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Hydrogen Production from Biogas in Membrane Reactor

Submitted:

29 May 2026

Posted:

02 June 2026

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Abstract
The rapid depletion of fossil fuels, increased air pollution, global warming, and the ever-growing global energy demand have collectively heightened interest in renewable energy sources and high-performance alternative energy technologies. In this context, the use of fuel cells in portable, stationary, and vehicle applications has grown rapidly. Producing the hydrogen required for fuel cells from renewable sources is among the most actively researched topics. The high cost of electrolysis and their performance degradation during long-term operation make thermochemical hydrogen production from biogas an increasingly attractive option. This project carries out both experimental and mathematical modelling studies of a membrane reactor used to produce hydrogen from biogas. An experimental setup at the Institute on Membrane Technology (ITM) in Italy is used to validate the developed model and to conduct permeability and reaction tests. A multi-physics mathematical model is developed to examine the effects of operating temperature, reaction pressure, steam-to-carbon ratio, and flow direction on biogas conversion, hydrogen recovery, and hydrogen yield. Finally, the membrane reactor is integrated with a PEM fuel cell to form a combined heat and power (CHP) system, whose thermodynamic model is developed and assessed parametrically.
Keywords: 
membrane reactor
;  
numerical modelling
;  
biogas
;  
experimental
;  
hydrogen production
Subject: 
Engineering  -   Electrical and Electronic Engineering

I. Introduction

The purpose of this project is to develop experimental and mathematical modelling studies for a fixed-bed membrane reactor that produces hydrogen from biogas, determine the design and operating parameters that maximize system performance, and integrate the membrane reactor with a PEM fuel cell to evaluate the combined heat and power (CHP) system.
Fossil fuels currently supply the majority of global energy, but their rapid depletion and associated environmental consequences necessitate a transition to cleaner energy carriers. Hydrogen is widely regarded as the most suitable clean energy carrier owing to its high energy content and zero-emission combustion. Among the various hydrogen production pathways, thermochemical methods applied to biogas (a mixture primarily composed of CH₄ and CO₂ obtained by anaerobic digestion of biomass) offer a promising and near-term viable route.
Conventional steam–methane reforming (SMR) reactors dominate industrial hydrogen production but suffer from thermodynamic equilibrium limitations, high operating temperatures, carbon deposition, and the need for downstream purification units. Membrane reactors overcome these drawbacks by combining reaction and separation in a single compact unit, enabling higher conversion at lower temperatures. This project therefore focuses on the development and analysis of a fixed-bed membrane reactor for biogas-based hydrogen production and its thermodynamic integration with a PEM fuel cell system.
The primary mathematical modelling framework employed in this work consists of coupled ordinary differential equations (ODEs) representing one-dimensional mass, energy, and momentum balances along the reactor axis. These are solved using MATLAB. The system-level CHP model is developed in Aspen Plus, with the two platforms linked via MS Excel. No machine-learning or artificial intelligence components are incorporated; all modelling is physics-based and relies on established transport phenomena, reaction kinetics, and electrochemical relations.

