1. Introduction and Prior Work
As the world transitions to a more environmentally conscious economy, the importance of hydrogen (H
2) production processes is paramount. Hydrocarbons such as petroleum, natural gas, coal and biomass serve as the principal sources of H
2, which will see use as a feedstock in myriad clean energy and chemical production processes. As H
2 production from hydrocarbons generates carbon dioxide (CO
2), processes incorporating carbon capture technologies are necessary to achieve the objective of reduction of CO
2 emissions in accordance with protocols that seek to mitigate global climate change. Based upon extrapolation of the rates of consumption and available reserves, projections posit that petroleum resources may be depleted within 50 years and natural gas resources within 100; however, coal resources may exhibit their current availability for a couple hundred years [
1]. Consequently, emerging energy technologies that utilize coal as the feedstock, such as integrated gasification combined cycle (IGCC) power plants operated with carbon capture, are particularly promising.
Coal-based IGCC units produce electricity through a synthesis gas (syngas) intermediate, which is subjected to the water-gas shift (WGS) reaction to maximize H
2 produced prior to the stream being sent to the gas turbine portion of the unit. An IGCC process scheme with carbon capture typically utilizes packed-bed WGS reactors followed by CO
2 removal by a Selexol process [
2,
3]. An alternative to this method of syngas conversion utilizes membrane reactors (MRs) equipped with H
2-selective membranes, which grant advantages such as increased carbon monoxide (CO) conversion, facilitated CO
2 removal/sequestration (CO
2-rich effluent is produced at high pressure), and process intensification through a reduction to the total number of process units [
2,
4].
There are challenges inherent to the use of MRs for such an application as the H2-selective membranes must be stable under high-temperature and extreme pressure conditions in the presence of water and contaminants such as hydrogen sulfide (H2S). H2-selective membranes commonly considered for this application are as follows: (i) zeolite-based molecular sieves; (ii) dense metals such as Pd; and (iii) polymeric membranes. Of these potential membrane materials, (i) and (ii) possess highly favorable gas separation properties in terms of selectivity and flux, but the cost for these materials may be prohibitive for industrial-scale application. Only some polymeric membranes can be considered for the WGS application, as the elevated operating temperature of the MR unit is often outside the stability limits of the membrane material or the membrane material exhibits limited gas separation properties at the operating temperatures defined by the WGS-MR. However, if the aforementioned performance and stability challenges are addressed, polymeric membranes possessing suitable gas separation properties offer the potential to greatly reduce the cost of industrial-scale-MR implementation.
Polybenzimidazoles (PBIs) represent one such class of high performance polymers having exceptional chemical and physical characteristics enabling H
2/CO
2 separation in challenging thermo-chemical environments. These materials exhibit molecular-sieving mechanisms analogous to those observed in zeolite-based membranes, which imbues these materials with attractive H
2/CO
2 selectivity for syngas separations. High-performance polymeric materials have also been found to exhibit good thermal stability up to 400 °C and chemical stability in the presence of common syngas contaminants [
5,
6].
One objective of this study is to assess the feasibility of the state-of-the-art high-performance polymeric materials for use in membrane reactor systems with respect to performance constraints set forth by the U.S. Department of Energy (DOE) for pre-combustion CO conversion/CO
2 separation processes within IGCC units [
3]. In this study, the performance characteristics of PBI-based membranes, as demonstrated by Berchtold and coworkers in [
5], are used to develop the benchmark case for the polymer membrane-based MR process schemes investigated and developed herein. These PBI-based membrane materials have demonstrated industrially attractive H
2/CO
2 separation characteristics including ideal H
2 permeabilities between 58 and 78 barrer and H
2/CO
2 selectivities between 23 and 43 at 250 °C [
5,
7]. Additionally, this study seeks to determine the minimum membrane characteristics needed to satisfy the DOE’s performance constraints by considering process models for several reactor designs. The performance of the various reactors is assessed in the base case conformations, which are then modified by considering different catalyst/membrane placement about the axial axis. Alternative reactor designs are developed by seeking to maximize reactor performance (H
2 recovery) for the minimum reactor cost as determined by the required membrane surface area. As demonstrated previously, an optimization problem is formulated to guide these designs [
2].
With regard to the systems analysis, there are several MR models (utilizing H
2-selective membranes) related to the WGS reaction available in the literature, encompassing the range from 1-D/isothermal to 2-D/non-isothermal. Also available in the literature are MR models that employ H
2-selective membranes relating to widely varied applications (see [
2] for a summary for MR models, efforts and applications). A review of literature shows a few computational modeling studies based on membrane reactors employing polymeric membranes [
8,
9], due in part to the temperature limitations imposed by available polymers. However, the literature suggests a lack of studies on optimization of polymer-based MR configurations. Recent and continued development and demonstration of high performance polymers such as PBIs for potential use in challenging membrane separation environments, such as those encountered in the vicinity of the WGS reaction, presents an opportunity to derive a MR model for a system utilizing such H
2-selective polymers and subsequently evaluate their potential in this challenging separations role [
5,
7,
10]. This study is focused on H
2-selective membranes due to their advantages over CO
2-selective membranes in IGCC process schemes, as discussed by [
11].
