Concentration In Product Gas Research Articles

Techno-economic analyses of Sulfinol-based absorber-stripper configurations for improving the energy consumption of natural gas sweetening process

This work presents a two-step method to reduce the energy consumption (in terms of the reboiler duty) of a natural gas sweetening process via a physical-chemical solvent mixture (Step 1) followed by a techno-economic analysis of 15 different absorber-stripper configurations (Step 2). Initially, an amine-based sweetening process using a H2S-free sour gas was simulated on Aspen HYSYS and the simulation results were validated against real plant data. In Step 1, different ratios of Sulfinol-M and Sulfinol-D based sweetening process were simulated and the superior physical-chemical solvent mixture that provides the lowest reboiler duty while meeting the sweet gas CO2 product concentration specification (i.e., less than 2 mol.%) is the Sulfinol-M solvent that contains 38 wt.% methyl diethanolamine (MDEA), 40 wt.% Sulfolane, and 22 wt.% water. This Sulfinol-M based model is then optimized via a parametric analysis to further improve its performance in terms of the reboiler duty prior to Step 2. The optimized Sulfinol-M based model achieved 65% saving in the reboiler duty while fulfilling the CO2 concentration specification in product gas relative to the base case. In Step 2, four main absorber-stripper configurations, namely absorber intercooling (AI), lean amine stream split flow (LASSF), rich amine stream split flow (RASSF), and mechanical vapor recompression (MVR) along with their 11 possible combinations were simulated in an attempt to decrease the energy consumption of the process and hence, ranked based on their total cost of production (TCOP). The results revealed that the integration of LASSF + RASSF provides the best option as it achieved the lowest TCOP of $4.60 M while fulfilling the CO2 concentration in product gas and contributed to 6.39% savings in the reboiler duty compared to the optimized conventional Sulfinol-M based model.

A continuous and high-efficiency process to separate coal bed methane with porous ZIF-8 slurry: Experimental study and mathematical modelling

Coal bed methane has been considered as an important energy resource. One major difficulty of purifying coal bed methane comes from the similar physical properties of CH4 and N2. The ZIF-8/water-glycol slurry was used as a medium to separate coal bed methane by fluidifying the solid adsorbent material. The sorption equilibrium experiment of binary mixture (CH4/N2) and slurry was conducted. The selectivity of CH4 to N2 is within the range of 2–6, which proved the feasibility of the slurry separation method. The modified Langmuir equation was used to describe the gas-slurry phase equilibrium behavior, and the calculated results were in good agreement with the experimental data. A continuous absorption–adsorption and desorption process on the separation of CH4/N2 in slurry is proposed and its mathematical model is also developed. Sensitivity analysis is conducted to determine the operation conditions and the energy performance of the proposed process was also evaluated. Feed gas contains 30 mol% of methane and the methane concentration in product gas is 95.46 mol% with the methane recovery ratio of 90.74%. The total energy consumption for per unit volume of product gas is determined as 1.846 kWh Nm−3. Experimental results and process simulation provide basic data for the design and operation of pilot and industrial plant.

Comparison of gasification performances between raw and torrefied biomasses in an air-blown fluidized-bed gasifier

A CFD-DEM model already developed by the authors has been extended to directly compare the gasification performances between raw and torrefied grassy biomasses in an air-blown fluidized-bed gasifier. The bed material is non-calcined olivine which acts as the solid heat carrier. Furthermore, effects of four key operating parameters (i.e., gasification temperature Tr, excess air ratio λ, steam addition, and biomass feed location) are also systematically examined. The results are analyzed both qualitatively and quantitatively by various indices: the fluidization behavior, bed pressure drop, product gas concentration profiles, total gas yield, and carbon conversion (CC). For both raw and torrefied biomasses, increasing Tr can enhance both the total gas yield and CC; rising λ decreases the H2 yield but increases the CO2 yield and CC; the steam addition has a positive influence on the total gas yield and CC and it can also be used to adjust the H2/CO ratio in the product gas; both the total gas yield and CC decrease with raising the height of the biomass feed location. For all cases, the torrefied biomass obtains a lower H2 yield and CC but a higher CO yield than its raw counterpart under the same operating conditions, suggesting that torrefied biomass requires a longer conversion process compared with raw fuel. Moreover, the gasification behavior of torrefied biomass is more dependent on the fuel feed location than raw fuel and such knowledge is important for the optimal design of fluidized-bed gasifier for torrefied feedstock.

