Analyzing Cooking Efficiency of Gradoli Purgatory Beans: Effects of Dehulling, Malting, and Monovalent Carbonates

Legumes, rich in protein, fiber, and micronutrients, are increasingly popular in pulse-based and gluten-free foods despite global consumption stagnating at 21 g/day due to taste, low protein digestibility, anti-nutrients, and long cooking times. Bean resistance to cooking causes textural defects like the hardshell and hard-to-cook phenomena. The pectin–cation–phytate hypothesis explains why soaking beans in sodium salts reduces cooking time by enhancing pectin solubility in water. Gradoli Purgatory beans (GPB), from Italy′s Latium region, were malted, reducing phytic acid by 32% and oligosaccharides by 63%. This study evaluated the hardness of cooked GPB seeds in various conditions, including decorticated or malted states, using a modified standard method. Cooking at 98 °C for 7–75 min on an induction hob with a water-to-seed ratio of 4 g/g was tested. Soaking was applied before cooking for conventional seeds only, followed by texture analysis. Conventional GPBs were adequately cooked if their cotyledons disintegrated upon pressing, requiring a force peak of 250 to 220 N and cooking times of 52 to 57 min. Malted, decorticated, and split GPBs cooked similarly to raw decorticated and split ones, with times of 32 and 25 min, respectively. Faster cooking was due to bean coat removal and splitting, not chemical changes. Sodium or potassium carbonate/bicarbonate at 1–2 g/L improved cooking efficiency, with 2 g/L of sodium carbonate reducing cooking time to 13 min. Higher concentrations caused non-uniform cooking. Cooking malted, decorticated, and split GPBs in sodium-carbonated water reduced greenhouse gas emissions from 561 to 368 g CO2e/kg, meeting the demand for eco-friendly and nutritionally enhanced plant protein sources.