A. Membrane Reactors for Hydrogen Production

Hydrogen is recognized as the most suitable clean energy carrier with a wide application range. Interest in hydrogen production has been growing continuously, driven by rapid developments in proton exchange membrane (PEM) fuel cell technology. Various methods are available to produce high-purity hydrogen, including steam–methane reforming of hydrocarbons, gasification of coal and biomass, electrolysis of water, and direct photolysis, thermolysis, and photo-fermentation using solar energy. Although producing hydrogen from water via electrolysis powered by renewable electricity is an attractive option, thermochemical production remains the more realistic near-term route due to the high cost and technological limitations of electrolysis [1,2,3,4,5].
Today, more than 80% of industrially produced hydrogen is derived from hydrocarbons through conventional steam–methane reformers that carry out the reactions in Equations (1)–(3). However, these systems require additional downstream separation units such as pressure swing adsorption (PSA), membrane modules, or cryogenic distillation to purify the product hydrogen [6].
C H ₄ + H ₂ O   ⇌   C O + 3 H ₂
C O + H ₂ O   ⇌   C O ₂ + H ₂
C H ₄ + 2 H ₂ O   ⇌   C O ₂ + 4 H ₂
Due to the rapid depletion of fossil fuels and the need to reduce associated negative impacts, biogas obtained by anaerobic digestion of biomass (wastewater, municipal waste, etc.) has come to the fore as a fuel. Biogas primarily consists of methane (CH₄, 35–75%) and CO₂ (25–55%), with minor components such as N₂, H₂, H₂S, H₂O, CO, NH₃, siloxanes, and aromatics [8]. Hydrogen production from biogas requires, in addition to reactions (1)–(3), the dry reforming reaction:
C H ₄   +   C O ₂   ⇌   2 C O   +   2 H ₂
Conventional SMR technology suffers from several important disadvantages [9]:
  • Thermodynamic chemical-equilibrium constraints that limit conversion;
  • High internal diffusion resistance arising from large catalyst particles;
  • Carbon deposition and catalyst deactivation;
  • Demanding heat-transfer requirements and expensive high-temperature alloy tubes; and
  • NOₓ and CO₂ emissions from the furnace.
Membrane reactors overcome these limitations by combining reaction and separation in a single compact unit. Their key advantages include: production of pure hydrogen by means of a selective-permeable membrane, which shifts the equilibrium fully forward and allows operation at lower temperatures; improved heat and mass transfer (depending on reactor type); and the possibility of incorporating CO₂ sorbents to further enhance purity [6,9].
Membranes used in membrane reactors are fundamentally barriers that prevent certain components of a feed-gas mixture from passing through. Dense metal membranes are currently the most suitable materials owing to their exceptionally high hydrogen selectivity, achieved through a six-step solution–diffusion mechanism:
  • Dissociation of H₂ at the gas/metal interface;
  • Adsorption of atomic hydrogen on the membrane surface;
  • Dissolution into the Pd matrix;
  • Diffusion through the membrane;
  • Recombination into H₂ molecules; and
  • Desorption [10].
Among membrane reactor types (fixed-bed, fluidised-bed, micro-reactors), fixed-bed (packed-bed) membrane reactors are the most widely used. The catalyst is packed on either the tube side or the shell side, and the produced hydrogen diffuses through the membrane and exits from the permeate side. The hydrogen driving force is the partial pressure difference between the retentate and permeate sides [15,16].

B. Experimental Studies

Experimental studies in the literature have concentrated on the type and preparation method of the membrane, catalyst, and support material, and their effects on reactor performance. Representative examples are summarized below.
Wieland et al. [18] investigated the effects of different metal membranes (Pd₇₅Ag₂₅, Pd₆₀Cu₄₀, and coated vanadium Pd/V/Pd) on hydrogen permeability, recovery, and fuel conversion, finding that Pd/V/Pd exhibited the highest permeability but was unstable above 4.2 bar, while Pd₆₀Cu₄₀ offered the best stability.
Li et al. [19,20] developed a pre-treatment method for porous stainless-steel supports and prepared thin Pd-based composite membranes by electroless plating. Among three membranes tested, Pd/Ceramic/PSS (5 µm) showed the highest hydrogen permeance (95 m³/m²) at 823 K and 3.4 bar.
Ryi et al. [21] developed an EDTA-free electroless Pd deposition method on an alumina-modified porous Hastelloy substrate, achieving a hydrogen permeation flux of 0.33 mol/m² at 823 K with a 100 kPa pressure difference.
Iulianelli et al. [22] produced a Pd-Au membrane by electroless plating and tested it in a membrane reactor for methane steam reforming, obtaining 40% methane conversion and 35% hydrogen recovery at 420 °C and 300 kPa. Kim et al. [23] achieved H₂/N₂ selectivity of 145 using a Ru/Al₂O₃ catalyst and a Pd-based composite membrane.

