Equilibrium Oxygen Concentration Research Articles

Investigation of the Effect of Stress on Oxygen Diffusion in Pure Titanium Using a Phase-Field Model.

Diffusion plays a vital role during the fabrication of many materials. It is a well-known fact that stress can influence diffusion behavior. In order to optimize material processing techniques, a quantitative evaluation of the effect of stress on diffusion is essentially required. By analyzing the free energy change in a Ti-O system during diffusion, a phase-field model was developed to address this issue. Using this model, the diffusion of oxygen atoms in pure titanium under different stress states was investigated. It was observed that the true equilibrium concentration of oxygen was proportional to its hydrostatic pressure. Tensile stress can increase the oxygen concentration. This raise in concentration decreased with temperature. However, the promotion of diffusion can be attained in deeper regions at a higher temperature. On the contrary, compressive stress inhibited the diffusion of oxygen in pure titanium. Under a certain compressive stress, the decrease in the oxygen concentration at the surface layer was more significant at a lower temperature, while a decrease could be observed at a deeper distance from the surface at a higher temperature. A thermodynamic explanation of the effect of stress on diffusion was given based on the proposed phase-field model.

Electrochemical and metallographic characterization of Ni-NiO-NiBi3 equilibrium in molten lead-bismuth eutectic

This study aims to investigate the chemistry of the Ni-O-Pb-Bi system through a combined microscopic and electrochemical analysis of the Ni-NiO-NiBi3 equilibrium in molten lead-bismuth eutectic (LBE). Through SEM-EDX metallographic characterization, we examined to the precipitates formed on the solid nickel substrate in molten LBE, confirming the formation of the NiBi3 within the temperature range of 469–748 K. Subsequently, we induced the Ni(LBE)-NiO(s)-NiBi3(s) ternary equilibrium in LBE and measured the equilibrium oxygen concentrations at different temperatures. The equilibrium nickel activity was derived using the measured equilibrium oxygen concentration in the temperature range of 518–595 K. Finally, the Ni-Bi IMCs floating on LBE at the end of the measurements were collected and characterized by X-ray diffraction (XRD), confirming the presence of the NiBi3 phase.

Particularities of the thermal and oxygen concentration instabilities in a Czochralski process for solar silicon growth

A previous presented numerical model was used to study the time behavior particularities of temperature and oxygen concentration in a Czochralski (Cz) growth process of 200 mm diameter silicon single crystals for photovoltaic applications. First, some important model issues have been addressed: the dependence of the numerical results on the refinement level of the grid and on the model for oxygen equilibrium concentration at the melt-crucible interface. Then a parametrical study have been performed to study how the pulling rate and the rotation rate of the crucible influence the fluctuations of temperature and oxygen concentration near the crystallization interface. The numerical simulations have revealed that the temperature oscillations are closer to a normal distribution than the oxygen concentration, which is closer to a skewed left distribution.Both the increase of crucible rotation rate and pull speed has an effect of “pushing to the left”: the histogram of temperature fluctuations tends from a skewed right distribution to a normal distribution with the increase of the pull speed and crucible rotation values while the oxygen concentration is more skewed to the left. As a general conclusion, the numerical simulations have shown that the oxygen concentration is more sensitive to the crucible rotation than the temperature field, while the pull speed has a stronger effect on temperature oscillations than on the oxygen concentration oscillations.

SUCTION FORCE ANALYSIS FOR DIGITAL LIGHT PROCESSING-BASED PROJECTION STEREOLITHOGRAPHY

Digital light processing (DLP)-based projection stereolithography is one of the most important photo-polymerization based additive manufacturing technologies that has distinctive advantages such as high-resolution and fast printing speed. But the excessive suction force in the liquid resin film limits the further improvement of printing speed. The existing researches mainly focus on the improvement of the transparent window of the resin tank and the technological process while the mechanism of suction force is poorly understood. In this work, a multi-physical model coupled with resin flow, free radical polymerization and phase transition is established. The evolution process of the resin liquid film is studied under the combined action of mass transfer, photopolymerization, curing deposition and oxygen polymerization inhibition by numerical simulation. It is found that the solid-liquid interface presents a stable non-uniform wave attenuation morphology and the liquid film thickness is small and fluctuates sharply at the boundary which is completely different from the assumption of flat interface in previous research. The effects of elevating velocity, oxygen concentration distribution and UV intensity on the interface morphology and suction force are discussed. The results indicate that increasing the equilibrium concentration of oxygen and decreasing the UV intensity can effectively reduce the suction force while significantly affect the printing precision. We propose that adjusting the distribution of UV intensity can improve the inhomogeneity of the interface morphology and is an effective measure to reduce the suction force and increase the printing speed. This research has important reference significance for the study of different types of photo-polymerization based additive manufacturing technologies.