Introduction
The global production of legumes reached approximately 102 million metric tons (Mg) in 2023 [1].Among these, dry beans, chickpeas, and lentils accounted for around 28.35, 18.1, and 6.66 million Mg, respectively [2].Despite the positive trend in pulse sales, particularly in foods formulated for diabetic and celiac patients, and a projected market growth with a compound annual growth rate of 1.7% between 2024 and 2032 [1], the global per capita consumption of legumes remains stagnant at around 21 g per day [3].This might be related to the extensive time needed for meal preparation, potential digestive problems [4], and high levels of nutrient inhibitors [5].Furthermore, raw or undercooked beans contain phytohemagglutinin, a toxic protein that can be inactivated by cooking beans for 10 min at 100 • C after soaking them for at least 5 h and discarding the soaking water [6].
Bean resistance to cooking often involves two main textural defects: hardshell (HS) and hard-to-cook (HTC).HS involves an impermeable seed coat, while HTC involves water-imbibed cotyledons that do not soften during boiling.These defects stem from prolonged storage at elevated temperatures and fluctuating relative humidity, both low and high [7].The hydration of beans during steeping and cooking is determined by factors such Foods 2024, 13, 2505 2 of 16 as bean size, seed coat thickness, chemical makeup, and hilum and micropyle dimensions, as well as external conditions, such as temperature, pH levels, and the concentration of solids in the soaking medium.
Three primary mechanisms are thought to cause the HTC effect in stored beans: (i) the limited hydration of intracellular protein; (ii) pectin insolubilization in the middle lamella due to calcium and/or magnesium ions, following the action of pectin methyl esterase (PME) and phytase; and (iii) the cross-linking of phenolics and/or protein in the middle lamella [8,9].Recent studies [8,10,11] support the pectin-cation-phytate hypothesis or the dual enzyme mechanism, which involves the actions of phytase and PME.During storage, phytic acid, which strongly binds to calcium and magnesium ions, is hydrolyzed by phytase, releasing phosphate, Ca ++ , and Mg ++ into the cotyledon cells.These ions then cross-link with middle lamella pectin.Concurrently, PME hydrolyzes pectin to methanol and pectinic acid, forming insoluble calcium and magnesium pectates, leading to hard beans.Microscopic observations revealed that bean softening mainly results from the solubilization of pectin and cell wall polysaccharides, with seed coats playing a minor role [8].Additionally, Chen et al. [11] found that during unfavorable postharvest storage condition of red haricot beans, Ca cations released during storage remained bound to cell wall pectin during soaking, whereas Mg cations leached out due to their weak binding and cell membrane damage.
Soaking beans in aqueous solutions with different sodium salts (including chloride, carbonate, bicarbonate, and phosphate) or ethylenediaminetetraacetic acid significantly decreased total cooking time by enhancing the water solubility of pectin, compared to soaking in plain water [12].For example, Avila et al. [13] reported that using 2.5% NaHCO 3 and 1% KCl efficiently increased the hydration level, decreases HTC in cowpeas, and reduces the time of cooking.Microscopic observations have revealed that beans soaked in sodium salt solutions exhibit improved cell separation [14].Monovalent cations like Na + and K + weaken cotyledon tissue by quickly breaking pectin linkages and increasing pectin solubility [15].Similarly, common bean cooking in 0.1 mol/L NaHCO 3 solution accelerated softening [8].Moreover, beans steeped in solutions containing sodium phytate reduced cooking time by chelating calcium ions from pectates, which improved cellular separation [16].These salt treatments effectively reduced bean cooking time but slightly affected the cooked bean flavor [17].The most effective soaking solution contained as much as 0.5% NaHCO 3 and 2.5% K 2 CO 3 (w/v), but the soaking water needed to be discarded and the soaked beans were washed with fresh water before cooking [17].However, it remains uncertain whether reducing the concentration of these saline solutions might improve the final taste of cooked beans.
Among various technologies tested to reduce anti-nutrients in legumes [18,19], soaking beans to stimulate sprouting was found to enhance nutritional quality, reduce antinutrients, and shorten cooking time for red beans [20].Moreover, Cimini et al. [21][22][23] showed that malting, a process commonly used in brewing, was effective for three typical varieties-Gradoli Purgatory beans, Valentano Straight Furrow chickpeas, and Onano lentils-traditionally grown in the province of Viterbo, Italy [24].Gradoli Purgatory beans resemble Cannellini beans but have a thinner skin.Since the 17th century, they have been a traditional feature of the Purgatory Lunch in Gradoli, Italy, on the first Lensel day [25].Rich in protein and resistant starch [22], these beans are ideal for vegetarian diets and beneficial for individuals with celiac disease or diabetes.
Longer cooking times result in higher energy use, leading to efforts to breed fastercooking bean varieties to encourage consumption [26].
Various methods have been tested to assess cooking times, but no standardized method has been established [27].For instance, the degree of seed penetration by the 25 plungers of an automated Mattson cooker varies from 50% to 100%, affecting cooking times.Wang and Daun [28] suggest that the nominal cooking time for pulses is based on penetrating 80% of 25 seeds pre-soaked in distilled water for 24 h at room temperature and then cooked in 1.2 L of boiling water.In contrast, the American Association of Cereal Chemists (AACC) standard method 56-36.01[29] evaluates the firmness of a 40-g sample (pre-soaked in 160 mL of distilled water for 24 h and cooked in 1.0 L of boiling water) using a mini-Kramer shear cell compression test [29].This method helps determine the optimal cooking time by evaluating how the firmness changes with cooking.Although this approach is more reliable due to the larger sample size, it is labor-intensive due to the difficulty of cleaning the Kramer shear cell [27].To address this, the method was modified by increasing the cooked bean sample size from 40 to 70 g and replacing the Kramer shear cell with the Ottawa Texture Measuring System (Techlab Systems, Itasca, IL, USA), which features a square test cell with solid walls and a perforated base.Compression tests with this system generated texture profile analysis (TPA) graphs comparable to those from the Kramer shear cell [30].
Thus, this study aimed to assess the hardness of GPB seeds in various forms, including decorticated and malted, as a function of cooking time in boiling tap water or low-salt water.The evaluation utilized an adapted method to illustrate how malted decorticated beans can help reduce greenhouse gas emissions from cooking while providing nutritionally enhanced plant-based protein.

Processing
The beans either underwent a sequential process of soaking, drying, decortication, and splitting or were subjected to malting.A schematic overview of both processing methods is provided in Figure 1.
times.Wang and Daun [28] suggest that the nominal cooking time for pulses is based on penetrating 80% of 25 seeds pre-soaked in distilled water for 24 h at room temperature and then cooked in 1.2 L of boiling water.In contrast, the American Association of Cereal Chemists (AACC) standard method 56-36.01[29] evaluates the firmness of a 40-g sample (pre-soaked in 160 mL of distilled water for 24 h and cooked in 1.0 L of boiling water) using a mini-Kramer shear cell compression test [29].This method helps determine the optimal cooking time by evaluating how the firmness changes with cooking.Although this approach is more reliable due to the larger sample size, it is labor-intensive due to the difficulty of cleaning the Kramer shear cell [27].To address this, the method was modified by increasing the cooked bean sample size from 40 to 70 g and replacing the Kramer shear cell with the Ottawa Texture Measuring System (Techlab Systems, Itasca, IL, USA), which features a square test cell with solid walls and a perforated base.Compression tests with this system generated texture profile analysis (TPA) graphs comparable to those from the Kramer shear cell [30].
Thus, this study aimed to assess the hardness of GPB seeds in various forms, including decorticated and malted, as a function of cooking time in boiling tap water or low-salt water.The evaluation utilized an adapted method to illustrate how malted decorticated beans can help reduce greenhouse gas emissions from cooking while providing nutritionally enhanced plant-based protein.