C. Mathematical Modelling Studies

The literature contains a number of one-dimensional modelling studies for fixed-bed membrane reactors. Key contributions are summarised in Table 1 and described below.
Patel and Sunol [24] developed a mathematical model for a three-channel membrane reactor and analysed the effects of fuel concentration, steam-to-methane ratio, inlet temperature, and co-current/counter-current sweep configurations on methane conversion and hydrogen recovery.
Brunetti et al. [25] modelled the water–gas shift (WGS) reaction in a Pd-alloy membrane reactor under non-isothermal conditions, examining CO conversion and H₂ recovery for two different feed streams.
Iulianelli et al. [26] mathematically modelled a Pd-Ag membrane reactor for methane steam reforming at relatively low temperatures (400–500 °C) and pressures (1–3 bar), obtaining 50% methane conversion and approximately 70% COₓ-free hydrogen recovery at 450 °C and 3 bar, compared with only 6% methane conversion in a conventional SMR.
Adrover et al. [27] developed a model for a multi-tubular membrane reactor for the WGS reaction and compared co-current and counter-current configurations.
Piemonte et al. [28] showed that placing the membrane only in the second half of the reactor (Lm/Ltotal = 0.5) yielded a higher hydrogen flux than a full-length membrane arrangement.
Boutikos and Nikolakis [29] performed a simulation study on the WGS membrane reactor, examining CO conversion, H₂ recovery, and permeate/retentate H₂ fluxes.
Abbasi et al. [30] developed a steady-state one-dimensional heterogeneous catalytic model for a Pd-Ag membrane reactor combined with chemical-looping combustion, finding improvements in methane conversion and hydrogen production of 7.54% and 25.48%, respectively, over conventional SMR.
Ghasemzadeh et al. [31] developed a 1-D isothermal model for a Pd membrane reactor for methanol steam reforming and reported 100% methanol conversion in the membrane reactor versus 91% in a conventional reactor.
Castillo et al. [32] modelled a fixed-bed membrane reactor for biogas steam reforming and validated it experimentally, achieving 80% hydrogen recovery when the reaction-side pressure was raised to 0.4 MPa at 723 K. Marcoberardino et al. [33] developed a 1-D finite-volume model and identified 873 K and 500 kPa as the optimal operating conditions, with 47.4% methane conversion and 28.1% hydrogen recovery. Alavi et al. [34] developed a 1-D model and performed multi-objective optimization, reporting increases in CH₄ conversion and H₂ recovery of 19.8% and 6.8%, respectively.

C. Membrane Reactor; Fuel Cell Applications

The hydrogen demand driven by PEM fuel cell technology is growing continuously. PEM fuel cells require very pure hydrogen and have extremely low CO tolerance, making the membrane reactor; highly attractive for integration.
Arsalis et al. [35] modelled a HT-PEMFC system with a conventional SMR and found a maximum cogeneration efficiency of 83.08%. Herdem et al. [36] modelled an integrated methanol reformer–PEM fuel cell system and conducted a parametric study. Nalbant et al. [37] performed energy and exergy analyses of an SMR-based HT-PEMFC CHP system.
Campanari et al. [38] compared three hydrogen production options for fuel cells (conventional SMR, autothermal reforming, and innovative membrane reactor) and found that the membrane reactor provided 43% electrical efficiency; approximately 10% higher than the conventional alternatives. Lattner and Harold [39] demonstrated that a membrane reactor eliminates the need for a separate WGS unit, achieving 97% hydrogen recovery.
Only a single study in the literature integrates a membrane reactor with a fuel cell in a CHP system: Ribeirinha et al. [40] developed a 3-D non-isothermal Ansys™ model of a fixed-bed membrane reactor coupled with a fuel cell, reporting a hydrogen permeability of 2.94×10⁻⁶ mol·m·s⁻¹·m⁻²·bar⁻⁰·⁸ at 473 K and highlighting the need for further research. No thermodynamic CHP system model for such an integrated system has been reported, which constitutes one of the main original contributions of the present project.