Some issues of industrial scale boron isotopes separation by the laser assisted retarded condensation (SILARC) method

Abstract More cheap production of boron isotopes is needed to provide further progress in nuclear engineering, microelectronics, and nuclear medicine. In this paper feasibility of boron isotopes separation scheme by laser assisted retarded condensation (SILARC) on industrial scale is investigated. Proposed industrial scale facility has a modular structure. Each module corresponds to irradiation cell with nozzle and skimmer installed on the opposite sides. BCl 3 was chosen as a target gas mixed at low molar fraction with argon carrier gas. Photo-absorption line, corresponding to 11 B 35 Cl 2 35 ; 37 Cl , can be excited by CO 2 laser emission line 10P(4), but corresponding to boron-10, has no overlap with CO 2 laser emission spectrum. Therefore, core gas flow will be enriched by boron-10. It is shown that continuous gas flow irradiation is preferable. In this case excitation time (gas flow length) is desirable to make as long as possible (its upper limit is constrained by optimal pressure and temperature range and condensation rate) in order to increase excitation probability. Saving of expensive laser photons is implemented by fabrication of irradiation cell as resonator. Increasing of isotope separation rate at smaller energy expenses can be provided by appropriate choice of gas flow expansion conditions, which include concentration of target gas, carrier gas choice, gas flow and ambient gas pressure and temperature. Related optimization criterion was introduced. It was found, that even at optimal conditions isotopes separation rate is rather small, which suggests, that isotope separation should be extracted iteratively. It was considered one of possible schemes for iterative isotope recovery on industrial scale. Corresponding final equilibrium isotopic concentration in product gas is rather small. Nevertheless, this method remains attractive, because energy spent per separated isotope is still significantly smaller than other prospective methods (about three times smaller than in Molecular Obliteration Laser induced Isotope Separation (MOLIS)).

Double-stage chemical looping combustion combined with sorption enhanced natural gas steam reforming process for hydrogen and power cogeneration: Thermodynamic investigation

Chemical looping combustion (CLC) is a high efficiency and clean power generation system. With the principle of energy cascade utilization and methodology of system integration, a cogeneration system for hydrogen and power from natural gas was proposed by thermally coupling high-pressure (HP) and low-pressure (LP) double-stage CLC and sorption-enhanced steam reforming unit. The effects of operating parameters on the different performances indicators (including product gas concentration, H2 yield, and CH4 conversion) were investigated. The proposed novel process and a benchmark cogeneration process (i.e., natural gas CLC combustion unit along with sorption-enhanced steam reforming process) were both evaluated and compared from a thermodynamic point of view.Results show that increasing the FuelHP/C and FuelLP/C ratio (i.e., natural gas as fuel for HP-/LP-CLC divided by the feed molar flow for reformer ratio) leads significantly in improving the H2 yield and CH4 conversion. The addition of Ca-based sorbent and steam in reformer also has positive impacts on system performances. Under the conditions of FuelHP/C=0.42 and FuelLP/C=0.70, the novel process has a H2 concentration of 92%, H2 yield of 3.64, and CH4 conversion of 75%, while for the benchmark process, the H2 concentration is 89%, H2 yield is 3.55, and has a CH4 conversion of 69%. In addition, the optimized process minimizes exergy destruction and increases exergy efficiency over 6% when compared to the base-case system.

Floating-fixed-bed-gasification: From Vision to Reality

Over the last years, numerous gasification concepts have been developed to a reliable and commercially available state leading to a strongly increasing numbers of built plants. One of these describes a novel way in the thermochemical gasification of biomass by using a unique reactor design and operational mode – the floating-fixed-bed reactor. Comparable gasification concepts show bottlenecks in downsizing possibilities and tar concentration in product gas from fluidized bed gasification as well as problems of channeling or compaction of the fuel bed in fixed-bed systems. The idea of the floating-fixed-bed reactor is to build up a stable bulk bed, which is floating on the inlet gas stream from pyrolysis and oxidation. Without uncontrolled particle movement in the reduction reactor and only relative movement of the fuel particles within the bed, relatively long gas residence could be provided, resulting in low tar concentrations in the product gas. The technology has proven the potential to bypass issues of comparable gasification technologies and verified the advantages of the innovative reactor design in several long-term test runs on pilot plants and also commercial plants. Beside continuous improvement of the gasification technology, the current development aims for upscale possibilities and increased fuel flexibility.