Processing
The beans either underwent a sequential process of soaking, drying, decortication, and splitting or were subjected to malting.A schematic overview of both processing methods is provided in Figure 1.The malting process was conducted in a 100 kg pilot-scale malting unit (Bbc Inox Srl, Possagno, TV, Italy), which automates all phases of the process (see Figure 2).The procedure involved the following steps: (1) Washing: A total of 50 kg of dried GPBs was washed using 200 L of water and measured using an LZS-25 (D) Jectse flow meter with a measuring range of 60-600 L/h and an accuracy of 4% at the upper range.(2) Steeping: The first phase of the malting process involved soaking the beans for 5 h in 200 L of water at 25 °C.This increased the bean water level from 12 to 54.7 ± 1.4 % (w/w) [22].The malting process was conducted in a 100 kg pilot-scale malting unit (Bbc Inox Srl, Possagno, TV, Italy), which automates all phases of the process (see Figure 2).The procedure involved the following steps: (1) Washing: A total of 50 kg of dried GPBs was washed using 200 L of water and measured using an LZS-25 (D) Jectse flow meter with a measuring range of 60-600 L/h and an accuracy of 4% at the upper range.(2) Steeping: The first phase of the malting process involved soaking the beans for 5 h in 200 L of water at 25 • C.This increased the bean water level from 12 to 54.7 ± 1.4 % (w/w) [22].(3) Germination: After draining the steeping water, the beans were kept germinating at 25 • C with continuous humidification for 72 h.The degradation of major antinutrients, such as phytic acid and α-galactosides, was analyzed utilizing specific assay kits from Megazyme Ltd. (Bray, Ireland).(4) Dehydration: The germinated beans were dried to a final water fraction of 10 ± 2% (w/w) by setting the maximum temperature at 55 • C for 12-18 h.
The cotyledons of the malted GPBs were separated from the sprouted rootlets and cuticle fragments using a stone roller dehuller model D-250 (Zanotti srl, Casalvolone, Italy), which had a nominal capacity of 250 kg/h.The stone rollers gently broke the bean cuticles and rootlets without damaging the inner cotyledons.As waste materials were aspirated away, the recovery yield of split cotyledons reached 85 ± 2% of the input GPBs [22].

Characterization of Bean Seeds
All seeds, both before and after the malting process, were evaluated using the following physical tests: seed weight (mS), seed volume (VS), average radius (RS), density (ρS), hydration capacity (HC), and swelling capacity (SC), as previously detailed [21].
Moisture content was measured by splitting the beans and then drying them at 110 °C for about 20 min with a Kern DAB 100-3 thermostatic scale (Kern & Sohn GmbH, Balingen, Germany).The total starch and resistant starch contents were measured using specific kits from Megazyme Ltd. (Bray, Ireland).The protein content was determined according to method 992.23 [31], using a nitrogen conversion factor of 6.25.

Bean Cooking Procedure
Approximately 750 g of Gradoli Purgatory bean seeds, whether whole, split, or malted, were weighed and placed into a pot.Tap water at 20 °C was added to achieve a soaking ratio of 4 g of water per g of beans [32].The beans were soaked at this temperature for 16 h.After draining the soaking water, the hydrated beans were moved to a pot with 3 kg of water and cooked with the lid on at 98 °C for 20 to 75 min using a 2-kW induction cooker (INDU, Melchioni Spa, Milan, Italy).Decorticated and split GPB cotyledons, whether raw or malted, were cooked directly without pre-soaking.They were placed in room-temperature tap water and boiled at 98 °C for 20 to 57 min.Additionally, malted Energy consumption during the malting process was monitored using an intelligent digital AC/DC clamp multimeter model AP 570T-APP (Aoputtriver Technology Co., Ltd.).
The cotyledons of the malted GPBs were separated from the sprouted rootlets and cuticle fragments using a stone roller dehuller model D-250 (Zanotti srl, Casalvolone, Italy), which had a nominal capacity of 250 kg/h.The stone rollers gently broke the bean cuticles and rootlets without damaging the inner cotyledons.As waste materials were aspirated away, the recovery yield of split cotyledons reached 85 ± 2% of the input GPBs [22].

