Introduction

Primary energy consumption per capita is increasing and the consumption of fossil fuels is responsible for 87% of carbon dioxide (\({\mathrm{CO}}_{2}\)) emissions, which is a major cause of climate change [1, 2]. The continuous consumption of non-renewable fossil fuels is recognised as the leading cause of the current environmental and energy crises. The development and commercialisation of alternative renewable energy sources is part of the solution to these challenges. Biogas derived from the anaerobic digestion of biomass and organic waste is considered an important future renewable energy source.

There has been steady development in the application of the anaerobic digestion process to convert biomass into renewable energy [3,4,5,6,7,8]. The feedstocks suitable for anaerobic digestion can be divided into seven categories: (1) agricultural residues and energy crops, (2) food waste, (3) waste oils and animal fat, (4) livestock manure, (5) organic fraction of municipal solid waste, (6) sewage sludge, and (7) algae [9,10,11]. It has been estimated that energy that can be derived from biomass has the potential to provide 3000 terawatt hours (TWh) of electricity annually and could save 1.3 B t of \({\mathrm{CO}}_{2}\) equivalent emissions per year [12]. Currently, only a tiny fraction of this potential is realised which is a tremendous waste of resources, particularly since digestion is also beneficial for treating waste to make it easier to dispose of. The previously unattractive returns for investing in biogas plants are likely to improve as government incentives take effect in combination with rising costs for fossil fuels. However, alongside the regulatory and market environment, technical improvements are also capable of transforming the economics of biogas by radically lowering the costs of production.

Note that production cost varies for different wastes which, in turn, can produce biogas with different methane contents. For example, the cost is approximately 8 USD/GJ for food waste versus 10 USD/GJ for waste sludge in standard low pressure AD systems [13]. It is hoped that future, large-scale AD systems using algal feedstocks and higher pressures could, based on the results presented here, provide even cheaper biogas in the future.

Although biogas can be burnt directly in, for example, combined heat and power (CHP) applications, for direct injection into the gas network, it needs to be upgraded to a methane content of at least 97%. This can be achieved by various technologies [14, 15] which are summarised in Table 1:

Table 1 Summary of commercial technologies for biogas upgrading showing their operating pressures, operating costs, and prevalence based on 428 installed European systems in 2016 (taken from 13–14)
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The energy required for biogas upgrading has been reported to be 0.2 to 0.8 \(\mathrm{kWh}/{\mathrm{Nm}}^{3}\), which is a significant proportion of the energy content of biogas (6 \(\mathrm{kWh}/{\mathrm{Nm}}^{3}\) assuming 60% \({\mathrm{CH}}_{4}\) content). This energy is required to compress the biogas or, especially in the case of chemical separation, to heat up and therefore regenerate the amine by liberating the captured \({\mathrm{CO}}_{2}\). Furthermore, if the upgraded biomethane is to be used for electricity generation and an energy generation efficiency of 35% is assumed, then, based on the range of numbers given in Table 1, 9–37% of the useful energy of biomethane could be expended on the upgrading process. In addition to operating costs for a biogas plant, the capital cost of upgrading the equipment is typically a lot higher than the digesters. The contention of this paper is that pressurised anaerobic digestion can reduce upgrading CAPEX and OPEX required for biogas upgrading in two ways:

Firstly, by increasing the methane content of the digestor off-gas — thereby decreasing or potentially eliminating the work required to upgrade the biogas (e.g., smaller amine column, reduced amine recirculation); and, secondly, by reducing the energy required for biogas compression which is required for all upgrading processes except for chemical separation.

As discussed, biogas upgrading to biomethane entails extra costs in comparison with the direct utilisation of biogas, for example, in a combined heat and power (CHP) unit. Nonetheless, the upgrading strategy is beneficial from a circular economy perspective as its utilisation has the potential for reducing imports of natural gas as well as reducing \({\mathrm{CO}}_{2}\) emissions. Recent studies [9, 16,17,18] have shown that, even though anaerobic digestion with biomass and waste is a developed and extensively employed technology, there is still plenty of room for improvement of its overall efficiency, reducing operating cost and increasing added value. Various strategies, such as optimisation of operating parameters and pre-treatment, using additives etc., have been proposed to achieve those goals [19]. Modification of the concentration of dissolved gas species has also been investigated to increase biogas productivity. Sparging with small \({\mathrm{CO}}_{2}\) bubbles, for example, has been shown to increase the rate of methane production [20].