Thermodynamic and kinetic characteristics of a Cu-Mn composite oxygen carrier for low-temperature chemical-looping air separation

Abstract The further development of the chemical-looping air separation (CLAS) technology is hindered by the required high redox temperature. Improving the thermodynamic properties of oxides by elemental composition is an effective way to decrease the reduction temperature of oxygen carrier. In this paper, a Cu-Mn composite oxygen carrier was prepared by the addition of Mn2O3 to CuO, with CuxMn3−xO4 as the active phase, and the oxygen uncoupling properties of the Cu-Mn/Zr composite oxygen carrier were investigated, focusing on the redox reactivity under different oxygen concentrations of CuxMn3−xO4 ⇋ CuxMn2−x + O2(g). The oxygen transport capacity of this type of oxygen carrier was determined as 0.0463 g O2/g oxygen carrier. With an increase in the oxygen concentration (0.001–50%) in the carrier gas, the required oxygen uncoupling temperature increases (625.5–921 °C). Based on relationship between initial reduction temperature and equilibrium oxygen concentration, the following thermodynamic characteristics of the redox reaction were obtained: ΔG = –0.119 T + 150.41 kJ/mol and Kp = exp(14.31–18090.8/T). Compared to a Cu-based oxygen carrier, the reduction temperature is significantly reduced and the equilibrium oxygen concentration at the same reaction temperature is greatly increased. The redox reactivity under different heating rates and reaction temperatures were also investigated, and the results show that both the reduction and oxidation reactions are temperature driven at the considered temperatures. The reduction and oxidation kinetic models were established by the iso-conversional method. When the relative conversion X

Comparison of deoxidation capability of solid solution and intermetallic titanium alloy powders deoxidized by calcium vapor

A comparison of the deoxidation capability of solid solution and intermetallic titanium alloy powders deoxidized by calcium vapor was investigated. The oxygen concentration of Ti–6Al–4V, Ti–27Nb, Ti–42Nb, Ti–35V–15Cr, Ti–25Fe–5Al, and Ti65Fe35 alloy powders before deoxidation were 2,610 ppm, 3,300 ppm, 3,780 ppm, 5,880 ppm, 1,725 ppm, and 4,635 ppm, respectively. After deoxidation, the oxygen concentration of the Ti–6Al–4V, Ti–27Nb, Ti–42Nb, and Ti–35V–15Cr solid-solution alloy powders were 355 ppm, 210 ppm, 330 ppm, 95 ppm, respectively, while the Ti–25Fe–5Al and Ti65Fe35 intermetallic alloy powders were 385 ppm and 1250 ppm, respectively. Compared with the oxygen concentration before deoxidation, the solid-solution Ti alloy powders showed a high oxygen reduction rate of approximately 80% or more, while the intermetallic Ti alloy powders showed a lower oxygen reduction rate of approximately 70%. Based on the theoretical deoxidation limit of pure Ti and the actual deoxidation result of pure Ti powder, solid-solution Ti alloy powders have reduced oxygen solubility due to the addition of alloying elements, resulting in reduced oxygen concentration after deoxidation. However, the intermetallic Ti alloy powders showed a difference in oxygen concentration among them due to the effect of TiFe intermetallic phase with high equilibrium oxygen concentration in the deoxidation reaction.