Characterization of Bean Seeds
All seeds, both before and after the malting process, were evaluated using the following physical tests: seed weight (m S ), seed volume (V S ), average radius (R S ), density (ρ S ), hydration capacity (HC), and swelling capacity (SC), as previously detailed [21].
Moisture content was measured by splitting the beans and then drying them at 110 • C for about 20 min with a Kern DAB 100-3 thermostatic scale (Kern & Sohn GmbH, Balingen, Germany).The total starch and resistant starch contents were measured using specific kits from Megazyme Ltd. (Bray, Ireland).The protein content was determined according to method 992.23 [31], using a nitrogen conversion factor of 6.25.

Bean Cooking Procedure
Approximately 750 g of Gradoli Purgatory bean seeds, whether whole, split, or malted, were weighed and placed into a pot.Tap water at 20 • C was added to achieve a soaking ratio of 4 g of water per g of beans [32].The beans were soaked at this temperature for 16 h.After draining the soaking water, the hydrated beans were moved to a pot with 3 kg of water and cooked with the lid on at 98 • C for 20 to 75 min using a 2-kW induction cooker (INDU, Melchioni Spa, Milan, Italy).Decorticated and split GPB cotyledons, whether raw or malted, were cooked directly without pre-soaking.They were placed in room-temperature tap water and boiled at 98 • C for 20 to 57 min.Additionally, malted bean cotyledons were cooked without pre-soaking in tap water that contained 1 or 2 g/L of sodium (E500) or potassium (E501) carbonate (i) or bicarbonate (ii).The induction hob was first set to its maximum power of 2 kW until the water reached boiling point, then was reduced to 0.4 kW for the rest of the cooking.Keeping the pot covered throughout further minimized water evaporation.The electric energy consumed by the hob (E S ) was recorded using a digital power meter (model MP600, RCE Srl, Salerno, Italy).Cooked beans were retrieved from the cooking water with a colander, cooled under running tap water for 90 s, and then allowed to drain.

Analytical Methods
A quantity of 70.0 ± 0.5 g of cooked beans was placed into an Ottawa Texture Measuring System (Techlab Systems, Itasca, IL, USA).A 4 cm × 4 cm probe was affixed to the compression plate of a Universal Testing Machine model 3342 (Instron Int. Ltd., High Wycombe, UK), which was equipped with a 1000-N load cell to measure the compression force applied.The probe speed was set to 1 mm/s.The compression plate was initially adjusted to ensure each cooked sample was at a height of 20 mm, ensuring uniform seed orientation on the probe.After this adjustment, the plate was returned to its starting position.Following a 5-s relaxation time, each sample underwent two successive 25% compression cycles to simulate jaw action.Textural parameters were extracted from the resulting force-versus-time curves, according to Bourne [33].The hardness of the cooked beans at 25% deformation was defined by the peak force during the first (H 1 ) or second (H 2 ) compression cycle.Cohesiveness, or cohesion energy resilience (CER), was calculated as the ratio of the areas under the force-versus-time curves for the second (AC 2 ) and first (AC 1 ) compression cycles, while the cohesion force resilience (CFR) was defined as the ratio of H 2 to H 1 .Each texture profile analysis (TPA) test was performed at least five times.
Seed softening was modeled using a two-parameter non-linear exponential regression equation [34], given by: where H 1 and H 10 denote the current and initial peak forces during the first compression cycle, t C is the cooking time, and K F is the rate constant for seed softening.
The optimal cooking time (OCT) for the beans was established by six trained panelists who evaluated the firmness of the beans at various cooking intervals.Additionally, a sensory cookability test, known as the pinching test, was performed to evaluate the softness of the beans by pressing them between the thumb and index finger.Beans were considered properly cooked if their cotyledons broke down under this pressure [35].