D. Problem Definition

The core engineering problem addressed in this project is the efficient production of pure hydrogen from biogas using a compact membrane reactor, and the subsequent integration of this reactor with a PEM fuel cell to generate electricity and useful heat in a CHP configuration.
Physical description of the system: The system consists of a tubular fixed-bed membrane reactor in which biogas (primarily CH₄ and CO₂) and steam enter the reaction (retentate) side, where they undergo steam reforming and water–gas shift reactions over a Ni/Al₂O₃ catalyst. A Pd-Au membrane selectively permeates hydrogen from the retentate to the permeate (separation) side, where a nitrogen sweep gas carries it away. The purified hydrogen is then fed to the anode of a PEM fuel cell stack. Cathode air, a catalytic burner for the retentate off-gas, and heat exchangers for steam generation and hot-water production complete the CHP system.
Input–output relationships: Inputs to the membrane reactor include the biogas flow rate and composition, steam-to-carbon (S/C) ratio, reaction pressure, temperature, and flow direction (co-current or counter-current). Outputs are biogas conversion, hydrogen recovery, and hydrogen yield. Inputs to the CHP system additionally include fuel cell operating temperature, anode stoichiometric ratio, and current density; outputs are electrical efficiency and cogeneration efficiency.
System boundaries: The membrane reactor boundary encompasses the tube and shell sides of the reactor, including the Pd-Au membrane. The CHP system boundary encompasses the reactor, pre-heater, catalytic burner, PEM fuel cell stack, and heat exchanger for hot-water production.

III. Methodolgy

A. Selected Analysis Method: One-Dimensional Multi-Physics Modelling

A one-dimensional (1-D) steady-state heterogeneous model is selected for the fixed-bed membrane reactor. This approach assumes that all concentration, temperature, and pressure variations occur only in the axial direction, and that axial dispersion is negligible. The model couples mass balances, energy balances, a momentum equation (pressure drop), and reaction kinetics; hence the designation ‘multi-physics’. The governing equations are discretized over differential control volumes of length dz and solved as a system of coupled first-order ODEs using MATLAB.

B. Mass Balance

Mass balances for each species j on the retentate (reaction) side and the permeate (separation) side are written for a differential control volume of length dz.
Retentate side (j = CH₄, H₂O, CO, CO₂):
d F ⱼ / d z = ρ b · A c · Σ ᵢ ν ᵢ , ⱼ · R ᵢ
Retentate side (j = H₂):
d F H ₂ / d z = ρ b · A c · Σ ᵢ ν ᵢ , H ₂ · R ᵢ − J H ₂ · ( 2 π · r ᵢ , ₀ )
Permeate side (j = H₂):
d F H ₂ , p e r m e a t e / d z = J H ₂ · ( 2 π · r ᵢ , ₀ )
Permeate side (j = N₂):
d F N ₂ / d z = 0
Here Fⱼ is the molar flow rate of species j, ρb is the bed density, Ac is the retentate cross-sectional area, νᵢ,ⱼ is the stoichiometric coefficient of species j in reaction i, Rᵢ is the reaction rate of reaction i, JH₂ is the hydrogen flux through the membrane, and rᵢ,₀ is the membrane inner radius.
The hydrogen flux through the membrane is calculated using Sieverts’ Law:
J H ₂ = ( B H ₂ / δ ) · ( P ⁰ · ⁵ H ₂ , r e t − P ⁰ · ⁵ H ₂ , p e r m )
where BH₂ is the hydrogen permeability, δ is the membrane thickness, and PH₂,ret and PH₂,perm are the hydrogen partial pressures on the retentate and permeate sides, respectively. BH₂ is expressed via an Arrhenius relationship:
B H ₂ = B ⁰ H ₂ · e x p ( − E m / ( R · T ) )
where Em is the activation energy for permeation, T is temperature, and R is the universal gas constant.

