# Effect of manipulating dietary fat and carbohydrates on methane potential of dairy cow faeces

Giulio Giagnoni, Alastair James Ward, Coralie Masclet, Henrik Bjarne Møller,

Martin Riis Weisbjerg

► To cite this version:

Giulio Giagnoni, Alastair James Ward, Coralie Masclet, Henrik Bjarne Møller, Martin Riis Weisbjerg. Effect of manipulating dietary fat and carbohydrates on methane potential of dairy cow faeces. Livestock Science, 2025, 302, 10.1016/j.livsci.2025.105832. hal-05421816

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Submitted on 17 Dec 2025

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# Effect of manipulating dietary fat and carbohydrates on methane potential of dairy cow faeces

Giulio Giagnoni<sup>a, *</sup> , Alastair James Ward<sup>c, D</sup> , Coralie Masclet<sup>b</sup> , Henrik Bjarne Møller<sup>c, D</sup> , Martin Riis Weisbjerg<sup>a</sup>

## HIGHLIGHTS

* Supplementation of dietary fat in dairy cows affect faecal biogas production.

* Maximum methane yield and production rate increase by feeding fat as rapeseed.

* Palm kernel fatty acids supplementation did not affect biogas production.

* Dietary carbohydrate sources for dairy cows affect faecal biogas production.

* The effect of carbohydrate from forages and concentrates on biogas is additive.

## GRAPHICAL ABSTRACT

1. COLLECTION

<figure><img src="image_4.png" /></figure>

Experiment 1

- Six diets with different fat source and fat concentration

- Individual faeces from 24 cows

- 36 pooled manure samples

Experiment 2

<figure><img src="image_5.png" /></figure>

- Four diets with:

- Maize or grass-clover silage

- Barley or dried beet pulp

- Individual faeces from 24 cows

- 8 pooled manure samples

<figure><img src="image_6.png" /></figure>

3. MEASURING

Displacement of water (pressure difference): biogas volume yield

3 replicated samples

<figure><img src="image_7.png" /></figure>

CONTROL (t applications)

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

4. RESULTS

## ARTICLE INFO

Keywords:
rapeseed
Lauric acid
Myristic acid
Gompertz

## ABSTRACT

The objective of this study was to evaluate the effect on the *in vitro* methane yield from dairy cow faeces, when the diet is manipulated for either source or concentration of dietary fat (rapeseed or palm kernel fatty acids; 20 to 50 g/kg DM), or a source of carbohydrate (grass-clover vs maize silage, and barley vs dried beet pulp). The faecal samples from two nutrition trials were used in an *in vitro* system for anaerobic digestion for measuring gas volume and methane concentration at given times, from 5 to 90 d. The ultimate methane yield measured at d 90, and the coefficients estimated from a modified Gompertz model (maximum methane yield, methane production rate, and lag time) were analysed in a linear mixed model. Increasing dietary concentration of fat increased the maximum methane yield, the methane production rate, and the lag time when rapeseed was used as fat source, but use of palm kernel fatty acids in the diet did not result in an increase of any parameter. The effect of the carbohydrate inclusion from forage and concentrate was additive, so no interaction was observed, and maximum methane yield increased with increasing dietary starch concentration. Ultimate and maximum methane yield were highly correlated, with the latter underestimating ultimate methane yield by 3-4%. Estimated coefficients from a modified Gompertz model are useful to understand the effect of diet on biogas yield and production rate from faeces, but slight under-estimation of maximum methane yield was observed at incubation time of three months.

<footnote><sup>a</sup> Department of Animal and Veterinary Sciences, AU Viborg, Research Center Foulum, Aarhus University, Blichers Allé 20, DK, 8830, Tjele, Denmark</footnote>

<footnote><sup>b</sup> UniLaSalle, FR, 60026, Beauvais, France</footnote>

<footnote><sup>c</sup> Department of Biological and Chemical Engineering, Aarhus University, Blichers Allé 20, DK, 8830, Tjele, Denmark</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: gigi@anivet.au.dk (G. Giagnoni).</footnote>
# 1. Introduction

The manure from livestock can be used for producing methane ($CH_4$) by anaerobic digestion, which upcycles manure by creating renewable energy, as well as reducing emission of $CH_4$ from manure management. The diet of dairy cows is usually optimized for milk production performance, but due to the large amount of enteric $CH_4$ emitted there is growing interest in formulating diets to influence rumen function and reducing enteric $CH_4$ emission (Beauchemin et al., 2022; Knapp et al., 2014). Carbohydrate and fat concentrations in the diet can be manipulated to reduce enteric $CH_4$ (Knapp et al., 2014). Dietary manipulation does not only affect the enteric $CH_4$ emission, but it also affects the biogas and $CH_4$ potential of the manure when utilised in a biogas plant (Hassanat and Benchaar, 2019; Møller et al., 2014). Therefore, increasing the $CH_4$ yield of the manure by dietary modification might lower the need for biomass energy crops and increase profitability, thus reducing biogas competition with feed and food production (Esteves et al., 2019).