Moreover, several optimization studies relating to packed-bed MRs and reactor systems employing membrane separators are available in the literature. These studies have utilized H
2-selective membranes (ceramic or Pd) to formulate optimization problems that examine staged membrane reactors [
12,
13,
14] and traditional MRs [
2]. In the case of the staged membrane reactors, the optimization problems were formulated with the objective of maximizing methane conversion, H
2 recovery or H
2 yield in a steam methane reforming (SMR) process employing a Pd-based membrane. These studies considered a permeative stage membrane reactor (PSMR) with a fixed number of stages, or a staged membrane reactor (continuous membrane, catalyst packing with inert stages). The decision variables were composed of the catalyst/membrane stage lengths, but the problem was not subject to performance constraints. For the case of the traditional MR performing the WGS reaction, the study formulated an optimization problem in terms of economic variables that maximizes performance (H
2 recovery) for the minimum cost (membrane surface area) subject to multiple constraints on reactor effluent streams by considering alternative catalyst/membrane placement about the axial axis of the reactor. With regard to the available literature, it is worth noting that computational studies of SMR or WGS processes that use Pd/micro-porous ceramic membranes have H
2 selectivity values that are comparatively larger than those of polymeric membranes.
Thus, the computational study performed here of MR systems employing novel polymeric membrane materials provides insight into their feasibility for WGS reaction applications. Additionally, such a study may be used to identify performance limitations associated with the material, which may be used to guide the development of future polymeric materials with desired membrane characteristics. To this end, mathematical models are developed for traditional MRs and PSMRs using the performance characteristics of PBI membranes; these models are subsequently employed to develop reactor designs that satisfy the set of performance constraints set forth by the U.S. DOE for pre-combustion CO conversion (WGS reaction)/CO2 separation processes within IGCC units. Using these process models for the MR and PSMR cases, constrained optimization problems are formulated that seek to maximize performance (H2 recovery) through minimization of membrane surface area—this is achieved by considering alternate membrane placement about the axial axis of the reactor. Through the formulation of two optimization problems, the performance-limiting membrane parameter is identified and a minimum value that satisfies all equipment/stream constraints is successfully calculated for each configuration. This study contributes insight into identifying and prioritizing the membrane parameters that should be the focus of future polymeric membrane development efforts, and provides a minimum value for key parameters that satisfy the set of six performance constraints; to this end, it is worth noting that the minimum selectivity value (one such key parameter) presented here is unique to the operating temperature and pressure of the process units, and the syngas feed/steam sweep flowrates.
4. Conclusions
One-dimensional isothermal models were developed for traditional MRs and PSMRs, and used to assess high-performance polymeric membrane reactor systems. Constrained cost optimization problems were formulated so as to systematically determine optimal reactor designs through more efficient membrane placement. As the solutions to these optimization problems also corresponded to a maximization of the limiting performance parameter, , an incremental search of H2/CO2 selectivity was then performed with the intent of determining as a function of αH2/CO2 at constant permeance. These designs were generated through the cost minimization optimization problem and the result that the economic optimum corresponds to maximization of carbon capture was verified by way of the second optimization problem formulation (utilizing identical decision variables), which sought to maximize subject to the other five performance constraints. This analysis was successfully completed for the three reactor designs considered (2-stage PSMR, 3-stage PSMR, MR). Graphs of carbon capture as a function of selectivity for fixed conditions were produced, which can guide the development of polymeric membrane materials to achieve all the desired specifications for their implementation in IGCC WGS environments.
Using the unit design framework considered herein, one may generalize from the process conditions of feed/sweep molar flow rate, flow composition/arrangement, reactor operating conditions (temperature, pressure), catalyst mass, tube dimensions and membrane properties to grant insight into future membrane material development by identifying the limiting parameter and determining a minimum value that satisfies all imposed constraints. Having identified a minimum value for a given parameter (αH2/CO2 in this case), a clear goal can be set for researchers in material development (should it be desired to use the process designs considered here). As the optimization results presented here are sensitive to membrane cost, it is desirable to investigate membranes with varied cost (i.e., hollow fibers) to further understand the resulting outcomes in terms of required performance characteristics and optimized PSMR design. To that end, the presented modeling framework can be extended to evaluate performance of membrane materials in a systematic manner by considering several process designs in which material placement (catalyst, membrane) is guided by economic considerations and/or satisfaction of a set of performance constraints. The formulated optimization problem can also be extended to consider different operating conditions (temperature, pressure) for each reaction/separation module.