Improving steel melting intensity in the process of electrosmelting from waste and pellets (HBI)

The paper addresses the issue on improving the intensity of melting in the production of steels using hot briquetted iron (HBI) in the charge that mostly consists of metal waste. An analysis has been performed into the features of melting that uses charge of complex composition. To ensure the boiling of metal bath, it is recommended to introduce to the bath carbon-containing raw materials in the form of steel waste in the amount exceeding 80 %. It was established that applying HBI almost does not reduce the yield of usable metal due to a high content of metal waste that makes up the charge.At the same time, the paper analyses the role of silicon and manganese oxidation process in the refining of liquid steel at melting the alloy wastes used as charge materials in an electric arc furnace. The dependences of equilibrium concentrations of oxygen and silicon at different temperatures in the system Fe‒Si‒O have been given. In addition, the dependence diagram of manganese oxidation products in a liquid iron on the temperature and concentration of manganese in the alloy MnO‒FeO has been constructed. The equilibrium concentrations of oxygen and silicon with carbon deoxidizing capability have been defined, in the field of liquid silicates and in the field of solid SiO2.The high-quality silicon and manganese oxidation when smelting steel made from metal waste and hot briquetted iron (HBI) contributes to the fullest refining of liquid steel through the phases metal-slag or metal-gas.It has been shown that the content of silicon during electrical steel refining drops to traces. Thus, when using metal waste and pellets as charge in the steel-making process, a silicon oxidation reaction does not reach equilibrium. If a sour process is performed, then the oxidation of silicon reaches equilibrium and, under certain conditions for melting the charge under the influence of heat from an electric arc, there may occur a significant reduction of silicon that takes place at a higher temperature (a silicon-reducing process). The basic process of melting the charge from metal waste and hot briquetted iron in an electric arc furnace has been recommended. In this case, the reducing period of melting is aimed at metal deoxidation, sulphur removal, at bringing the chemical composition of steel to the preset composition, at controlling the process temperature. All these tasks are solved in parallel throughout the entire reduction period. The complete removal of oxidative slag was followed by adding to the furnace of slag-forming mixes together with deoxidizing agents, that is the new slag (carbide or white) was introduced.A rise in the furnace bath temperature decreases the equilibrium constant of manganese. Therefore, in the absence of ferromanganese additives in the bath in the process of melting refinement, the behavior of manganese in the bath can be an indicator for the metal temperature.

OXYGEN SOLUBILITY IN CARBON-CONTAINING Fe –Co MELTS

Thermodynamic analysis of oxygen solutions in carbon-containing Fe – Co melts has been carried out. The equilibrium constants of interaction of carbon and oxygen, the activity coefficients at infinite dilution, and the interaction parameters for melts of different composition at 1873 K were determined. The dependences of the oxygen solubility on the contents of cobalt and carbon in the studied melts were calculated. Carbon has a high affinity for oxygen in iron-cobalt melts. Deoxidation ability of carbon increases significantly with the increasing of cobalt content in the melt. Deoxidation ability of carbon in pure cobalt more than an order of magnitude higher than that in pure iron. Reaction products of carbon deoxidation are gaseous oxides – monoxide (CO) and carbon dioxide (CO 2 ). The interaction reaction of carbon and oxygen dissolved in the melt, and hence deoxidation ability of carbon depends on the total pressure of the gaseous phase above the melt. Deoxidation ability of carbon increases significantly with the gaseous phase pressure lowering. The minimum oxygen concentration achieved for alloys of the same composition decreased practically an order of magnitude at decrease 10 times the total pressure of the gaseous phase. The gaseous phase composition above Fe – Co melts and equilibrium carbon and oxygen concentrations in the melt at a total pressure of the gaseous phase P, of 1.0; 0.1 and 0.01 atm were calculated. Optimum oxygen concentration (1 – 10 ppm) in Fe – Co melts, depending on the total pressure of the gaseous phase (0.01 – 1 atm) is achieved at carbon contents from 0.01 to 1 %. The curves of the oxygen solubility in carbon-containing iron-cobalt melts pass through a minimum, which shifts toward lower carbon contents with increasing cobalt content in the melt. Further carbon additions leads to an increase in the oxygen concentration of the melt so that the higher cobalt content of the melt, the steeper the increase in the oxygen content after the minimum as carbon is added to the melt.