The type and amount of forage included in the diet can affect $CH_4$ yield from manure. Hellwing et al. (2014) found that manure from cows fed a maize silage-based diet had 30% higher maximum $CH_4$ biogas yield than cows fed grass silage-based diet. Hassanat and Benchaar (2019) found an increase of 50%, when maize silage was used instead of red clover silage. An interaction between forage and concentrate as carbohydrate sources was found for enteric $CH_4$ measurements (Giagnoni et al., 2024). Methane production from manure could be improved in presence of favourable interactions of dietary carbohydrate sources, however is necessary to understand if and how the interaction between forage and concentrate affects the manure $CH_4$ yield. Hellwing et al. (2014) and Hassanat and Benchaar (2019) found that maximum $CH_4$ production from manure was 20% higher when supplementing the diet with 3 percentage units of fat as rapeseed or linseed oil, respectively, in maize based diets. Møller et al. (2014) estimated that maximum $CH_4$ yield increased by 8% for each percentage unit of added fat in the diet, however curvilinear response was not tested due to the experimental design used. Huhtanen et al. (2021) estimated manure $CH_4$ yield for dietary nutrients, their digestibility, and the resulting faecal nutrients, including fat, however, to our knowledge there is no study investigating the linear effect of individual fat sources. Finally, the previously mentioned studies have had the ultimate $CH_4$ yield in focus,

but lacking estimation of modelling parameters such as gas production rate, and lag time (Lay et al., 1997), which are relevant for optimization of the substrate for anaerobic biogas fermentation.

The objective of this study is to evaluate the effect on the *in vitro* $CH_4$ yield from dairy cow faeces, when the diet is manipulated with fat or carbohydrates, using faeces samples from two experiments. More specifically, for fat the effect of rapeseed or palm kernel fat supplemented at increasing dietary concentration, and for carbohydrates the effect of grass-clover vs maize silage, and barley vs dried beet pulp as carbohydrate sources from forages and concentrates were tested. For the fat, it was hypothesised that increasing dietary fat concentration increases $CH_4$ yield from faeces. For the carbohydrates, it was hypothesised that the effect of the carbohydrate inclusion from forage and concentrate is additive, meaning that there is no interaction between forage and concentrate. This study used samples from the feeding trials reported by Giagnoni et al. (2025), for the fat, and by Giagnoni et al. (2024), for the carbohydrates.

# 2. Materials and methods

In the feeding trials all animals were treated according to the guideline of the Danish Ministry of Environment and Food (Law No. 474, 15 May 2014) regarding animal experimentation and care for animals used for scientific purposes. Since the current study used frozen faeces from the feeding trials, no animal experiment permit was necessary.

## 2.1. Animals, experimental design and diets

### 2.1.1. Experiment 1

In Experiment 1 (Giagnoni et al., 2025), 48 lactating Danish Holstein cows (24 primiparous and 24 multiparous) were used. The cows were divided in eight blocks, by parity and days in lactation, and each block was assigned to a unique 6 × 6 Latin square design, with 6 treatments and 6 periods of 21 d each. The treatments were balanced for first order carry-over effect across Latin square replicates. The dietary treatments of Experiment 1 were dietary concentrations of fat and fat source. The fat sources were cracked rapeseed (RS) and palm kernel fatty acids (PKFA). The six dietary treatments were: control (CO), low RS (LR), medium RS (MR), high RS (HR), low PKFA (LP) and medium PKFA (MP), with 20.4, 32.7, 45.0, 57.3, 32.2, and 44.2 g fatty acids/kg DM,

<caption>**Table 1**</caption>

Ingredients and nutrient composition in feed and faeces of the treatments in Experiment 1 (g/kg of DM unless otherwise noted, average ± SD).

<table><thead><tr><th rowspan="3">Ingredient</th><th colspan="6">Treatment<sup>1,2</sup></th></tr><tr><th rowspan="2">CO</th><th colspan="3">Cracked rapeseed</th><th colspan="2">Palm kernel fatty acids</th></tr><tr><th>LR</th><th>MR</th><th>HR</th><th>LP</th><th>MP</th></tr></thead><tbody><tr><td>Rapeseed meal</td><td>220</td><td>203</td><td>186</td><td>170</td><td>220</td><td>220</td></tr><tr><td>Cracked rapeseed</td><td>0</td><td>29.7</td><td>59.3</td><td>89.0</td><td>0</td><td>0</td></tr><tr><td>Palm kernel fatty acids</td><td>0</td><td>0</td><td>0</td><td>0</td><td>12.7</td><td>25.4</td></tr><tr><td>Basal diet<sup>3</sup></td><td>780</td><td>767</td><td>754</td><td>742</td><td>767</td><td>754</td></tr><tr><td>Diet nutrients</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Dry matter, g/kg</td><td>445 ± 9.52</td><td>452 ± 11.3</td><td>446 ± 12.3</td><td>447 ± 10.3</td><td>448 ± 10.5</td><td>452 ± 9.99</td></tr><tr><td>Organic matter</td><td>931 ± 1.5</td><td>932 ± 2.2</td><td>933 ± 1.5</td><td>934 ± 1.2</td><td>932 ± 0.98</td><td>933 ± 0.71</td></tr><tr><td>Neutral detergent fibre</td><td>321 ± 8.4</td><td>321 ± 13</td><td>324 ± 5.3</td><td>324 ± 14</td><td>322 ± 7.3</td><td>319 ± 6.6</td></tr><tr><td>Starch</td><td>182 ± 20</td><td>179 ± 20</td><td>176 ± 20</td><td>173 ± 19</td><td>180 ± 20</td><td>176 ± 20</td></tr><tr><td>Crude protein</td><td>169 ± 5.9</td><td>164 ± 3.3</td><td>163 ± 3.7</td><td>160 ± 2.1</td><td>166 ± 4.9</td><td>164 ± 2.5</td></tr><tr><td>Crude fat</td><td>29.8 ± 0.63</td><td>43.3 ± 0.53</td><td>56.8 ± 0.43</td><td>70.3 ± 0.33</td><td>42.8 ± 0.65</td><td>56.2 ± 0.62</td></tr><tr><td>Fatty acids<sup>4</sup></td><td>20.4 ± 0.37</td><td>32.7 ± 0.60</td><td>45.0 ± 0.99</td><td>57.3 ± 1.42</td><td>32.2 ± 0.37</td><td>44.2 ± 0.36</td></tr><tr><td>Faeces nutrient</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Dry matter, g/kg</td><td>135. ± 6.65</td><td>139. ± 4.46</td><td>141. ± 6.36</td><td>147. ± 8.39</td><td>144. ± 5.53</td><td>154. ± 4.22</td></tr><tr><td>Organic matter</td><td>877 ± 19.7</td><td>879 ± 13.6</td><td>883 ± 11.8</td><td>882 ± 18.5</td><td>879 ± 10.8</td><td>879 ± 26.2</td></tr></tbody></table>