C. Energy Balance

Non-isothermal energy balances for the retentate and permeate sides are:
Σ ⱼ F ⱼ C p ⱼ ( r e t ) · d T r e t d z = ρ b · A c · Σ ᵢ ( ν ᵢ , ⱼ R ᵢ · ( − Δ h ᵢ ) ) + 2 π · r o , o · U s h e l l · ( T w a l l − T r e t ) − 2 π · r i , o · U t u b e · ( T r e t − T p e r m )
Σ ⱼ F ⱼ C p ⱼ ( p e r m ) · d T p e r m / d z = 2 π · r i , o · U t u b e · ( T r e t − T p e r m )
where Cpⱼ is the specific heat at constant pressure for species j, Δhᵢ is the enthalpy change of reaction i, and U is the overall heat transfer coefficient.

D. Pressure Drop

The pressure drop in the retentate side is calculated using the Ergun equation [43]:
d P / d z = [ 150 · ( 1 − ε ) ² · µ g · u s / ( d p ² · ε ³ ) ] + [ 1.75 · ( 1 − ε ) · ρ g · u s ² / ( d p · ε ³ ) ] × 10 ⁻ ⁵
where P is pressure, ε is bed void fraction, dp is catalyst particle diameter, µg is the gas mixture viscosity, ρg is the gas mixture density, and us is the superficial velocity. Pressure in the permeate side is assumed constant.
Physical property correlations for gas mixture density, heat capacity, and viscosity used in the model are listed in Table 2.

E. Reaction Kinetics

The kinetic rate expressions reported by Xu and Froment [45] for reactions (1)–(3) are used:
R ₁ = A ₁ · e x p ( − E ₁ / R T ) · [ P C H ₄ · P H ₂ O − P H ₂ ³ · P C O / K p , 1 ] / ( P H ₂ ² · ⁵ · D E N ² )
R ₂ = A ₂ · e x p ( − E ₂ / R T ) · [ P C O · P H ₂ O − P H ₂ · P C O ₂ / K p , 2 ] / ( P H ₂ · D E N ² )
R ₃ = A ₃ · e x p ( − E ₃ / R T ) · [ P C H ₄ · P H ₂ O ² − P H ₂ ⁴ · P C O ₂ / K p , 3 ] / ( P H ₂ ³ · ⁵ · D E N ² )
where Aᵢ, Kp,i, and Eᵢ are the pre-exponential factor, equilibrium constant, and activation energy of reaction i, respectively, taken from [45,46,47,48]. Pⱼ denotes the partial pressure of species j (CH₄, CO, H₂, CO₂, H₂O). The denominator term DEN accounts for adsorption of species on the active catalyst sites:
D E N = 1 + K C H ₄ · P C H ₄ + K C O · P C O + K H ₂ · P H ₂ + K H ₂ O · P H ₂ O / P H ₂
The adsorption equilibrium constants Kⱼ are calculated using the van’t Hoff equation [45]:
K ⱼ = K ⱼ , ₀ · e x p ( − Δ h ⱼ / ( R · T ) )

F. PEM Fuel Cell Model

The PEM fuel cell model is based on electrochemical half-reactions at the anode, cathode, and overall:
H ₂ → 2 H ⁺ + 2 e ⁻
½ O ₂ + 2 H ⁺ + 2 e ⁻ → H ₂ O
H ₂ + ½ O ₂ → H ₂ O
The single-cell voltage is calculated as:
V c e l l = V N e r n s t − η a c t , a − η a c t , c − η o h m
where VNernst is the Nernst voltage, ηact,a and ηact,c are the anode and cathode activation overpotentials, and ηohm is the ohmic overpotential:
η a c t , a = ( R · T c e l l ) / ( α a · F ) · s i n h ⁻ ¹ ( i / ( 2 · i ₀ , a ) )
η a c t , c = ( R · T c e l l ) / ( α c · F ) · s i n h ⁻ ¹ ( i / ( 2 · i ₀ , c ) )
η o h m = i · A S R o h m i c
The electrical power output of the fuel cell stack is:
W f c = i · V s t a c k · A a c t i v e
The general steady-flow energy equation applied to each system component is:
0 = Q − W + ṁ · h i n − ṁ · h o u t