Another way of raising biogas energy density is demonstrated in a study by Hayes, Isaacson, Pfeffer, and Liu in 1990 [21] in which the digestate is circulated through a bubble column in which \({\mathrm{CO}}_{2}\) is stripped out using an inert gas stream such as air or nitrogen. Although this concept of pressurised and non-pressurised in situ methane enrichment technology was first proposed nearly 30 years ago [21], this technology remains at the stage of modelling and pilot scale [22].

The studies above show that \({\mathrm{CO}}_{2}\) is 40 to 60 times more soluble than \({\mathrm{CH}}_{4}\) in water under digestion conditions. Therefore, if the digestion process occurs in a reactor with headspace pressure higher than atmospheric pressure, the amount of \({\mathrm{CO}}_{2}\) dissolved in the digestate increases more than the amount of \({\mathrm{CH}}_{4}\) dissolved in the digestate, and so the concentration of this latter species is elevated in the gas phase. Experimental studies on pressurised anaerobic digestion have confirmed this. For example, recent studies [23,24,25] reported a methane content of up to 90% at operating pressures of up to 50 bar. Such high pressures do not significantly inhibit biogas production and can be used to reduce the cost of compression of biomethane into the gas grid.

The objective of this study is to use the custom-built twin bioreactor to confirm that modestly elevated pressures can increase the methane concentration of the biogas. Different sampling frequencies were used to achieve different average headspace pressures. We have also extended previous work with a mass balance to measure the true solubilities of biogases in the digestate, compared with those reported for pure water.

Materials and Methods

Experimental Setup

The bioreactors used in this study were a novel design of twin bioreactor produced in collaboration with David Morris (Autichem Ltd, UK). Further information is given in the Supplementary Material. The reactors each have a working volume of 1500 mL, temperature and pressure sensors, heating mat with insulation, sampling and feeding ports at the top, and sampling ports at the bottom, of the reactor. One reactor has a rectangular stainless steel blade for mechanical mixing. There are pipes and bellows to transfer the biogas produced in one bioreactor to sparge the other bioreactor through the bottom for mixing effect. The pondweed used as feedstock and the sludge, containing hydrolytic bacteria, acidogens, acetogens, and methanogens, were collected from the same pond at the Thornton Science Park Campus of the University of Chester (UK). 18S rRNA gene sequencing was performed to identify the species of the pondweed and was only able to find that it belongs to the Hydrocharitaceae family but not the exact species.

Figure 1 details the workflow for sampling the anaerobic bioreactors. After putting everything in the bioreactor and starting up the process, it is left to digest and build up the headspace pressure [26,27,28,29]. If the headspace pressure is not at the desired level, it is left for another day or two. When the headspace pressure is at the desired level, the biogas is carefully sampled to determine its composition. It is then left to digest for a few days and repeat the digestion and sampling process until the production rate starts to slow down. Once the production rate starts slowing down after a few sampling cycles, the process is left to digest until the production rate stops. Final sampling is then performed to determine the biogas composition.

Fig. 1
figure 1

Workflow for sampling the anaerobic bioreactors

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Experimental Procedure

For the atmospheric pressure run, the total volume of culture was determined to be 1300 mL, then the corresponding headspace volume was 780 mL. Following the food ratio of 6 g/L from previous experiment, the feed needed for this experiment is 7.8 g of dry plants. It was measured with the AX223/E balance (OHAUS Europe GmbH, Switzerland) and was roughly ground with a pestle and mortar before being put into vessel 1.

Next, a full laboratory bottle of sludge, containing hydrolytic bacteria, acidogens, acetogens, and methanogens, was poured into the same vessel. Two portions of 200 mL of deionised water were subsequently used to rinse the laboratory bottle to get the remaining sludge into the reactor. More deionised water was poured into the reactor until it reached the marked line on the plastic sleeve of the reactor, so that the total volume of the culture was 1300 mL before the lid was put on and sealed. Lastly, compressed air was pumped through the bottom of the reactor for 10 s to provide mixing before the all the valves of the reactor were fully closed.

For the evaluated pressure run, two vessels were run almost simultaneously in order to provide duplication [30] and the results for biogas production show good agreement as shown in Fig. 5. An additional 380 mL of sludge, containing hydrolytic bacteria, acidogens, acetogens, methanogens, and 15 g of feed was added to the reactor to reduce the headspace volume so that the headspace pressure could increase more for a given amount of biogas production. Vessel 2 was used to run an experiment with similar conditions to the second run in vessel 1. The remaining 9.7 g of dry plant matter was roughly ground with a pestle and mortar and put into vessel 2. A litre of sludge, containing hydrolytic bacteria, acidogens, acetogens, and methanogens, was poured into vessel 2, and the remaining sludge was rinsed with deionised water and poured into vessel 2.