Energy Balance and GHG Emissions Associated with Bean Cooking
The theoretical energy needed to raise the initial quantities of cooking water (m WC ) and pre-hydrated beans (m HB ) from the initial temperature T 0 to the boiling temperature of water (T b ) can be calculated as follows: where q sW and q sHB indicate the energy needed to increase the temperature of the cooking water and pre-soaked beans from the initial temperature (T 0 ) to the boiling temperature (T b ≈ 98 • C), and c pW (=4.186 kJ kg −1 K −1 ) and c pHB are the specific heats of the cooking water and the pre-hydrated beans, respectively.Since the pre-soaked beans had an initial moisture content of approximately 55% (w/w), the specific heat was calculated as follows: where c Pdm is the specific heat of the dry matter.The dry matter of the beans used, which had an initial moisture content of 12% (w/w), was: m Pdm = 0.88 × 750 = 660 g After soaking, the mass of the pre-hydrated beans (their dry matter content having reduced to 45%) was: m HB = 660/0.45= 1466.67g In this case, the theoretical energy E th would be: Given that the energy supplied by the stove (E S ) to bring the mixture to T b was 0.43 ± 0.04 kWh, the efficiency of the induction stove was approximately 85%.
According to the Category Rules of the Product Environmental Footprint for cooking dry pasta [36], the environmental impact of bean cooking was evaluated considering only the impact category of climate change.Thus, the carbon footprint of bean cooking (CF BC ) depends on the overall direct and indirect greenhouse gas (GHG) emissions resulting from this activity [37].In this case, the inventory analysis included only the consumption of electricity, tap water, and salts used, as the impact resulting from the production of beans is constant for each cooking method, while the impact of disposing of cooking water was considered negligible, as observed in the case of cooking pasta [38].Thus, CF BC was estimated as follows: CF BC = m BD (e S,eff EF EE + WPR EF TW + WPR c Si EF Si ) ( 5) where e S,eff indicates the specific electrical energy actually absorbed from the Italian grid to cook 1 kg of dry beans, η IG (=6.1%) represents the average electrical energy grid lost in 2021 [39], WPR (=4 L/kg) is the ratio between the volume of cooking water and the quantity of dried beans to be cooked (m BD ), c Si is the concentration of the i-th salt dissolved in the cooking water; while EF EE , EF TW , and EF Si are the emission factors (referring to a 100-year time horizon) associated with the production and distribution of low-voltage electrical energy in Italy, the use of tap water, and the production of the i-th salt used, respectively.Table 1 reports these emission factors, which were retrieved from the Ecoinvent database v. 3.9.1 of the LCA Simapro 9.5.0.0 software (Prè Consultants, Amersfoort, The Netherlands).
In particular, by referring to the dry carbonation of potassium carbonate with a gaseous stream composed of carbon dioxide gas and steam in unitary molar ratio at 100 • C in a fluidized bed reactor, as patented by Kurtz and Winston [40], it was possible to estimate the emission factor for potassium bicarbonate using the aforementioned Simapro software, as reported in Table 1.

Statistical Analysis of Data
All data were reported as mean values with standard deviations.Statistical comparisons of means were conducted using Tukey ′ s test, with the significance level set at p = 0.05.

Physical Properties
Table 2 summarizes the key chemical and physical properties of the Gradoli Purgatory beans studied.The crude protein, total starch, phytic acid, and raffinose contents on a dry matter basis were like those found in various global bean varieties [3,[41][42][43].GPBs, with an average weight of 0.161 g per seed, are classified as very small beans [43].Each seed had an equivalent spherical radius of 0.319 cm.Their density was comparable to certain Tunisian and Ethiopian bean varieties [44].The swelling capacity (SC) and hydration capacity (HC) of GPBs were approximately 0.16 g/seed and 0.32 cm 3 /seed, respectively.In other dry bean genotypes [44,45], HC ranged from 0.17 to 0.54 g/seed and SC from 0.16 to 0.50 cm 3 /seed.As shown in Table 2, GPBs contained around 5.3 ± 0.3 g of raffinose and 1.15 ± 0.12 g of phytic acid per 100 g of dry mass, like common beans, which contain 0.4 to 16.1 g of α-galactosides [46] and 0.3 to 2.9 g of phytic acid [47] per 100 g of dry mass.Decorticated and split beans in their original form (DSGPB) or malted (MDSGPB) showed decreased physical properties, with HC and SC not being statistically different at a 95% confidence level.Moreover, the latter exhibited significant reductions in flatulence-inducing sugars and phytate, by about 63% and 32%, respectively, compared to the raw counterpart.In each row, values with the same letter have no significant difference at p < 0.05.