One-Dimensional Modeling of an Entrained Coal Gasification Process Using Kinetic Parameters

A one-dimensional reactor model was developed to simulate the performance of an entrained flow gasifier under various operating conditions. The model combined the plug flow reactor (PFR) model with the well-stirred reactor (WSR) model. Reaction kinetics was considered together with gas diffusion for the solid-phase reactions in the PFR model, while equilibrium was considered for the gas-phase reactions in the WSR model. The differential and algebraic equations of mass balance and energy balance were solved by a robust ODE solver, i.e., an semi-implicit Runge–Kutta method, and by a nonlinear algebraic solver, respectively. The computed gasifier performance was validated against experimental data from the literature. The difference in product gas concentration from the equilibrium model, and the underlying mechanisms were discussed further. The optimal condition was found after parameter studies were made for various operating conditions.

Novel sample preparation for operando TEM of catalysts

A new TEM sample preparation method is developed to facilitate operando TEM of gas phase catalysis. A porous Pyrex-fiber pellet TEM sample was produced, allowing a comparatively large amount of catalyst to be loaded into a standard Gatan furnace-type tantalum heating holder. The increased amount of catalyst present inside the environmental TEM allows quantitative determination of the gas phase products of a catalytic reaction performed in-situ at elevated temperatures. The product gas concentration was monitored using both electron energy loss spectroscopy (EELS) and residual gas analysis (RGA). Imaging of catalyst particles dispersed over the pellet at atomic resolution is challenging, due to charging of the insulating glass fibers. To overcome this limitation, a metal grid is placed into the holder in addition to the pellet, allowing catalyst particles dispersed over the grid to be imaged, while particles in the pellet, which are assumed to experience identical conditions, contribute to the overall catalytic conversion inside the environmental TEM cell. The gas within the cell is determined to be well-mixed, making this assumption reasonable.

An Unreacted Shrinking Core Model for Calcination and Similar Solid-to-Gas Reactions

A variation on the unreacted shrinking core model has been developed for calcination and similar non-catalytic solid-to-gas decomposition reactions in which no gaseous reactant is involved and the reaction rate decreases with increasing product gas concentration. The numerical solution of the model has been validated against an analytical solution for the isothermal case. The model parameters have been tuned using literature data for the thermal dehydration (calcination) of gibbsite to alumina over a wide range of temperatures, from 490 to 923 K. The model results for gibbsite conversion agreed well with the published experimental data. A reaction order with respect to water vapor concentration of n = −1 was found to give a good fit to the data and yield activation energies consistent with literature values. Predictions of the non-isothermal unreacted shrinking core model compare well with a more complex distributed model developed previously by the authors.

Modeling and simulation of high pressure water scrubbing technology applied for biogas upgrading

Depending on the end of use, the quality of biogas must be upgraded in order to utilize the maximum amount of energy necessary for proper applications. Upgrading biogas refers to the increase of methane concentration in product gas by removal of CO2, which increases its heating power. Several treatment technologies are available for biogas upgrading: high pressure water scrubbing (HPWS), pressure swing adsorption, membrane separation, chemical absorption, and gas permeation. Water absorption based on the physical effect of dissolving gases in liquids (HPWS) is a well-known technology and the most effective upgrading process, since provides a simultaneous removal of CO2 and H2S. This could ensure an increasing methane concentration and energy content per unit volume of biogas. In spite of this, few studies are published on biogas upgrading using pressurized water technology. In order to elucidate the performance of HPWS technology at industrial scale with the possibility of water regeneration and recirculation, effects of different operating parameters on the removal of undesired components from biogas were examined, based on modeling and simulation tools. For simulation, the commercial software tool Aspen Plus was applied. Equilibrium model was applied for simulating the absorption process. The simulation results were validated with experimental data from the literature. The results are summarized in terms of system efficiency, expressed as CH4 enrichment, methane loss, and CO2 removal. Finally, new data which can be further applied for scale-up calculations and techno-economic analysis of the HPWS process are provided.