<footnote n="1">¹ CO = control, LR = low rapeseed, MR = medium rapeseed, HR = high rapeseed, LP = low palm kernel, MP = medium palm kernel.</footnote>

<footnote n="2">² n = 6, 1 sample for each period, unless stated otherwise.</footnote>

<footnote n="3">³ Basal diet composition (g/kg of DM): 172 rolled spring barley, 121 rolled dried beet pulp, 181 primary growth grass-clover silage, 121 first regrowth grass-clover silage, 383 maize silage, 16.1 sodium bicarbonate, 5.0 minerals, 1.0 vitamins and 1.5 $TiO_2$.</footnote>

<footnote n="4">⁴ Analysed based on the weighted average between PMR and bait concentrate concentration. In the case of crude fat, the concentration is calculated from the analysis on the individual ingredients pooled by 2 consecutive periods (n = 3).</footnote>
<table><caption>**Table 2**

Ingredients and nutrient composition (g/kg DM, unless otherwise noted) in feed and faeces of the diets used in Experiment 2.</caption><thead><tr><th rowspan="2"></th><th colspan="4">Diet<fnref n="1" /></th></tr><tr><th>GB</th><th>GD</th><th>CB</th><th>CD</th></tr></thead><tbody><tr><td>Ingredients<sup>b</sup></td><td></td><td></td><td></td><td></td></tr><tr><td>Grass-clover silage, spring growth</td><td>275</td><td>275</td><td>-</td><td>-</td></tr><tr><td>Grass-clover silage, 1st regrowth</td><td>275</td><td>275</td><td>-</td><td>-</td></tr><tr><td>Maize silage</td><td>-</td><td>-</td><td>542</td><td>542</td></tr><tr><td>Barley</td><td>215</td><td>-</td><td>215</td><td>-</td></tr><tr><td>Dried beet pulp</td><td>-</td><td>215</td><td>-</td><td>215</td></tr><tr><td>Other ingredients<sup>2</sup></td><td>234</td><td>234</td><td>242</td><td>242</td></tr><tr><td>Diet nutrients</td><td></td><td></td><td></td><td></td></tr><tr><td>Dry matter, g/kg</td><td>505 ± 10.5</td><td>510 ± 11.1</td><td>454 ± 7.61</td><td>456 ± 8.48</td></tr><tr><td>Organic matter</td><td>919 ± 1.7</td><td>904 ± 0.99</td><td>946 ± 1.2</td><td>930 ± 2.5</td></tr><tr><td>Neutral detergent fibre</td><td>292 ± 6.3</td><td>340 ± 4.4</td><td>258 ± 9.2</td><td>312 ± 3.6</td></tr><tr><td>Starch</td><td>143 ± 1.4</td><td>7.45 ± 4.3</td><td>340 ± 0.96</td><td>199 ± 1.3</td></tr><tr><td>Crude protein</td><td>177 ± 3.6</td><td>171 ± 4.2</td><td>174 ± 5.1</td><td>158 ± 5.8</td></tr><tr><td>Fat</td><td>41.8 ± 1.01</td><td>34.9 ± 1.01</td><td>41.8 ± 0.735</td><td>34.9 ± 0.735</td></tr><tr><td>Faeces nutrients</td><td></td><td></td><td></td><td></td></tr><tr><td>Dry matter, g/kg</td><td>109 ± 4.64</td><td>116. ± 5.40</td><td>142. ± 1.53</td><td>140. ± 7.86</td></tr><tr><td>Organic matter</td><td>916 ± 4.14</td><td>911 ± 2.33</td><td>918 ± 1.53</td><td>916 ± 1.64</td></tr></tbody></table>

respectively (Table 1). The diets were formulated to meet animal requirements according to NorFor feeding system (Volden, 2011), and the diets were mixed as partial mixed rations and fed ad libitum. The diet consisted of a basal diet, which was diluted with rapeseed meal and the fat source to reach the required fat concentration (Table 1). In addition, the cows could receive up to 1 kg of pelleted concentrate from a GreenFeed unit (C-Lock, Rapid City, South Dakota, United States) that measured enteric gas exchange by spot sampling, with up to 5 measurements per cow per day. Enteric CH₄ emission and GreenFeed settings are reported in Giagnoni et al. (2025). The basal diet was based on maize silage, grass-clover silage, rolled barley, dried beet pulp and rapeseed cake. Mineral and vitamin supplements were added in the basal diet to avoid deficiencies.

