming this problem. The materials are strongly solubility selective for the removal of CO2 from natural gas. Studies have also demonstrated that the materials are strongly selective for CO2 in CO2/H2 mixtures. The research has shown that membrane performance can be improved by introducing methoxy chain ends to the polymers or by adding MgO nanoparticles to the polymer matrix.  Network modeling may be able to guide some of this research Conclusions