Next, more deionised water was poured into vessel 2 to make the total volume of culture in vessel 2 up to 1635 mL, which left the vessel with 400 mL of headspace volume when the top of the reactor, with the mixing blade, was replaced. Lastly, compressed air was pumped through the bottom of vessel 2 for 10 s to mix the culture before all the valves were shut to seal the reactor.

Analysis

The key parameters of the experiment, such as headspace pressure, were recorded by the on-board memory in the control platform of the system which was set to log them every 10 min. The recorded data were then downloaded to a computer for further analysis. Once the headspace pressure reached the target level, the biogas was drawn directly from the needle valve on the top of the reactors and the composition of the biogas was analysed by the Rapidox 5100 Portable Gas Analyser (Cambridge Sensotec, UK). Note that the volume of gas required to be withdrawn for sampling was a significant fraction of the headspace volume, which therefore resulted in a large reduction in the headspace pressure. The suction from this device is the reason why the headspace pressure is sometimes recorded as slightly below atmospheric.

It is instructive to perform a mass balance for each gas species for two reasons:

  1. 1.

    To estimate the relative production of biogases (methane and carbon dioxide) between each venting (sampling) event. These production amounts could be expected to be reasonably constant, in the steady phase of anaerobic digestion, since they are determined by the metabolic pathways of the bacterial consortium in the reactor.

  2. 2.

    To estimate the actual value of the Henry’s law constant which determines the distribution of the gaseous species between the liquid and gas compartments of the reactor. This is likely to be significantly less than the value for pure water, due to the competing presence of other dissolved species (other gases, salts, sugars, acids etc.) in the digestate.

Figure 2 details the three key reactor states that are used to develop the mass balance, which are cycled through repeatedly for each venting/sampling event.

Fig. 2
figure 2

Different states of each bioreactor which apply for each sampling/venting event

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In state 1, just before the sampling, the reactor is pressurised with the liquid and gas compartments in equilibrium as determined by Henry’s law. During sampling, the crucial assumption is made that no desorption occurs from the liquid phase, since the duration of the sampling is relatively short (1–2 min) and the liquid phase appears to be quiescent during this time. This means that on completion of sampling and resealing the headspace at the new lower pressure, the mole fractions in the headspace and concentrations in the liquid phase remain constant at their pre-venting values.

State 2, immediately after venting, represents a non-equilibrium situation whereby there is an excess concentration of each gaseous species in the liquid. This gradually desorbs over 1–2 h to restore equilibrium and go into state 3, in which the headspace pressure is slightly higher than in state 2 (pressure recovery). The further reasonable assumption can be made that the total mass of each species in the reactor in state 3 is unchanged from state 2, since the rate of generation of biogases due to fermentation is slow compared to the rate of restoration of gas–liquid equilibrium. The mass balance and Henry’s law relationship can therefore be employed to calculate the new pressure and concentrations in state 3.

Critically, by comparing the calculated value of the recovered headspace pressure in state 3 to the actual measured value, the Henry’s law constant can be treated as an adjustable parameter that can be inferred to make the calculated value agree with the measured value.

For state 1, the biogas composition is detected by the gas analyser which involves venting the reactor headspace for 1–2 min by manually opening the needle valve. The headspace pressure forces the headspace gas into the sampling line for the analyser where it flushes the existing gas (air or the previously sampled gas) from the sampling line and 1–2 min are required until the reading becomes steady. The partial pressure of each gas in headspace is given as follows:

$${p}_{i}^{a}={P}^{a}{y}_{i}$$
(1)

where \({p}_{i}^{a}\) is the partial pressure of each gas \(i\) in the headspace, \({P}^{a}\) is the total pressure in the headspace, and \({y}_{i}\) is the mole fraction of each gas in the headspace as reported by the gas analyser. Assuming ideal gases, the mass of each gas \({m}_{i,g}^{a}\) in the headspace in state 1 is calculated by:

$${m}_{i,g}^{a}=\frac{{M}_{i} {{p}_{i}^{a}V}_{g}}{RT}$$
(2)