### 2.1.2. Experiment 2

For Experiment 2 (Giagnoni et al., 2024), 24 Danish Holstein cows (12 primiparous and 12 multiparous) were used in a cross-over design with two periods of 21 d. The cows were divided in blocks of four according to their parity and days in lactation. Within block, each treatment appeared once within each period, and the treatments were balanced for carry-over effect across blocks. In Experiment 2, the dietary factors studied were carbohydrates sources from silages and concentrates (Table 2). Two silage types were used: maize silage, included at 54.2% dry matter (DM), and a 1:1 DM ratio of spring growth and first regrowth grass-clover silage, included at 55% DM. The concentrates used were barley and dried beet pulp (21% DM inclusion). The four diets used were based on: grass-clover silage and barley (GB), grass-clover silage and dried beet pulp (GD), maize silage and barley (MB) and maize silage and dried beet pulp (MD). Diets were mixed as total mixed ration and offered ad libitum, and enteric CH₄ was measured in respiration chambers.

### 2.2. Sampling and laboratory analyses

For Experiment 1, four subsamples of faeces each of 200 mL were collected from each of the 24 multiparous cows in every period. Faecal samples were collected on d 19 at h 1400, on d 20 at h 0800 and 1400 and on d 21 at h 0800 of each period. For Experiment 2, two subsamples of faeces each of 500 mL were collected from each of the 24 cows in every period. Faecal samples were collected on d 18 at h 0800 and 1400 of each period. In both experiments the subsamples were frozen after collection, thawed when the experiment was completed to be pooled

within cow and period in a single sample, then manually homogenised and split in two replicated samples, first and second. The two samples were stored again in the freezer at -16.5°C. The first replicated samples of faeces from individual cows were used for chemical analysis, where it was first dried in a forced air oven at 60°C for 48 h where DM was determined. Then, the samples were ground to 1 mm (Ultra Centrifugal Mill ZM 200, Verder Scientific, Hann, Germany) and analysed for ash by combustion at 525°C for 6 h in a furnace (Nabertherm GmbH, Lilienthal, Germany). Organic matter (OM) was obtained by difference between total DM and ash. The same methods were used for DM and OM determination of the diets in each period. Furthermore, the diet samples were analysed for neutral detergent fibre (NDF), according to Mertens et al. (2002), and crude protein, using the Dumas method (Hansen, 1989). Dietary fat was analysed by soxhlet extraction with petroleum ether after acid hydrolysis (Stoldt, 1952), and fatty acids were analysed by gas chromatography as described in Giagnoni et al. (2025). Dietary fat was analysed in the partial mixed rations in Experiment 1, but in Experiment 2 it was analysed in the individual ingredients and then calculated for the total mixed ration by factorial approach. Fatty acids were analysed on individual ingredients, and then calculated for the total mixed ration by factorial approach. Dietary starch was analysed according to the method by Kristensen et al. (2007). Dietary starch was analysed in Experiment 1 in the individual ingredients and then calculated for the partial mixed ration by factorial approach, but in Experiment 2 it was analysed in the total mixed rations.

The second replicate samples of faeces from individual cows were thawed and pooled within diet and experimental period the day before starting the in vitro system for biogas measurements. Samples from Experiment 1 were composed of manure from four individual cows, and samples from Experiment 2 were composed of manure from six individual cows. In total, 36 samples from Experiment 1 (6 diets × 6 period) and eight sample from Experiment 2 (4 diets × 2 periods) were run in the in vitro batch assay system.

### 2.3. Biogas and methane measurements

An inoculum from an active full-scale biogas reactor (Aarhus University, Denmark) operating at 51°C and fed cattle slurry, pig slurry and deep litter manure, was collected, and filtered using a 1 mm sieve to improve its homogeneity and reduce its potential gas production due to substrate addition via the inoculum. In addition, the inoculum was incubated for 15 d at 50 ± 2°C, to reduce biodegradable organic

<footnote n="1">¹ Cell values with a dash mean that the ingredient was not used.</footnote>

<footnote n="2">² The other ingredients were (g/kg DM): 105 rapeseed cake, 105 soybean meal, 9 sodium carbonate, 6 mineral and vitamin mix, 6 limestone, 3 salt, and for the maize diets 8 urea mix (80% urea, 13.5% sodium sulphate and 6.5% limestone).</footnote>
<caption>**Table 3**</caption>

Ultimate CH₄ yield and estimated coefficients for the modified Gompertz function for the manure of dairy cows fed diets including cracked rapeseed (RS) or palm kernel fatty acids (PKFA) at different concentrations from Experiment 1.

<table><thead><tr><th rowspan="2">Coefficient<sup>1</sup></th><th colspan="6">Diet<sup>2</sup></th><th rowspan="2">SEM</th><th colspan="4">P-value<sup>3</sup></th></tr><tr><th>CO</th><th>LR</th><th>MR</th><th>HR</th><th>LP</th><th>MP</th><th>Diet</th><th>RS.L</th><th>RS.Q</th><th>PKFA.L</th><th>PKFA.Q</th></tr></thead><tbody><tr><td>B<sub>0</sub></td><td>283<sup>a</sup></td><td>297<sup>ab</sup></td><td>308<sup>bc</sup></td><td>319<sup>c</sup></td><td>276<sup>a</sup></td><td>288<sup>ab</sup></td><td>6.2</td><td>&lt;0.001</td><td>&lt;0.001</td><td>0.79</td><td>0.46</td><td>0.16</td></tr><tr><td>P</td><td>271<sup>a</sup></td><td>283<sup>ab</sup></td><td>294<sup>bc</sup></td><td>304<sup>c</sup></td><td>265<sup>a</sup></td><td>276<sup>ab</sup></td><td>5.7</td><td>&lt;0.001</td><td>&lt;0.001</td><td>0.82</td><td>0.45</td><td>0.16</td></tr><tr><td>R<sub>max</sub></td><td>21.5<sup>ab</sup></td><td>25.1<sup>abc</sup></td><td>26.2<sup>bc</sup></td><td>29.0<sup>c</sup></td><td>21.1<sup>a</sup></td><td>22.8<sup>ab</sup></td><td>1.3</td><td>&lt;0.001</td><td>&lt;0.001</td><td>0.68</td><td>0.40</td><td>0.49</td></tr><tr><td>λ</td><td>1.25<sup>a</sup></td><td>1.80<sup>ab</sup></td><td>1.95<sup>ab</sup></td><td>2.35<sup>b</sup></td><td>1.33<sup>a</sup></td><td>1.40<sup>a</sup></td><td>0.20</td><td>&lt;0.001</td><td>&lt;0.001</td><td>0.66</td><td>0.55</td><td>1.00</td></tr></tbody></table>