Oxygen Solubility in Fe–Co Melts Containing Carbon

In thermodynamic analysis of solutions of oxygen in Fe–Co melts containing carbon, the equilibrium constants of reactions between carbon and oxygen are determined, as well as the activity coefficients at infinite dilution and the interaction parameters in melts of different composition at 1873 K. The dependence of oxygen solubility in such melts on the cobalt and carbon content is calculated. In iron–cobalt melts, carbon has high oxygen affinity. The deoxidizing ability of carbon increase significantly with increase in cobalt content in the melt. In pure cobalt, it is more than an order of magnitude greater than in pure iron. Deoxidation by carbon produces gaseous oxides: carbon monoxide (CO) and dioxide (CO2). The reaction of carbon and oxygen dissolved in the melt and hence the deoxidizing ability of carbon depend on the total gas pressure above the melt. Decrease in gas pressure significantly improves the reducing properties of carbon. The minimum oxygen concentration for alloys of the same composition is reduced by practically an order of magnitude with tenfold decrease in the total gas pressure. The gas composition above Fe–Co melts and the equilibrium carbon and oxygen concentrations in the melt are calculated with total gas pressures of 1.0, 0.1, and 0.01 atm. The optimal oxygen concentration (1–10 ppm) in Fe–Co melts is reached at carbon concentrations between 0.01 and 1% depending on the total gas pressure (0.01–1 atm). The solubility of oxygen in iron–cobalt melts containing carbon passes through a minimum, which is shifted to lower carbon content with increase in the melt’s cobalt content. Further additions of carbon increase the oxygen concentrations in the melt. With increase in cobalt content, this increase will be sharper.

Experimental and computational studies of oxygen transport in a Taylor-Couette bioreactor

With research and development for almost one century, the Taylor-Couette device is now applied in many practical applications such as reaction, filtration, extraction and bioreactor. We intend to use the Taylor-Couette bioreactor to culture cells that are seeded in a biodegradable porous scaffold. Oxygen concentration is always the most significant constraint in a bioreactor and can limit the cell proliferation rate. It is therefore important to know the mass transfer phenomenon and oxygen transport pattern inside the system. In this study, the equilibrium oxygen concentrations at different Reynolds numbers and operation conditions were measured and the mass transfer coefficients were also calculated. CFD simulation was carried out to compare with the experimental results. Both experimental and simulation results showed that the equilibrium oxygen concentration and mass transfer coefficient increased with Reynolds number. To further improve the mass transfer efficiency, air bubble was introduced to the bottom of the rotating inner cylinder and the vortex center. It was shown that the mass transfer coefficient of oxygen could be significantly increased with the trapped bubble.

Fast Ecotoxicity Detection Using Biosensors

The article provides information about a new device, AlgaTox developed in the R&D project sponsored by the Technology Agency (n.TA02030179) and patented in Czech Republic (CZ 305687). Its functionality is based on the use of biosensor, and its main advantage is fast response rate. The toxicity detection is achieved through precise measurement of green algae oxygen production dynamics after their exposure to light of wavelength of 680 nm. Clark sensor with a resolution of 0.05% of the equilibrium oxygen concentrations and stability at a constant pressure and temperature of 0.1% of the equilibrium oxygen concentration at the 24-h measurement is used for the oxygen detection. Laboratory testing of the device has been made using silver nitrate, substance with known inhibitory effect on algae. Real samples of aqueous soil extracts and waste sample from old dried-up industrial tailing pond enriched with insecticide have been also tested. The values of oxygen production inhibition or stimulation determined with the new device in the evaluation of real samples were up to six times higher in comparison with the corresponding values of inhibition (stimulation) of growth rates determined by standard procedure.

Accumulation of α-tocopherol and β-carotene in Euglena gracilis Cells Under Autotrophic and Mixotrophic Culture Conditions

The aim of the work was to find the mode of cultivation of unicellular flagellate Euglena gracilis, favorable for the simultaneous accumulation of α-tocopherol and β-carotene. Cells were grown either in photoautotrophic or photoheterotrophic conditions in the presence of 100 mM ethanol (variant Et) or 40 mM glutamate (variant Gt), or their combination (variant EtGt). The exogenous substrates significantly stimulated light-dependent growth of E. gracilis. The largest increase of biomass was recorded on the 20th day in the variant EtGt and exceeded the autotrophic control by 7 times. The content of β-carotene and chlorophyll (Chl) per cell in mixotrophic cultures exceeded the control by 2-3 and 1.6-2 times, respectively. At the same time, α-tocopherol accumulation in autotrophic cells was greater than in the cells of mixotrophic cultures by 2-7 times. Total yield of tocopherol per unit volume of culture medium, which depended not only on its intracellular content, but also on the amount of accumulated biomass was highest in EtGt variant. A correlation between the accumulation of the antioxidants and the equilibrium concentration of oxygen in the growth medium, which depended on the intensities of photosynthesis and respiration has been analyzed.