G. CHP System Performance Metrics

The electrical efficiency of the CHP system is defined as the ratio of net electrical power output to the lower heating value (LHV) of the biogas input:
η e l e c t r i c a l = W n e t , e l e c t r i c a l / ( ṁ b i o g a s , i n · L H V b i o g a s )
The cogeneration efficiency additionally accounts for heat recovered by the heat exchanger:
η c o g e n = ( W n e t , e l e c t r i c a l + Q h e a t e x c h a n g e r ) / ( ṁ b i o g a s , i n · L H V b i o g a s )

H. Software Tools

The following software platforms are used in this project:
• MATLAB: Solves the 1-D multi-physics ODE system for the membrane reactor model (Equations 8–21). All conservation equations, pressure drop, and kinetics are implemented here.
• Aspen Plus: Used for system-level CHP modelling and simulation. The membrane reactor MATLAB model is coupled to Aspen Plus via MS Excel using a co-simulation approach.
• MS Excel: Acts as the data-exchange interface between MATLAB and Aspen Plus.

I. Experimental Setup

Experimental studies are carried out in collaboration with the Institute on Membrane Technology (ITM) in Italy. The experimental setup for hydrogen production from biogas in a membrane reactor is schematically described in the original proposal. The main components are:
  • A tubular membrane reactor with a Pd-Au membrane on a porous stainless-steel support.
  • A Ni/Al₂O₃ catalyst packed on the tube or shell side.
  • Two electrical heating bands to reach target temperatures (300–420 °C) and a thermocouple for temperature measurement.
  • Mass flow controllers to regulate biogas and de-ionised water (as steam, after a pre-heater) at defined S/C ratios.
  • N₂ sweep gas delivered co-currently or counter-currently to the permeate side.
  • A condenser to separate unconverted water from the retentate stream.
  • A gas chromatograph to analyse both retentate and permeate gas compositions.
A pure N₂ leak test is performed at ambient temperature before each experiment. Experiments are repeated ten times at identical conditions to verify reproducibility.

J. Permeability and Reaction Tests

Following the methodology of Bagnato et al. [42], two sets of tests are conducted:
  • Permeability tests: Conducted at temperatures 350–450 °C and reaction-side pressures 150–300 kPa. The reactor is heated at 2 °C/min in a N₂ atmosphere, and the test continues until no N₂ is detected in the permeate (i.e., the membrane is fully H₂-selective).
  • Reaction tests: Examine the effects of temperature, reaction pressure, S/C ratio, and flow direction on biogas conversion (Equation 5), hydrogen recovery (Equation 6), and hydrogen yield (Equation 7).
The performance indicators are defined as:
X f u e l = ( F f u e l , i n − F f u e l , o u t ) / F f u e l , i n × 100
R H ₂ = F H ₂ , p e r m e a t e , o u t / ( F H ₂ , p e r m e a t e , o u t + F H ₂ , r e t e n t a t e , o u t ) × 100
Y H ₂ = F H ₂ , p e r m e a t e , o u t / F f u e l , i n × 100

K. Mathematical Modelling Steps

The MATLAB membrane reactor model is built incrementally to minimize the risk of convergence failure. Physical phenomena are added one at a time in the following order:
  • Mass transport
  • Pressure drop
  • Energy transport
  • Reaction kinetics
Once the MATLAB model is validated against experimental data (target: ±5% agreement), it is integrated into the Aspen Plus CHP model via MS Excel.