a-c Different letters indicate significant difference within row ($p < 0.05$)

¹ $B_0$ = ultimate CH₄ yield (mL/g of OM) at d 90; P = maximum CH₄ yield (mL/g of OM); $R_{max}$ = maximum CH₄ production rate (mL/g of OM/d), $\lambda$ = lag time (d)

² CO = control, LR = low RS, MR = medium RS, HR = high RS, LP = low PKFA, MP = medium PKFA; where superscript letters indicate statistical difference between treatment within row

³ L = linear effect, Q = quadratic effect, by dietary fat concentration within fat source, including control diet as a baseline

residues. The bottles (500 mL) were first filled with 200 g of inoculum, and then calculated masses of faeces were added to give an inoculum to substrate ratio of 1:1 based on the OM. Each sample was incubated in three bottles (three replicates). In addition, three control bottles containing only inoculum (200 g each) were incubated to correct for biogas and CH₄ yield from inoculum alone.

The bottles were flushed for 2 min with N₂ gas (>99.999%) to expel the air in the bottles, and to re-establish an anaerobic environment. After this, rubber stoppers were used to close the bottles, which were then fixed with an aluminium screw ring. All bottles were incubated at 50 ± 2°C for 90 d in a temperature controlled room. The volume and composition of biogas were measured at 5, 7, 11, 18, 26, 61, 74 and 90 d of incubation. The volume of gas in the bottle was quantified by transferring the headspace gas from the bottle to a graduated cylinder (built in-house), by piercing the rubber stopper in the bottle with a needle connected to a tube, which vented at the base of the respective measurement cylinder. The volume of water displaced in the cylinder was considered as the volume of biogas produced in the bottle. Three cylinders were used simultaneously to measure the three replicated samples together. After each measurement, the cylinders were emptied of water and gas, and refilled with water for the following measurement. The graduated cylinders were calibrated for the slight negative pressure caused by the weight of the water hanging in each tube. The cylinders were made of polycarbonate and had an internal diameter of 44 mm internal. The water in the cylinder was acidified with sulphuric acid, targeting 2 pH, which was checked with a coloured paper strip.

During each volume measurement, a gas sample was taken from one of the three replicate bottle by drawing ca. 50 mL of gas from the measurement tube with a syringe and injecting it into a glass vial for analysis by gas chromatography. Gas chromatography was performed with a Perkin Elmer Clarus 500 gas chromatograph (Waltham, Massachusetts, USA), equipped with a thermal conductivity detector (Sutaryo et al., 2012). The carrier gas used was He injected with a flow rate of 30 mL/min.

## 2.4. Calculations and parameter estimation

The kinetic model used for estimating the CH₄ production was the modified Gompertz model (Lay et al., 1997), reported below:

$$M_t = P \cdot \exp \left\{ - \exp \left[ \frac{R_{max} \cdot e}{P} \cdot (\lambda - t) + 1 \right] \right\}$$

where $M_t$ is the cumulative CH₄ yield (mL/g of OM) at time $t$ (0 to 90 d), P is the maximum CH₄ yield (mL/g of OM); $R_{max}$ is the maximum CH₄ production rate (mL/g of OM/d); $\lambda$ is the lag time (d), and e is exp(1). The coefficients of the modified Gompertz model were estimated for each experimental unit (dietary treatment × experimental period within experiment) using the function nlsList from the nlme package (Pinheiro et al., 2024) in R software (R Core Team, 2024), using starting coefficients of 228, 14 and 1 for P, $R_{max}$ and $\lambda$, respectively. The ultimate

CH₄ yield was the cumulative CH₄ yield measured at d 90, and defined as $B_0$ (mL/g of OM).

## 2.5. Statistical analyses

The effect of the dietary treatments on the estimated coefficients was tested separately for the two experiments using a linear mixed models in R software from the lmer function from lme4 package (Bates et al., 2015). In Experiment 1 the following linear mixed model was used:

$$Y_{ik} = \mu + D_i + P_k + \varepsilon_{ik}$$

where $Y_{ik}$ is the dependent variable (coefficients P, $R_{max}$, or $\lambda$), $\mu$ is the main intercept, $D_i$ is the intercept change for the dietary treatment ($i$ = CO, LR, MR, HR, LP or MP), $P_k$ is the random effect of the period ($k$ = 1,...,6), and $\varepsilon_{ik}$ is the random residual error assumed to be independent, normally distributed, and with homogeneous variance. In Experiment 2 the following model was used:

$$Y_{sck} = \mu + S_s + C_c + S_s C_c + P_k + \varepsilon_{sck}$$

where $Y_{sck}$ is the dependent variable (coefficients P, $R_{max}$, or $\lambda$), $\mu$ is the main intercept, $S_s$ is the intercept change for the silage treatment ($s$ = G or M), $C_c$ is the intercept change for the concentrate treatment ($c$ = B or D), $S_s C_c$ is the intercept change for the interaction between $S_s$ and $C_c$, $P_k$ is the random effect of the period ($k$ = 1 or 2), and $\varepsilon_{sck}$ is the random residual error assumed to be independent, normally distributed, and with homogeneous variance. P-values ($p$) were calculated with type 2 ANOVA. P-values below 0.05 were considered significant, and P-values between 0.05 and below 0.10 were considered as tendencies. Estimated marginal means (EMM) were produced from the emmeans package (Lenth et al., 2023). In Experiment 1, the contrast for linear and quadratic effects were evaluated for the RS treatments (CO, LR, MR, HR) and PKFA treatments (CO, LP, MP).

The response of maximum CH₄ yield (P) to fat concentration in Experiment 1, and starch and NDF concentrations in Experiment 2, were evaluated by estimating intercept and slope coefficient (nutrient concentration as % of DM) with a linear regression model (Fig. 2). Finally, the fit of the modified Gompertz model was visually evaluated at each time point, by calculating the residual (observed – predicted), as the proportion of the mean observed value at a given time point (Fig. 3).

# 3. Results and discussion

## 3.1. Experiment 1

Experiment 1 investigated the effect of source and concentration of dietary fat on CH₄ production of the manure when anaerobically digested. The maximum CH₄ yield increased linearly with increasing fat concentration for RS ($p < 0.001$; Table 3), but not for PKFA diet ($p = 0.45$). The faeces from cows fed HR resulted in the highest $B_0$, P, and $R_{max}$, as well as $\lambda$, among faeces from Experiment 1. Compared to faeces
<caption>**Table 4**</caption>

Ultimate CH₄ yield and estimated coefficients for the modified Gompertz function for the manure of dairy cows fed diet with either maize silage or grass-clover silage (M vs G) as a forage source, and including either barley or dried beet pulp (B vs D) in the concentrate fraction from Experiment 2.

<table><thead><tr><th rowspan="2">Coefficients<sup>1</sup></th><th colspan="4">Diet<sup>2</sup></th><th rowspan="2">SEM</th><th colspan="3">P-value</th></tr><tr><th>GB</th><th>GD</th><th>MB</th><th>MD</th><th>Silage</th><th>Concentrate</th><th>Silage:Concentrate</th></tr></thead><tbody><tr><td>B<sub>0</sub></td><td>289<sup>ab</sup></td><td>246<sup>a</sup></td><td>310<sup>b</sup></td><td>282<sup>ab</sup></td><td>6.3</td><td>0.01</td><td>0.005</td><td>0.30</td></tr><tr><td>P</td><td>276<sup>b</sup></td><td>234<sup>a</sup></td><td>296<sup>b</sup></td><td>268<sup>ab</sup></td><td>6</td><td>0.01</td><td>0.004</td><td>0.30</td></tr><tr><td>R<sub>max</sub></td><td>20.6<sup>a</sup></td><td>17.1<sup>a</sup></td><td>27.7<sup>a</sup></td><td>25.2<sup>a</sup></td><td>1.6</td><td>0.02</td><td>0.16</td><td>0.75</td></tr><tr><td>λ</td><td>1.05<sup>ab</sup></td><td>0.754<sup>a</sup></td><td>2.09<sup>b</sup></td><td>2.05<sup>ab</sup></td><td>0.21</td><td>0.009</td><td>0.44</td><td>0.56</td></tr></tbody></table>

a-b Different letters indicate significant difference within row ($p < 0.05$)

¹ B₀ = ultimate CH₄ yield (mL/g of OM) at d 90; P = maximum CH₄ yield (mL/g of OM); Rₘₐₓ = maximum CH₄ production rate (mL/g of OM/d), λ = lag time (d)

² Where superscript letters indicate statistical difference between treatment within row

of cows fed CO diet, faeces from cows fed HR diets resulted in 12% higher P (304 vs 271 mL/g of OM), had 35% higher Rₘₐₓ (29.0 vs 21.5 mL/g of OM/d), and around 1 d longer λ. Increasing the dietary fat concentration with PKFA diets did not have linear nor quadratic effect on B₀, P, and Rₘₐₓ, or λ (Table 3 and Fig. 2). These results confirmed partially the hypothesis that increasing dietary fat would increase maximum CH₄ yield, as this was observed for RS but not for PKFA diets. An increase in maximum CH₄ yield by increased dietary fat was found by Møller et al. (2014) when supplementing fat with rapeseed, but no effect was found by Hellwing et al. (2014) when fat was supplemented in diet with the forage fraction based on maize silage. The increase in maximum CH₄ yield can be explained by the increased faecal fat concentration, as to be expected with an increased dietary fat concentration (Huhtanen et al., 2021). The relationship between fat concentration of the biomass and maximum CH₄ yield has been found positive, as long as the fat concentration of the biomass does not exceed 50% (Ren et al., 2024). This is not an issue for dairy cows fed high dietary fat concentrations, but it should be considered if high proportions of high fat biomasses are co-digested.