Bean Softening upon Cooking
The softening of beans upon cooking was monitored using several TPA tests as a function of cooking time (t C ).As an example, Figure S1 in the electronic supplement shows the main results of a two-cycle TPA test performed with raw GPBs, pre-soaked in tap water for 16 h and cooked for 20, 45 or 75 min.
Table S1 in the electronic supplement shows the effect of cooking time (t C ) on a few TPA parameters (i.e., H 1 , AC 1 , AD 1 , H 2 , AC 2 , AD 2 , CER, and CFR) of GPBs in various forms.
Firstly, all the textural parameters H 1 , AC 1 , AD 1 , H 2 , AC 2 , or AD 2 exhibited an exponential decrease as t C increased, as shown for instance for H 1 in Figure 3.In contrast, the cohesion force (CFR) and energy (CER) resiliencies displayed statistically significant variations close to the optimal cooking time.
Firstly, all the textural parameters H1, AC1, AD1, H2, AC2, or AD2 exhibited an exponential decrease as tC increased, as shown for instance for H1 in Figure 3.In contrast, the cohesion force (CFR) and energy (CER) resiliencies displayed statistically significant variations close to the optimal cooking time.
Figure 3.Effect of cooking time (tC) on the experimental hardness H1 of GPBs in various forms: 16 h pre-soaked (, ); unsoaked, decorticated, and split (, ---); malted, decorticated and split (, ---).The continuous, dotted, and broken lines were plotted using Equation ( 1) and the empirical coefficients listed in Table 3.The horizontal broken line represents the H1 value that indicates the beans are adequately cooked.
The attempt to compare the textural properties found in this study with those reported by other researchers was challenging due to variations in measurement methodologies.Different studies used various setups, such as a texture analyzer equipped with either a 25 kgf [48] or 250 kgf [8,14] load cell, as well as different bean varieties, preparation methods, and equipment calibrations.Additionally, the beans were positioned differently: some studies used a single half bean with the flat side of the cotyledon facing the instrument [8,48], while others compressed five beans at once [14].Despite these differences, a  ---); malted, decorticated and split (▲, ---).The continuous, dotted, and broken lines were plotted using Equation ( 1) and the empirical coefficients listed in Table 3.The horizontal broken line represents the H 1 value that indicates the beans are adequately cooked.The attempt to compare the textural properties found in this study with those reported by other researchers was challenging due to variations in measurement methodologies.Different studies used various setups, such as a texture analyzer equipped with either a 25 kg f [48] or 250 kg f [8,14] load cell, as well as different bean varieties, preparation methods, and equipment calibrations.Additionally, the beans were positioned differently: some studies used a single half bean with the flat side of the cotyledon facing the instrument [8,48], while others compressed five beans at once [14].Despite these differences, a consistent trend was observed across all studies, including ours: bean hardness decreases exponentially with cooking time.This trend was noted regardless of factors like average bean weight, cultivar, seed age (fresh or aged), seed coat thickness [48], and cooking water temperature [49].These variations underscore the need for a more standardized approach to measuring and reporting the textural properties of beans to enable more accurate cross-study comparisons, as emphasized by Wood [27].
The rate of bean softening was expressed using the first peak force (H 1 ) as described in Equation (1).
Table 3 presents the different least-squares empirical coefficients (H 10 , K F ). Unsoaked, decorticated, and split GPBs exhibited a statistically significant (p = 0.05) greater softening rate constant (K F ) than the malted, decorticated, and spliGPBs, likely due to the kilning process delaying the cookability of the latter.The softening rate constants as-Foods 2024, 13, 2505 9 of 16 sessed here ranged from 0.028 to 0.064 min −1 , which is consistent with the range observed for different non-aged bean accessions with individual bean weights varying from 0.16 to 0.56 g/seed [48].
The pinch test was not effective in precisely determining the optimal cooking time for beans.All samples cooked for more than 20 min tended to disintegrate when pressed between the thumb and index finger (Figure 4).As the cooking time (t C ) increased from 20 to 32 min, the beans lost small pieces.For cooking times exceeding 45 min, the beans became increasingly pasty and softer when pressed, though they still retained some degree of cohesion (Figure 4).In each column, values with the same letter have no significant difference at p < 0.05.
The pinch test was not effective in precisely determining the optimal cooking time for beans.All samples cooked for more than 20 min tended to disintegrate when pressed between the thumb and index finger (Figure 4).As the cooking time (tC) increased from 20 to 32 min, the beans lost small pieces.For cooking times exceeding 45 min, the beans became increasingly pasty and softer when pressed, though they still retained some degree of cohesion (Figure 4).When the trained panelists considered the Gradoli Purgatory beans (GPBs) cooked, the first peak hardness (H1) varied between 200 and 250 N, regardless of their pretreatments.Thus, this H1 range was identified as representative of optimal cooking conditions When the trained panelists considered the Gradoli Purgatory beans (GPBs) cooked, the first peak hardness (H 1 ) varied between 200 and 250 N, regardless of their pretreatments.Thus, this H 1 range was identified as representative of optimal cooking conditions based on sensory evaluations of texture and the pinch test not only for GPBs, but also for dehulled and split GPBs (DSGPBs), or malted, decorticated, and split GPBs (MDSGPBs).
The optimal cooking times corresponding to a first peak force of around 220 N were approximately 55 min for pre-soaked GPBs, 25 min for unsoaked DSGPBs, and 32 min for MDSGPBs.Prolonged cooking times resulted in a progressive loss of texture in all beans examined.This behavior is likely associated with structural and chemical differences in the cotyledons and cuticles of the cooked beans.
It is important to note that DSGPBs were obtained by soaking, low temperature drying (as in the case of MDSGPBs), and subsequent dehulling and splitting, and were cooked without prior soaking.Despite having an initial moisture content lower than that of presoaked GPBs (12% vs. 55% w/w), the absence of skin and splitting into halves facilitated faster hydration and softening during cooking.
Conversely, the production of decorticated, split, and malted Purgatory beans (MDS-GPBs) involved several steps: soaking, germination, drying, dehulling to remove the outer skin and rootlets, and splitting the cotyledons.These beans were also cooked without prior soaking.Although these processing steps typically reduce cooking times compared to raw beans due to the partial degradation of cotyledons during germination, the kilning phase may have contributed to the hard-to-cook phenomenon, as indirectly indicated by the lower hydration capacity (HC) of MDSGPBs (Table 2).Additionally, the reaction of pectinic acid with calcium ions released during phytic acid degradation may have stiffened the cell walls, affecting bean texture.Despite similar physical structures, the longer optimal cooking time for MDSGPBs (32 min compared to 25 min for decorticated and split GPBs) appeared to be primarily due to changes induced by the malting process.In this context, it was not possible to confirm the reduction of cooking time for red beans due to germination, as reported by Haileslassie et al. [20], especially if the germinated beans are then preserved in dried form.