IV. Result and Discussıon

A. Expected Simulation Results and Success Criteria

The 1-D multi-physics MATLAB model is expected to converge successfully for all targeted operating conditions. The convergence criterion is that the relative error between successive iterations (defined as the absolute difference between two consecutive iteration results divided by the first iteration result) must be less than 0.01% at every axial node. The model will yield axial profiles of species concentration, temperature, pressure, and velocity for both the retentate and permeate sides.

B. Membrane Reactor Mathematical Model

The 1-D multi-physics MATLAB model is expected to converge successfully for all targeted operating conditions. The convergence criterion is that the relative error between successive iterations (defined as the absolute difference between two consecutive iteration results divided by the first iteration result) must be less than 0.01% at every axial node. The model will yield axial profiles of species concentration, temperature, pressure, and velocity for both the retentate and permeate sides.

C. Experimental Results

Permeability and reaction tests are to be carried out without membrane leakage or sealing failure at the specified conditions (T = 300–450 °C, P = 150–300 kPa, S/C = 2–4, co-current and counter-current flow). Based on literature precedents [22,32,33], the following performance ranges are anticipated:
  • Biogas conversion: 40–80%, increasing with temperature and pressure.
  • Hydrogen recovery: 35–80%, strongly dependent on permeate-side pressure driving force.
  • Hydrogen yield: 20–60%, improving with higher S/C ratios.

D. Model Validation and Parametric Study

The 1-D model predictions are expected to agree with experimental results within ±5%. The parametric study will then identify the values of operating temperature, reaction pressure, S/C ratio, and flow direction that maximise reactor performance (biogas conversion, hydrogen recovery, and hydrogen yield). Based on findings from Castillo et al. [32] and Marcoberardino et al. [33], the optimal operating region is expected to be in the range of 600–873 K and 300–700 kPa, with counter-current flow providing superior hydrogen recovery.

E. CHP System Model

The integrated membrane reactor–PEM fuel cell CHP model in Aspen Plus is expected to converge to a feasible operating point under baseline conditions. The model will produce the electrical efficiency and cogeneration efficiency of the system, along with key intermediate results such as the hydrogen production rate and fuel cell power output.

F. CHP Parametric Study

The parametric study on the CHP system will examine the effects of fuel cell operating temperature, reactor operating temperature, reaction pressure, S/C ratio, and anode stoichiometric ratio on electrical efficiency and cogeneration efficiency. Based on the study of Campanari et al. [38], the membrane reactor–based CHP system is expected to achieve an electrical efficiency of approximately 43%, approximately 10% higher than a conventional SMR-based system. The cogeneration efficiency is anticipated to be in the range of 75–85%, consistent with the findings of Arsalis et al. [35].

G. Comparison with Conventional Technology

The final work package will compare the biogas-fed membrane reactor system with a conventional SMR-based system for PEM fuel cell applications. The membrane reactor is expected to demonstrate superior fuel conversion, higher hydrogen recovery, and a more compact system configuration. The improvements in performance will be explained on the basis of transport phenomena and thermodynamics.

H. Limitations

The 1-D modelling approach assumes radially uniform concentration, temperature, and pressure distributions, which may introduce inaccuracies at high heat fluxes or large-diameter reactors. Carbon deposition and catalyst deactivation are not included in the base model. Membrane degradation over time is not addressed in the mathematical model, though it will be monitored experimentally. The thermodynamic CHP model does not include dynamic or start-up effects.

I. Comparison with Literature

The proposed model extends the work of Castillo et al. [32] by including a fully non-isothermal energy balance and by integrating the reactor model into a CHP system. It also goes beyond Ribeirinha et al. [40], who modelled an integrated system but did not perform a systematic thermodynamic parametric study. The experimental component provides direct validation data under biogas conditions, which is absent from all modelling-only studies in the literature.