## 3.2. Experiment 2

Experiment 2 investigated the effect of carbohydrate source from forages and concentrates. No interaction was found between forage and concentrate for maximum CH₄ yield, maximum CH₄ production rate, and lag time, therefore the effect of carbohydrate source on CH₄ production measures was considered additive. Maximum CH₄ yield was higher in faeces from cows fed maize silage than from cows fed grass-clover silage (282 vs 255 mL/g of OM; *p* = 0.01), and it was higher in faeces from cows fed barley than cows fed dried beet pulp (299 vs 265 mL/g of OM, *p* = 0.004). These results confirmed the hypothesis that the effects of carbohydrates from forages and concentrates were additive, as both forages and concentrates have an effect on maximum CH₄ yield, but no interactions were observed. Higher maximum CH₄ yield was also observed when substituting grass-clover with maize silage by Hellwing et al. (2014), but the difference was not clear in the study by Møller et al. (2014). Both studies applied a complete substitution of the forage, meaning that either maize or grass-clover silage were used in the forage fraction, which was similar to the samples used in the current study, from Giagnoni et al. (2024). The samples used by Møller et al. (2014) were from a feeding trial where a maize silage diet gave an increase in starch concentration of around 10 percentage units (Brask et al., 2013). In the current study, when dietary concentration of starch was related to maximum CH₄ yield, a linear relationship was found, with an increase of 2 mL/g of OM per percentage unit increase of dietary starch (Fig. 2C). A reduction in maximum CH₄ yield was also observed as the NDF concentration in the diet increased (Fig. 2D). Therefore, an effect on maximum CH₄ yield from substitution of grass-clover silage with maize silage seems to be explained by the changes in dietary starch and NDF concentrations in the current study. Maximum CH₄ production rate was higher in faeces of cows fed maize than cows fed grass-clover silage (43.6 vs 22.9 mL/g of OM/d, *p* = 0.006) and the lag time was around one

day longer for faeces of cows fed maize than cows fed grass-clover silage (*p* = 0.007). The difference between the diets, in the case of Experiment 2, could be given by the chemical composition of the manure, but also by the accuracy of the modified Gompertz model, with higher under-prediction for G than for M at d 5 of incubation (Fig. 3).

## 3.3. Modelling methane production

Fig. 2 shows that the maximum CH₄ yield increased linearly by 8.2 mL/g of OM per percentage unit of dietary fat supplemented with RS in Experiment 1. These values, when adjusted for the baseline of the CO diet (271 mL CH₄/g of OM), correspond to an increase of 3%, a lower increase than the 7% found by Hassanat and Benchaar (2019) using linseed oil, and lower than 8% increase found by Møller et al. (2014) using rapeseed. Møller et al. (2014) estimated the coefficients of a linear regression model for maximum CH₄ yield (mL/g of OM) at 203 for the intercept and 15.4 for the slope coefficient of the dietary crude fat (% of DM). No quadratic effects for fat supplementation were found for RS nor PKFA (Table 3).

This result shows that dietary use of lauric and myristic acids, the two main FA of PKFA, does not result in advantages for biogas potential, and that fat source can affect the biogas potential of dairy cow manure. In addition, Giagnoni et al. (2024) reported lower feed intake but similar OM apparent total tract digestibility for MP (medium PKFA) compared to the other diets, which means a reduced amount of manure available for anaerobic digestion compared to the same dietary fat concentration from RS.

Fig. 2C also shows the increase in CH₄ of 2 mL/g of OM per g of starch supplemented by forages and concentrates from Experiment 2. The similar decrease due to the NDF concentration of the diet is shown in Fig. 2D. While the CH₄ maximum yield increase obtained by increasing the starch content is more modest per g of nutrient compared to fat addition, the dietary range of starch that can be achieved with common feedstuffs is larger than with fat, and this might make dietary manipulation of starch/NDF/carbohydrates a more convenient way to increase biogas potential of manure of dairy cows. These findings have to be put in perspective of the limitations of *in vitro* trials, which findings are most reliable when further validated in a continuous digester. However, given the number of treatments and samples used to test our hypotheses, an *in vitro* trial was considered the adequate solution to compare the dietary treatments at this research stage.

The residuals from the modified Gompertz model are shown in Fig. 3. The residuals are adjusted for the measured CH₄ yield for a given time point and shown as a percentage. The biggest error for the model is found on the first measurement day (d 5), with residuals deviating between 20 to 50% below zero, which means an overprediction of the modified Gompertz model. This might not represent a big issue, since the amount of produced biogas at the start of the process is still a small fraction of the maximum CH₄ yield, although it will have more effect on the modelled Rₘₐₓ values. On the other hand, the residuals at two and three months of incubation (d 61 and 90) resulted in a underprediction below 10%. Therefore, the maximum CH₄ yield is slightly higher than
<figure><img src="image_10.png" /><figcaption>**Fig. 1.** Methane yield (mL/g of OM) as measured (left) and estimated by the modified Gompertz model (right). In Experiment 1 cows were fed either a control diet (CO), a low, medium, and high concentration of rapeseed (LR, MR, and HR, a low or medium concentration of palm kernel fatty acids (LP and MP, respectively). In Experiment 2 cows were fed grass-clover or maize silage (G or M), and barley or dried beet pulp (B or D).</figcaption></figure>

predicted by the models, due to a low but steady increase in CH₄ yield in the last month of incubation. The mean bias between B₀ and P is also shown in Table 3 and 4, as well as in Fig. 1 between left and right panels. From graphical observation, this deviation of the residual appears to be consistent whether fat or carbohydrates are manipulated in the diet, as well as shifting consistently regardless of the diet. This might indicate

that it should not invalidate comparison between treatments.