where \({M}_{i}\) is the molar mass of each gas, \({V}_{g}\) is the headspace volume, \(T\) is the operating temperature \((295.15 K)\), and \(R\) is the gas constant \((8.314 {\mathrm{m}}^{3}\bullet \mathrm{Pa}\bullet {\mathrm{K}}^{-1}\bullet {\mathrm{mol}}^{-1})\). The concentration of each gas dissolved in the liquid just prior to venting \({c}_{i}^{a}\) can be calculated by assuming gas–liquid equilibrium:

$${c}_{i}^{a}={H}_{i} {p}_{i}^{a}$$
(3)

where \({H}_{i}\) is the Henry’s law constant for the liquid digestate in the reactor. The mass of each gas dissolved in the liquid \({m}_{i,l}^{a}\) can then be calculated by:

$${m}_{i,l}^{a}={M}_{i}{c}_{i}^{a}{V}_{l}={M}_{i}{H}_{i} {p}_{i}^{a}{V}_{l}$$
(4)

where \({V}_{l}\) is the total volume of the culture. Therefore, the total mass \({m}_{i}^{a}\) of each gas species contained within the reactor headspace and liquid in state 1 is as follows:

$${m}_{i}^{a}={m}_{i,g}^{a}+{m}_{i,l}^{a}= \frac{{M}_{i} {{p}_{i}^{a}V}_{g}}{RT}+{M}_{i}{H}_{i} {p}_{i}^{a}{V}_{l}={M}_{i} {p}_{i}^{a}\left(\frac{{V}_{g}}{RT}+{H}_{i} {V}_{l}\right)$$
(5)

Mention should also be given to the mass of each gas that leaves the headspace during the venting since this represents the production of biogas and the mass that leaves the closed system:

$${s}_{i}=\frac{{M}_{i} {V}_{g}}{RT}\left({p}_{i}^{a}-{p}_{i}^{b}\right)=\frac{{M}_{i} {V}_{g}{y}_{i}}{RT}\left({P}^{a}-{P}^{b}\right)$$
(6)

For state 3, the liquid–gas equilibrium is restored and, assuming no biogas was produced during this short time, the total mass of each gaseous species in the reactor in state 3 \({m}_{i}^{c}\) is the same as in state 2. Introducing similar variables as in state 1 for the distribution of the total mass between the mass in the liquid \({m}_{i,l}^{c}\) and the mass in the gas \({m}_{i,g}^{c}\) in state 3, the mass balance between states 1 and 3 can be written as follows:

$${m}_{i}^{c}={m}_{i,g}^{c}+{m}_{i,l}^{c}={m}_{i}^{a}-{s}_{i}$$
(7)

Since Henry’s law applies, the total mass of each gas species in the reactor in state 3, as calculated from the sum of the masses in the gaseous and dissolved states, is given by an equation that is entirely analogous to Eq. 5. The only difference is that the superscripts need to be changed to ‘c’ to denote state 3 which yields the following:

$${m}_{i}^{c}={M}_{i} {p}_{i}^{c}\left(\frac{{V}_{g}}{RT}+{H}_{i} {V}_{l}\right)$$
(8)

For state 3, the objective is to calculate the partial pressure from the total mass (rather than the other way round as previously for state 1). Therefore, the total restored headspace pressure can be re-arranged (Eq. 8) to make the partial pressure of each gas the subject, and then summed to give \({P}^{c}\), the total predicted headspace pressure in state 3:

$${P}^{c}=\sum_{i}{p}_{i}^{c}=\sum_{i}\left\{\frac{{m}_{i}^{c}}{{M}_{i}\left(\frac{{V}_{g}}{RT}+{H}_{i} {V}_{l}\right)}\right\}$$
(9)

Provided the solubility of each dissolved gas in the digestate is known, the systematic applications of Eqs. 1, 5, 6, 7, and 9 provide a means to estimate the recovered headspace pressure \({P}^{c}\) in state 3, based on the measured values of:

  1. 1.

    the mole fractions of each gas in the headspace \({y}_{i}\), which are assumed to be constant during sampling and therefore the same in state 1 (prior to sampling) and in state 2 (immediately following sampling).

  2. 2.

    the total pressure in the headspace

As discussed later in the Results and Discussion, the recovered pressures in state 3 for each sampling event tend to be much less than the predicted values calculated using Henry’s law constant for gases dissolved in pure water (\(\alpha =1)\). In this work, it is assumed that the solubility of each gas dissolved in the digestate \({H}_{i}\) is related to that in pure water \({H}_{i}^{0}\) by a common ratio \(\alpha\), defined as follows:

$${H}_{i}=\alpha {H}_{i}^{0}$$
(10)

\(\alpha\) is used as single fitting parameter (using Excel goal seek) to find the value that minimises the sum of the squared differences between the measured and predicted values for the headspace pressure \({P}^{c}\) in state 3 — i.e., after re-equilibration following venting. The reduction in biogas solubility (Henry’s law constant) for the digestate, compared to pure water, is striking: a best fit value of \(\alpha =0.037\) is obtained which, to our knowledge, represents the first plausible experimental estimate of the depression of biogas solubility in digestate compared to that in pure water.