Development of a Kinetic Model for Biomass Gasification in Dual Fluidized Bed Gasifier

Biomass gasification is a promising technology for the utilization of biomass. In this study, a mathematical model for biomass gasification in dual fluidized bed (DFB) has been developed. The fluidized bed with biomass gasification was simulated as a bubbling fluidized bed, which was further divided into a bubble phase and an emulsion phase for modeling. The modeling results were compared with the experimental data to be in high agreement. The influences of steam to biomass mass ratio (S/B) and gasification temperature on the performances of the product gas concentration, the CO/H2 and CO2/CO molar proportions were focused on.

Evaluation of Structural Changes in the Coal Specimen Heating Process and UCG Model Experiments for Developing Efficient UCG Systems

In the underground coal gasification (UCG) process, cavity growth with crack extension inside the coal seam is an important phenomenon that directly influences gasification efficiency. An efficient and environmentally friendly UCG system also relies upon the precise control and evaluation of the gasification zone. This paper presents details of laboratory studies undertaken to evaluate structural changes that occur inside the coal under thermal stress and to evaluate underground coal-oxygen gasification simulated in an ex-situ reactor. The effects of feed temperature, the direction of the stratified plane, and the inherent microcracks on the coal fracture and crack extension were investigated using some heating experiments performed using plate-shaped and cylindrical coal specimens. To monitor the failure process and to measure the microcrack distribution inside the coal specimen before and after heating, acoustic emission (AE) analysis and X-ray CT were applied. We also introduce a laboratory-scale UCG model experiment conducted with set design and operating parameters. The temperature profiles, AE activities, product gas concentration as well as the gasifier weight lossess were measured successively during gasification. The product gas mainly comprised combustible components such as CO, CH4, and H2 (27.5, 5.5, and 17.2 vol% respectively), which produced a high average calorific value (9.1 MJ/m3).

An Eulerian modeling approach of wood gasification in a bubbling fluidized bed reactor using char as bed material

We present an Eulerian multiphase approach for modeling the gasification of wood in fluidized beds. The kinetic theory of granular material is used to evaluate constitutive properties of the dispersed solid phase. Comprehensive models for wood pyrolysis, char gasification and homogeneous gas phase reactions are taken into account. The dispersed solid phase within the reactor is modeled as three continuous phases, i.e., one phase representing wood and two char phases with different diameters. In contrast to most other studies we investigate a fluidized bed which consists of wood and char particles without additional inert particles such as limestone or olivine. 2D simulation results for a lab-scale bubbling fluidized bed reactor are presented and compared with experimental data for product gas and tar concentrations and temperature. We investigate the influence of two different classes of parameters on product gas concentrations and temperature: (i) operating conditions such as initial bed height, wood feeding rate, and reactor throughput and (ii) model parameters like thermal boundary conditions, primary pyrolysis kinetics, and secondary pyrolysis model. Two different pyrolysis models are implemented and are compared against each other. The numerical results indicate (i) a relatively low influence of the investigated operating conditions on the main product gas components, (ii) a high sensitivity of main product gas components CO and CO 2 on the thermal boundary condition, and (iii) a very strong influence of operating conditions and model parameters on the tar content in the product gas.

Prediction and Measurement of the Product Gas Composition of the Ultra Rich Premixed Combustion of Natural Gas: Effects of Equivalence Ratio, Residence Time, Pressure, and Oxygen Concentration

The ultra rich combustion (partial oxidation) of natural gas to hydrogen and carbon monoxide is theoretically and experimentally investigated. The effect of the process parameters equivalence ratio, residence time, pressure, and composition of the oxidizer is explored. Computations are performed with the use of the chemical kinetics simulation package CHEMKIN. First, the ultra rich combustion process is modeled as a freely propagating flame in order to establish the rich flame propagation properties. An Arrhenius correlation of the laminar flame speed with the adiabatic flame temperature is found with activation temperature 20,000 K. Subsequently, perfectly stirred reactor (PSR) computations were performed. From these, it is concluded that optimal natural gas conversion to hydrogen and carbon monoxide requires a residence time of at least 50 ms and, depending on residence time, an equivalence ratio between 2 and 4. To reach chemical equilibrium in ultra rich mixtures, the residence time is very long (> 1000 ms). The model predictions are validated by experiments on ultra rich combustion of natural gas by means of air enriched to 40% oxygen concentration at up to 3 bar and 300 kW. The effect of equivalence ratio at residence time 50 ms was investigated. Good comparison was found between measurements and model predictions on carbon monoxide, hydrogen, and the soot precursor acetylene. It can be concluded that the model provides reliable information on product gas concentrations as a result of ultra rich combustion of natural gas.