IV. Conclusion

This project addresses the development and analysis of a fixed-bed Pd-Au membrane reactor for the production of pure hydrogen from biogas, and its thermodynamic integration with a PEM fuel cell in a combined heat and power system. The work encompasses both experimental (permeability and reaction tests at ITM, Italy) and mathematical modelling (1-D multi-physics MATLAB model and system-level Aspen Plus CHP model) components.
The membrane reactor approach offers significant advantages over conventional SMR technology: it produces COₓ-free hydrogen directly in a single compact unit, operates at lower temperatures, and requires no downstream purification. When integrated with a PEM fuel cell, it is expected to deliver electrical efficiencies approximately 10% higher than conventional systems and cogeneration efficiencies in the range of 75–85%.
From a scientific standpoint, the project makes the following original contributions:
  • The first detailed multi-physics 1-D mathematical model for a biogas-fed membrane reactor, validated against experimental data;
  • The first thermodynamic CHP system model combining a biogas membrane reactor with a PEM fuel cell; and
  • A systematic parametric analysis of both the reactor and the integrated CHP system.
The results are expected to provide scientifically grounded design guidelines for biogas membrane reactors, contribute to the commercialization pathway of this technology, and reduce dependence on fossil fuels for hydrogen production. The project will generate publications in SCI or SCI-Expanded indexed journals and presentations at international conferences, disseminating the findings to the relevant scientific community. The doctoral student involved will gain research experience in both modelling and experimentation, including a research stay at ITM in Italy.

V. Future Work

  • Long-term durability tests of the Pd-Au membrane under biogas reforming conditions to assess membrane stability and guide commercialisation.
  • Extension of the 1-D model to a 2-D or 3-D computational fluid dynamics (CFD) model to capture radial gradients and more accurate transport phenomena.
  • Incorporation of catalyst deactivation kinetics due to carbon deposition and sulphur poisoning (H₂S present in raw biogas) into the reactor model.
  • Techno-economic analysis of the membrane reactor–PEM fuel cell CHP system to evaluate its commercial viability relative to conventional systems.
  • Exergy analysis of the CHP system to identify sources of irreversibility and guide thermodynamic optimisation.
  • Investigation of alternative membrane materials (e.g., Pd-Ag, Pd-Cu) and support geometries to further improve permeability and reduce material costs.

Acknowledgments

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Table 1. .
Table 1. .
Reference Reference Method Key Finding
Patel & Sunol [24] 3-channel MR 1-D steady-state Parametric study of fuel conc., S/C ratio, temperature, flow direction
Brunetti et al. [25] Pd-alloy MR (WGS) 1-D non-isothermal CO conversion & H₂ recovery for two feed compositions
Iulianelli et al. [26] Pd-Ag MR (SMR) 1-D, validated 50% CH₄ conv. vs 6% in conventional at 450 °C, 3 bar
Adrover et al. [27] Multi-tubular MR 1-D, two configs Counter-current shows higher temp. rise; co-current less so
Castillo et al. [32] Fixed-bed MR (biogas) 1-D, validated 80% H₂ recovery at 723 K, 0.4 MPa reaction-side pressure
Marcoberardino et al. [33] Fixed-bed MR 1-D finite-volume Best condition: 873 K, 500 kPa; 47.4% CH₄ conv., 28.1% H₂ rec.
Alavi et al. [34] Fixed-bed MR 1-D, optimised +19.8% CH₄ conv., +6.8% H₂ recovery after optimisation
Table 2. .
Table 2. .
Property Correlation
Gas mixture density ρ = P · M w / ( R · T ) , where Mw is the molecular weight of the gas mixture
Gas heat capacity C p , j = C ₁ + C ₂ [ C ₃ / T / s i n h ( C ₃ / T ) ] ² + C ₄ [ C ₅ / T / c o s h ( C ₅ / T ) ] ² , where C values are species-specific constants
Gas viscosity µ g , j = C ₁ · T C ₂ / ( 1 + C ₃ / T + C ₄ / T ² ) , where C values are species-specific constants
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