The deviation between B₀ and P was due to the presence of a small but steady increase in CH₄ yield after the plateau is reached. It is not clear what might cause such increase in the last weeks of incubation, it could be in relation to recycling microbial biomass, but we have not investigated it, and we are not aware of such specific study in the
A. Experiment 1 - rapeseed

<figure><img src="image_11.png" /></figure>

B. Experiment 1 - palm kernel

<figure><img src="image_12.png" /></figure>

C. Experiment 2

<figure><img src="image_13.png" /></figure>

D. Experiment 2

<figure><img src="image_14.png" /><figcaption>**Fig. 2.** Estimated marginal means and standard error for maximum CH₄ yield (*P*, circles and solid line) and ultimate CH₄ yield (*B*₀, triangles and dashed line) from faeces of cows fed increasing fat concentration with rapeseed (A) and palm kernel fatty acids (B) from Experiment 1, and with increasing starch concentration (C) and decreasing neutral detergent fibre (NDF) concentration (D) from Experiment 2. Linear regression between *y* and *x* axis for *P* resulted in *p* of <0.001, 0.52, 0.006 and <0.001 for the *x* slope coefficient, and R² of 0.56, 0.03, 0.74, 0.87, for plot A, B, C and D, respectively. The difference in slope coefficients between *P* and *B*₀, whether present, were negligible.</figcaption></figure>

literature. Across all dietary treatments in Experiment 1 and 2, the CH₄ production rate between day 26 and 90 ranged from 0.49 and 0.64 mL CH₄/d, which is well below the 1% required for the termination of incubation trials (Holliger et al., 2016).

The modified Gompertz model resulted in slight underprediction compared to use of $B_0$, however such modelling approach provides an advantage of understanding gas production rate and lag time, which are valuable parameters for optimizing mixing of biomass substrates for anaerobic digestion. We tested different modelling approaches, including a dual-pool model, however, none provided a clear improvement in the predictions. The modified Gompertz resulted in some error

($B_0$, triangles and dashed line) from the modelled parameters do not compromise the ranking of the incubated substrates, which can be observed comparing left and right graphs in Fig. 1.

The rate of gas production ($R_{max}$ in the modelled data) during the digestion of complex substrates can be considered as the apparent hydrolysis rate, as hydrolysis is the limiting factor (Batstone et al. 2009). The $R_{max}$ is relevant in full-scale applications as a faster process would require a shorter retention time and thus a smaller reactor for the same gas output. Although the quantified $R_{max}$ values found in batch studies such as those presented here are not directly comparable to rates in the
<figure><img src="image_15.png" /><figcaption>**Fig. 3.** Maximum CH₄ yield residuals (observed – predicted, y-axis) from the modified Gompertz model at different incubation days of dairy cow's faeces. Residuals are expressed as a proportion of the mean observed value at a given time point. In Experiment 1 cows were fed either a control diet (CO), a low, medium, and high concentration of rapeseed (LR, MR, and HR, a low or medium concentration of palm kernel fatty acids (LP and MP, respectively). In Experiment 2 cows were fed grass-clover or maize silage (G or M), and barley or dried beet pulp (B or D).</figcaption></figure>

continuously fed systems that are typical of full-scale process (Batstone
et al. 2009), they can however provide useful qualitative information to
operators of full-scale processes if they are measured in a single batch.
The differences in gas production rates between batch and continuously
fed processes is due to fundamental differences in feeding. A batch
process has a single relatively high loading of substrate and a gas pro-
duction that is very dynamic over time (Fig. 1), whereas a continuously
fed process can achieve very stable gas production if feeding rates and
feed composition are consistent, effectively becoming a chemostat. The
high loading of substrate in a batch assay has a direct effect on gas
production rate, with higher inoculum to substrate ratios giving higher
gas production rates (Ward et al., 2018) due to greater numbers of mi-
croorganisms available to digest the OM, hence the correlation between
gas production rate and hydrolysis rate. In fact, any variations in batch
set up, particularly inoculum source, will affect the production rates
(Ward et al., 2018). The λ values may also be relevant to full-scale
continuously fed processes, as this parameter represents a lag in gas
production. This is visible in Fig. 1, and Table 3 and 4, where decreasing
rapeseed concentration, and substitution of grass-clover silage with
maize diets reduced lag time. However, it is likely that the lag is due to

the shock of high loading, particularly of more rapidly degradable ma-
terial, in a batch assay and this may be less significant in a stable
continuous process.

4. Conclusion

Increasing dietary concentration of fat increased the maximum CH4
yield, the CH4 production rate, and the lag time when rapeseed was used
as a fat source, but use of palm kernel fatty acids in the diet did not result
in an increase of any parameter. Therefore, while fat source can increase
the CH4 yield in vitro, this is dependent on the fat source. The effect of
carbohydrate source, as forages and concentrates, was additive, and
maximum CH4 yield increased with increasing dietary starch concen-
tration. Therefore, given our carbohydrate sources and in vitro method,
there is no indication that interaction between carbohydrate sources
could increase or decrease CH4 yield. Estimated coefficients from a
modified Gompertz model are useful to understand the effect of diet on
biogas production from faeces, but slight under-estimation of maximum
CH4 yield was observed at incubation time of three months.
CRediT authorship contribution statement

**Giulio Giagnoni:** Writing – original draft, Visualization, Supervision, Formal analysis, Data curation, Conceptualization. **Alastair James Ward:** Writing – review & editing, Writing – original draft, Supervision, Resources, Methodology, Formal analysis, Data curation. **Coralie Masclet:** Writing – original draft, Formal analysis, Data curation. **Henrik Bjarne Møller:** Writing – review & editing, Resources, Methodology, Conceptualization. **Martin Riis Weisbjerg:** Writing – review & editing, Supervision, Conceptualization.

Declaration of competing interest

The authors have nothing to declare.

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