Thermodynamic laws of the oxygen solubility in liquid metals (Ni, Co, Fe, Mn, Cr) and the formation of oxygen-containing solutions in the alloys based on them

The solubility of oxygen in liquid Ni, Co, Fe, Mn, and Cr metals (Group IV in the periodic table) has been found for the first time. Linear dependences of the oxygen solubility on the standard Gibbs energy for the oxidation reaction of a liquid metal with gaseous oxygen are found. The revealed function of oxygen solubility is of scientific importance and allows one to develop a theory of oxygen solutions in liquid metals and liquid multicomponent metallic compositions and to calculate the energies of mixing of liquid metals with oxygen from ΔGMO° for metal oxidation reactions with allowance for pseudoregular-solution model equations. Using the energies of mixing and metal compositions, we calculated the equilibrium oxygen concentrations in a metal molten pool at the end of oxidation stage of melting 08Kh18N10T steel in an arc furnace. This fact indicates practical importance of the found function of the oxygen solubility in metals.

THERMODYNAMICS OF OXYGEN SOLUTIONS IN THE Fe – Ni, Fe – Co AND Ni – Co MELTS

Thermodynamic analysis of oxygen solutions in the Fe – Ni – O, Fe – Co – O, Co – Ni – O melts was determined. Composition of the oxide phase and the value of the equilibrium oxygen concentration in the melt of those systems were fi rst time obtained in a whole range of alloy compositions. In Fe – Ni – O and Fe – Co – O systems with increasing content of nickel and cobalt in the melts the oxide phase contains mainly FeO in a suffi ciently wide range of content of nickel and cobalt. Only when the mole fraction of nickel is close to unity and the mole fraction of cobalt is more than 0.8, content of NiO and CoO increases sharply. Oxide phase of Co – Ni – O system contains CoO and NiO in the entire range of alloy compositions. In the Fe – Ni and Fe – Co systems nickel and cobalt additives in the melt lead to decreased solubility of oxygen due to the attenuation, both nickel and cobalt, oxygen bonds in the melt and thus increases its activity. Further, by increasing the content of nickel and cobalt, the oxygen concentration in the melt increases slowly at fi rst and then quite rapidly. In Co – Ni system nickel additives to cobalt lead to increasing solubility of oxygen in the whole range of alloy compositions due to a substantially greater solubility of oxygen in nickel than in cobalt.

Thermodynamics of oxygen solutions in Fe-Ni, Fe-Co, and Co-Ni melts

By thermodynamic analysis of oxygen solutions in Fe-Ni-O, Fe-Co-O, and Co-Ni-O melts, the composition of the oxide phase is established for the first time. In addition, the equilibrium oxygen concentrations in these melts are determined over the whole range of alloy compositions. In Fe-Ni-O and Fe-Co-O melts, the oxide phase mainly contains FeO over a relatively broad of alloy compositions. Sharp increase in NiO content is only observed when the molar fraction of nickel exceeds one; sharp increase in CoO content is only observed when the molar fraction of cobalt exceeds 0.8. In the Co-Ni-O system, the oxide phase contains both CoO and NiO over the whole range of alloy compositions. In the Fe-Ni system, adding nickel to the melt reduces the solubility of oxygen as a result of weakening of the oxygen bonds in the melt by nickel and consequent increase in oxygen’s activity. With further increase in nickel content in the melt, the oxygen content rises at first slowly and then very sharply. In the Fe-Co system, analogously, adding cobalt to the melt reduces the solubility of oxygen as a result of weakening of the oxygen bonds in the melt and consequent increase in oxygen’s activity. With further increase in cobalt content, the oxygen content rises at first slowly and then relatively rapidly. In the Co-Ni system, adding nickel to cobalt increases the solubility of oxygen over the whole range of alloy compositions, on account of the significantly greater solubility of oxygen in nickel than in cobalt.

Numerical Study of the Influence of Ambient Pressure on the Inerting Effect of an Aircraft Fuel Tank Inerting System

The numerical study of the influence of the ambient pressure of the fuel tank on the inerting effect of an aircraft fuel tank inerting system was carried out. The mathematical model of ullage equilibrium oxygen concentration has been established using the differential time calculation method based on the mass conservation and ideal gas state equations. The variations of ullage oxygen concentration and dissolved oxygen concentration in the fuel with time under different working conditions have been obtained. The results have shown that the as the ambient pressure of the fuel tank became lower, the speed of the decreasing of oxygen concentration of the fuel tank ullge and the dissolved oxygen concentration of the fuel was slower.