Diesel Steam Reforming for PEM Fuel Cells

Different applications for the decentralized stationary or mobile power supply require the usage of liquid hydrocarbons such as fuel oil, diesel, or gas oil in fuel cell systems. Reducing the sulfur content of conventional liquid fuels such as diesel or gasoline below 10ppm, the usage of these fuels in fuel cell applications becomes increasingly promising. The first process step represents thereby the reforming, which can be carried out in different ways. One of the commonly favored gas process technologies is the steam reforming process, which is state of the art for natural gas applications. Using a proton exchange membrane (PEM) fuel cell requires a complex gas cleanup system. Using a pressurized steam reforming process offers a significant reduction of the whole system size by efficiently compressing the liquid educts. Complete PEM systems with steam reformers tend to have a higher efficiency than, for example, systems using the autothermal reforming process. Advanced diesel steam reformers for industrialization still have to be developed and improved. The Oel-Wärme-Institut gGmbH has successfully carried out research on steam reforming with variations of important parameters using a sulfur free reference fuel and desulfurized diesel. During the experiments, several parameters such as steam to carbon ratio, reformer inlet temperatures, catalysts, and fuels were varied. While running the process, a continuous product gas measurement was taken. The reformer is equipped with several thermocouples. Three of them are moveable to measure the temperature profile of the catalyst. The experiments show that product gas concentrations reach a nearly equilibrium concentration with reformer inlet temperatures ϑ>700°C of a reference fuel∕steam mixture. Hydrogen concentrations over 70% were feasible. Constant inlet temperatures of ϑ=850°C and a variation of the steam to carbon ratio only have a noticeable effect on the water gas shift equilibrium. After all experiments, carbon deposits were found in the steam reformer system and under some circumstances on the catalysts. Experiments with operating times of more than 20h were performed at a steam to carbon ratio of 4.5. The application of continuously desulfurized diesel fuel indicates a degradation of the catalyst after a few hours. For the overall system design of PEM fuel cell applications, an operation mode at a reduced steam to carbon ratio has to be developed.

Evaluation of Integrated Fuel Processor for Residential PEMFCs Cogeneration System

Natural gas fuel processor has been developed for 1 kW class residential PEMFCs system. Unit processes and auxiliary units are integrated into packaged hardware, which shows thermal efficiency of 78% as a HHV basis with methane conversion of 92% at rated load. After confirming the performance at rated load, partial load operations are carried out by investigating the composition of product gas and thermal efficiencies at discrete load levels. The start up time is about an hour for CO concentration in product gas below 10 ppm. Dynamic response of fuel processor with load fluctuation is investigated to establish the load change strategy. In the following paper, operation results of fuel processor as well as fuel processor failure analysis are presented to evaluate the developed fuel processor.

Ceria−Zirconia High-Temperature Desulfurization Sorbents

Ceria and ceria−zirconia desulfurization sorbents containing up to 20 mol % ZrO2 were prepared using a coprecipitation method. XRD analysis indicated the formation of solid solutions of ZrO2 in CeO2. ZrO2 addition produced larger specific surface area, improved sintering resistance, and increased the reducibility of the ceria. Desulfurization was studied using a laboratory-scale fixed-bed quartz reactor. Special precautions were taken to minimize interaction between sub-ppmv concentrations of H2S with stainless steel and eliminate contamination from residual sulfur in the reactor system. The performance of sorbents containing ZrO2 was superior to that of ZrO2-free sorbents. Product gas concentrations in the range of 0.1−0.2 ppmv H2S were achieved during the prebreakthrough period over the temperature range of 600−750 °C. In particular, the duration of the sub-ppmv prebreakthrough period lasted as much as twice as long when the sorbent contained 20 mol % ZrO2 compared to ZrO2-free CeO2.