Results and Discussion

Atmospheric Pressure

The effect of headspace pressure on biogas production rate and composition was examined using the twin pressurised bioreactor system. The biogas composition was analysed with the Rapidox 5100 Portable Gas Analyser (Cambridge Sensotec, UK). In the results presented below, the only gases detected in measurable (non-zero) amounts were \({\mathrm{CO}}_{2}, {\mathrm{O}}_{2},\mathrm{C}{\mathrm{H}}_{4}\), with the balance of the gas needed to make the total up to 100% being assumed to be nitrogen.

Figure 3 demonstrates the change of headspace pressure of vessel 1 during the first run. Following the initial start-up stage, the digestion process had 2 weeks of constant biogas production rate before the feedstock slowly ran out and the production rate slowly decreased. Each sampling event vented completely to atmosphere. The negative values indicate an offset error in the pressure sensor.

Fig. 3
figure 3

Pressure profile of vessel 1 during the first run. The reductions in headspace pressure occur when biogas is sampled

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Table 2 shows the composition of gas and the headspace pressure before and after each sampling event. Note that this run was somewhat exploratory in that pressures were only allowed to build up to modest levels. \({{\mathrm{N}}_{2}}^{\mathrm{a}}\) is the composition of nitrogen plus all other gases that cannot be detected by the analyser (i.e. calculated to make the total 100%). Pressures \({\mathrm{P}}^{\mathrm{a}}\) and \({\mathrm{P}}^{\mathrm{b}}\) are the absolute pressures (bar) just before and just after sampling, respectively, as discussed in the “Analysis” section.

Table 2 Biogas composition and absolute headspace pressure in vessel 1 during the first run. Note that the pressures of 0.89 bar are due to the suction of the sampler and should be assumed to be equal to atmospheric pressure i.e. 1.01 bar
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Elevated Pressure

For the second run, both vessels were used; however, vessel 2 was set up 8 days after vessel 1. Figure 4 shows the pressure profile of both vessel 1 and 2 during the second run. The sudden drop in pressure was caused by sampling of the biogas to determine its composition. It can be seen that there are several gaps in the recorded data (e.g. only a couple of values recorded between days 8 and 16) due to an unknown issue with the pressure recording. As illustrated in Fig. 4, even though the process in vessel 2 was set up eight days later than vessel 1, it still had a very similar biogas production rate compared to vessel 1.

Fig. 4
figure 4

Pressure profile of both vessels during the second run. Note this is to show trends rather than individual data points. The drop in headspace pressure is when biogas was sampled. Gaps in the data are due to pressure recording failures

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Table 3 shows the biogas composition from both vessels for each sampling during the second run. The main difference between the first run and second run was that, for the first run, headspace pressure was kept close to atmospheric pressure for most of the run. For the second run, the aim was to accumulate biogas in the headspace to increase the pressure as high as possible.

Table 3 Biogas composition and headspace pressure for both vessels during the second run
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\({{\mathrm{N}}_{2}}^{\mathrm{a}}\) is the composition of nitrogen plus all other gases that cannot be detected by the analyser (i.e. calculated to make the total 100%). Pressures \({\mathrm{P}}^{\mathrm{a}},{\mathrm{P}}^{\mathrm{b}},{\mathrm{and P}}^{\mathrm{c}}\) are, respectively, the absolute pressures (bar) just before sampling, just after sampling and following pressure recovery (re-equilibration) as discussed in the “Analysis” section. Pressures \({\mathrm{P}}_{1}^{\mathrm{d}}\) and \({\mathrm{P}}_{2}^{\mathrm{d}}\) are the calculated values of \({\mathrm{P}}^{\mathrm{c}}\) given by the mass balance equations using a Henry’s law constant adjustment factor of \(\alpha =1.0\) (pure water solubilities) and \(\alpha = 0.037\) (best fit value) respectively; refer to Eq. (10) above for the definition of α. The values highlighted in grey show the good agreement between the best fit predicted values and the measured values. The value ‘None’ denotes the lost data caused by the unknown data logging issue. The value ‘N/A’ denotes the start-up of the digestion for which no composition was measured.