Modelling the Influence of the Oxygen Concentration in the Gas Mixture (N2/O2) at Thermodynamic Equilibrium

Knowledge of the chemical composition of plasma is required for calculations and modeling in thermal plasmas. Indeed, from the knowledge of this composition can be calculated thermodynamic properties, transport coefficients and the radiative properties of a plasma environment. In this work, we propose to study the influence of thermodynamic equilibrium concentration of oxygen in a gas mixture N2/O2. Particularly we study the evolution of the species density in the plasma created according to the temperature and pressure variables for O2 mixtures. A thermodynamic equilibrium, when you want to take into account a large number of species, two main methods are usually employed, one is based on the law of mass action and the other on minimization of the Gibbs. We decided in our study to the law of mass action and the method of Newton-Raphson. The results show that when the plasma is in thermodynamic equilibrium densities of the different species present in plasma that are functions of temperature and pressure. They are not independent because they are bound by certain laws of thermodynamic equilibrium

Impact of carbon dioxide injection on oxygen dissolution rate during oxygen additions in a bubble column

Oxygen additions are common practice during oenological fermentations. Since oxygen dissolution under winemaking conditions is not completely understood, these additions are performed empirically. In particular, the influence of carbon dioxide produced by yeast cells on the oxygen dissolution rate remains unclear. In this paper, we present an oxygen mass balance model that describes the evolution of dissolved oxygen in a laboratory scale carbon dioxide bubbling column emulating wine fermentation hydrodynamic conditions during oxygen additions. The model consists of two partial differential equations for the liquid and gas phases and considers liquid recirculation and mixing. Considering only one fitting parameter, the model can reproduce well the observed dissolved oxygen evolution at different locations in the column. We found that carbon dioxide bubbling has two simultaneous antagonist effects: it enhances the volumetric mass transfer coefficient and decreases the oxygen equilibrium concentration mainly due to the dilution effect in the gas phase. Overall, the latter effect is shown to be more important and explains the reduction of almost 60% of the oxygen dissolution rate for high carbon dioxide bubbling conditions. The model developed here will help to design better oxygen addition systems for oenological fermentations.

Contribution to Modeling of Hydrogen Effect on Oxygen Diffusion in Zy-4 Alloy During High Temperature Steam Oxidation

Previous studies have shown that the numerical model EKINOX-Zr was able to simulate with accuracy oxide growth and oxygen diffusion into the matrix during high-temperature oxidation of Zy-4. In this study, the aim of the development was to evaluate if the observed effect of hydrogen cladding content on the increase of oxygen solubility in the high-temperature βZr was only a thermodynamic effect. Previous experimental studies have shown that hydrogen induces an evolution of equilibrium oxygen concentration at the αZr/βZr interface. The present work showed that EKINOX-Zr linked with the thermodynamic database Zircobase reproduced the evolution induced by hydrogen during the high-temperature steam oxidation. However, the results showed also that additional studies are necessary to better understand hydrogen behavior during high-temperature oxidation of Zr.

Estimation of Oxygen Concentration in the Slurry in Biogas Production Without O2 Removal in Initial Process

The existence of free molecular oxygen in the biogas production process will inhibit strict anaerobic methanogenic bacteria. The estimation of O2 concentration in the slurry is needed to see if the oxygen methanogenic inhibition happens in the biogas production without oxygen removal in initial process. The calculation begin with determine the digester volume, the gas space volume fraction in the digester, and the operation condition, i.e. the temperature and the pressure according to the good condition in the biogas production process. Based on the liquid-gas equilibrium principle, and with the assumption that the air consist of 80% of nitrogen and 20% of oxygen, it is obtained the equilibrium oxygen concentration in the slurry in various gas space volume fraction in the digester. The result of the calculation show that the oxygen concentrations in the slurry in all of gas space volume fraction in the digester are much higher than the methanogenic inhibition limit, indicating the possibility the happen of the methanogenic inhibition in the system. The inhibition possibility will be higher by the greater of the gas space volume fraction in the digester.