수소생산을 위한 디젤 개질용 촉매와 반응특성에 관한 연구

디젤은 높은 volumetric density<TEX>$[VD,\;kg\;H_2/m^3]\;(>100)$</TEX>와 gravimetric density<TEX>$(GD,\;\%\;H_2)\;(>17)$</TEX>를 가지는 우수한 수소저장매체 중의 하나이다. (Liquid Hydrogen의 경우 VD와 GD가 각각 50, 18 정도) 본 연구는 이러한 디젤연료의 개질에 적합한 촉매선정 및 반응특성에 관한 연구를 실시하였다 촉매는 자체 선정한 3가지 촉매(NECS-1, NECS-2, NECS-3)와 2가지 상용촉매(FCR-HCl4, FCR-HC35. Sud-Chemie, Inc)에 대하여 조사하였다. 실험결과 NECS-1이 디젤개질에 가장 적합한 것으로 판단되었다. 이와 함께 촉매 층의 길이에 따른 온도 및 농도를 분석하였으며, 디젤개질을 위한 연료의 delivery 문제로 인한 촉매 층 내의 급격한 온도 변화특성을 확인할 수 있었다. 또한 촉매 층 상단부에서 발생한 발열량을 하단부의 흡열부에 효과적으로 전달하는 것이 ATR(Autothermal Reforming) 반응 특성에 깊게 연관되어 있음을 확인할 수 있었다. Diesel is one of the best hydrogen systems, which has very high volumetric density <TEX>$[kg\;H_2/m^3]\;(>100)\;and\;gravimetric\;density[\%\;H_2]\;(>\;15)$</TEX>Several catalysts were selected for diesel reforming. 3 catalysts of our group (NECS-1, NECS-2, NECS-3) and 2 commercial catalysts (Sud-Chemie, Inc, FCR-HCl4, FCR-HC35) were used to reform diesel. NECS-1 showed the best performance to reform diesel. In addition to these results, we studied on reaction characteristics for better understanding about auto thermal reforming of diesel by investigating product gas concentrations and temperature Profiles along the catalyst bed. We found technological issues such as fuel delivery and thermal configuration between front exothermic part and rear endothermic part.

Removal of Carbon Dioxide from Air by Pressure Swing Adsorption and Application of Short Cycle Time Approximation

The removal of trace carbon dioxide from air was carried out in a two-bed pressure swing adsorption (PSA) packed with 1/16” MS13X zeolite as adsorbent in the depth of L = 0.79 m to find systematically the effect of design and operating variables on the product concentration Ca1 and the mass exchange efficiency ηa defined by ηa = (Ca0 – Ca1)/(Ca0 – Ca1Pd/Pa) for the feed concentration. The operation with a shorter cycle time resulted in a higher performance which approached a limiting value at a half cycle time of shorter than 20 min. The individual superficial velocities, Ua and Ud in the adsorption and desorption steps, and the velocity ratio Ud/Ua had a great effect on the product concentration Ca1. On the other hand, pressure in the desorption step Pd had little effect on the removal performance expressed in terms of the mass exchange efficiency ηa while higher pressure in the adsorption step Pa decreased the removal efficiency. This effect of pressure was explained by the decrease in the adsorption coefficient m and intraparticle diffusivity with an increasing pressure Pa. The experimental result agreed well with a simplified model called short cycle time approximation previously proposed by authors when it was applied to a linear isotherm of adsorption and a half cycle time shorter than 20 min. The model provides a distinctive relation between the product gas concentration Ca1 and operating and design parameters by the following equation(1 – ηaUa/Ud)/(1 – ηa) = exp[KFOa(L/Ua – L/Ud)]in which KFOa is the unified volumetric mass transfer coefficient based on gas phase driving force and inversely proportional to the sum of column pressure (Pa + Pd).

Conversion estimates for gas-solid reactions: reversible kinetics independent of solid concentrations

The mathematical formulation of gas-solid reactions are usually described by a system of nonlinear reaction-diffusion equations and closed-form solutions are not readily available for most cases. Back reactions are usually neglected in the analysis of solid conversion estimates for these systems. When reversible reactions are considered, the kinetics are assumed to be of first order in both the reactant and product gas concentrations, independent of the solid concentrations. In such a situation, a number of authors have investigated the two-stage model. This model uses the pseudo-steady-state assumption in conjunction with a special restriction that will allow the nonlinear problem to be mathematically tractable. In this work, we consider in detail the case where the form of kinetics is independent of both the reactant and product solid concentrations. First, we apply the pseudo-steady-state assumption and investigate the conditions under which the two-stage model need not be assumed. An extension, by means of the cumulative gas concentration method, is then made to allow for arbitrary values for all parameters and reaction orders in both the reactant and product gas concentrations. Expressions for the estimates of full conversion time for a range of kinetic models have been established.