By comparing the biogas composition from Tables 2 and 3, it can be seen that the biogas has a higher methane concentration when the headspace pressure is higher. The presence of oxygen from the sampling of vessel 2 on day 17 was due to a simple error from the sampling technique, in which air must have been allowed to ingress into the sampling line.

There is good agreement between the best fit predicted values (α= 0.037) and the measured values (both highlighted in grey). It can also be observed from Table 3 that the calculated headspace pressure after re-equilibration, \({\mathrm{P}}_{1}^{\mathrm{d}}\), when the Henry’s law constants for pure water are used \(\left(\alpha =1.0\right)\), is much lower than the measured pressure. If, however, all Henry’s law constants are reduced to 3.7% of this value \(\left(\alpha =0.037\right)\), then the calculated values for headspace pressure after re-equilibration, are in better agreement with the measured values (both highlighted in grey). This implies that the solubility of biogases, or at least that of carbon dioxide (the more soluble biogas compared to methane) is much less in digestate than that in pure water. A study by Gros et al. [31] showed that soluble gases such as \({\mathrm{O}}_{2}\) and \({\mathrm{CO}}_{2}\) have different solubilities in different aqueous solutions with dissolved media species; up to a maximum reduction of 20%. The depression of gas solubility due to the presence of salts and organic species in culture media has also been reported to be around 11% [32]. These previously published solubility reductions translate to α = 0.80 or α = 0.89 which are far more modest a reductions than that estimated in this work i.e. α = 0.037.

The mass balance analysis also gives the amount of biogas produced during the process as calculated using the equations mentioned in the “Analysis” section.

Figure 5 demonstrates the results of the mass balance analysis. The cumulative change of each gas during the second run was calculated from the composition of biogas obtained from each sampling. The results for each vessel are in quite close agreement. The fact that more \({\mathrm{CO}}_{2}\) is produced in the early phase is probably due to the presence of aerobic metabolism until any residual oxygen is consumed. Since \({\mathrm{N}}_{2}\) and \({\mathrm{O}}_{2}\) are not produced from the anaerobic digestion process, the cumulative change is negative due to the decrease in concentration after each sampling. The small spike of \({\mathrm{N}}_{2}\) and \({\mathrm{O}}_{2}\) in vessel 2 from the third sampling was caused by an error in the sampling technique, allowing an ingress of air as mentioned earlier.

Fig. 5
figure 5

Cumulative change of different gases during the second run for both vessel 1 and vessel 2

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Once each sampling action is finished, it takes some time (1–2 h) for the system to re-establish liquid–gas equilibrium. Figure 6 illustrates this phenomenon for one of the sampling events.

Fig. 6
figure 6

Pressure profile of the fourth sampling and recovery of headspace pressure for vessels 1 and 2

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Discussion

The effect of headspace pressure on biogas composition was investigated in this study. The results from both runs show that, as the anaerobic digestion process proceeds, the methane content of the biogas tended to increase. When operating at higher pressure, as illustrated by the second run, the biogas produced from the anaerobic digestion process had a higher methane concentration. Biogas composition analysis from both runs also showed that as the anaerobic digestion process continued, methane production rate gradually increased.

The slight increase in \({\mathrm{CO}}_{2}\) concentration right after the fourth sampling (second run) show that as the headspace pressure increased, more \({\mathrm{CO}}_{2}\) is dissolved in the liquid because of the increased pressure. Soon after sampling, assuming little biogas had been produced at this stage, some of the \({\mathrm{CO}}_{2}\) that was dissolved in the liquid was released into the headspace as equilibrium in the bioreactor was restored, causing the slight increase in \({\mathrm{CO}}_{2}\) concentration in the gas phase.

Conclusions

A novel method to reduce the need for biogas upgrading is presented in this study. The methane concentration of the biogas increases to at least 70.0% for a headspace pressure greater than 4 bara compared to 57.5% or less when the pressure is less than 1.6 bara at 22 °C, thereby reducing the requirement for the biogas to be upgraded before final use. The solubility of biogas in the digestate is found in this study to be 3.7% (best fit value) of its solubility in pure water, which is very much lower than the comparatively modest depression of only 11% or 20% that has been previously reported in the literature. The following caveat that should be emphasised; higher pressures will incur higher operating and capital costs, so further detailed analysis is required to determine the optimal trade-off of these increased costs versus reduced upgrading costs.