Effect of Monovalent Salts on Cooking Time
To reduce the optimal cooking time of malted and decorticated Gradoli Purgatory beans, they were cooked using different monovalent salt solutions.The salt concentrations used (1 or 2 g/L) were considerably lower than those tested previously [8,13,17] to avoid imparting any salted taste to the cooked beans.
Table S2 illustrates the impact of these salt solutions on the key TPA parameters of malted, decorticated, and split GPBs relative to cooking time (t C ).
Even in this study, comparing the textural properties of the beans cooked in saltwater with those reported by other researchers [8,[12][13][14][15] was challenging due to differences in measurement methodologies, average bean weights, cultivars, seed age (fresh or aged), seed coat thickness, and cooking water temperature.However, a consistent finding across studies was that adding monovalent salt carbonate/bicarbonate to the cooking water reduced cooking times.For example, de León et al. [17] found that soaking beans in a solution containing 0.5% (w/v) NaHCO 3 and 2.5% (w/v) K 2 CO 3 was effective, provided the soaking water was discarded and the beans were rinsed with fresh water before cooking to minimize the salty flavor.However, they did not specify the extent to which this method reduced cooking times compared to standard cooking conditions.
Figure 5 shows the first peak hardness (H 1 ) of MDSGPBs cooked in tap water or with different sodium or potassium salt concentrations versus cooking time (t C ), where the various lines were plotted based on the least-squares regressions detailed in Table 3. Due to the linearity of all the semilogarithmic plots, it was possible to estimate the optimal cooking time (OCT) at which malted, decorticated, and split Gradoli Purgatory beans (MDSGPB) cooked in different monovalent salt solutions exhibited the first peak hardness H1 of around 220 N.
Due to the linearity of all the semilogarithmic plots, it was possible to estimate the optimal cooking time (OCT) at which malted, decorticated, and split Gradoli Purgatory beans (MDSGPB) cooked in different monovalent salt solutions exhibited the first peak hardness H 1 of around 220 N.
Figure 6 shows that these OCT values are linearly correlated to the molar concentration (C i ) of the sodium or potassium salts used: OCT = (32.1 ± 0.9) − (475 ± 44) C i (r 2 = 0.93) (7) An optimal cooking time as short as 12.9 min was obtained when the cooking water contained about 0.038 mol/L of Na + , equivalent to a sodium carbonate concentration of 2 g/L.Thus, not only were carbonates found to be more effective than bicarbonates, but sodium carbonate was also more effective than potassium carbonate.Any addition of salts at levels greater than 2 g/L caused uneven cooking.For instance, two distinct zones can be observed in malted beans cooked in tap water containing 4 g/L of Na 2 CO 3 for 15 min, as shown in Figure 7a.The outer zone appeared well-hydrated and cooked, while the inner zone remained tough.Furthermore, Figure 7b illustrates the excessive cooking of the outer zone, which easily disintegrated upon pinching, leaving a gelatinous residue on the finger.This phenomenon also occurred in standard cooking, but the difference between the two zones was more pronounced at salt concentrations above 2 g/L compared to standard cooking.
Due to the linearity of all the semilogarithmic plots, it was possible to estimate the optimal cooking time (OCT) at which malted, decorticated, and split Gradoli Purgatory beans (MDSGPB) cooked in different monovalent salt solutions exhibited the first peak hardness H1 of around 220 N.
Figure 6 shows that these OCT values are linearly correlated to the molar concentration (Ci) of the sodium or potassium salts used: OCT = (32.1 ± 0.9) − (475 ± 44) Ci (r 2 = 0.93) Figure 6.Effect of the molar concentration (Ci) of monovalent cations (, Na + ; , K + ) in cooking water on optimal cooking time (OCT) of malted and decorticated Gradoli Purgatory beans.The broken line was plotted using Equation ( 7).
An optimal cooking time as short as 12.9 min was obtained when the cooking water contained about 0.038 mol/L of Na + , equivalent to a sodium carbonate concentration of 2 g/L.Thus, not only were carbonates found to be more effective than bicarbonates, but sodium carbonate was also more effective than potassium carbonate.Any addition of salts  at levels greater than 2 g/L caused uneven cooking.For instance, two distinct zones can be observed in malted beans cooked in tap water containing 4 g/L of Na2CO3 for 15 min, as shown in Figure 7a.The outer zone appeared well-hydrated and cooked, while the inner zone remained tough.Furthermore, Figure 7b illustrates the excessive cooking of the outer zone, which easily disintegrated upon pinching, leaving a gelatinous residue on the finger.This phenomenon also occurred in standard cooking, but the difference between the two zones was more pronounced at salt concentrations above 2 g/L compared to standard cooking.
(a) (b)    Therefore, the energy (E S ) consumed by the induction stove can be predicted as follows:

Bean Cooking Energy and Carbon Footprint Estimation
E Sc (t) = 0.0333 t C for t C ≤ 12.9 ± 1.3 min (8) E Sc (t) = (0.0054 ± 0.0004) t C + (0.353 ± 0.018) (r 2 = 0.93) for t C > 12.9 ± 1.3 min (9) Considering the optimal cooking times, the electric energy required to cook 1 kg of presoaked raw beans would be approximately 0.87 kWh.In contrast, this energy consumption decreased to 0.65 kWh or 0.70 kWh for 1 kg of unsoaked DSGPBs or MDSGPBs, respectively.Table 4 presents the parameters used to calculate the carbon footprint (CF BC ) associated with cooking dry beans in water, as GPBs are either hulled and split (DSGPB) or malted,       As highlighted previously, the hulling phase, which allows the removal of the outer cuticle, and the splitting of bean cotyledons reduced the cooking time of Gradoli Purgatory beans by 55%, from 55 to 25 min.A similar cooking time of 32 min was also observed for malted, hulled, and split beans, clearly demonstrating the negative effect of the cuticle on cooking time.The addition of sodium or potassium salts to the cooking water further reduced the cooking time of malted, hulled, and split beans.For example, adding 2 g/L of sodium bicarbonate or carbonate reduced the optimal cooking time of Gradoli Purgatory beans to about 21 or 13 min, respectively.

Bean Cooking Energy and Carbon Footprint Estimation
The impact of the bean cooking phase was primarily due to energy consumption, as the contribution of tap water and salts was negligible (Table 4).Cooking 1 kg of dried Gradoli Purgatory beans, pre-soaked in tap water for 16 h, on an induction stove resulted in estimated GHG emissions of 561 g CO 2e , which decreased by 25% for unsoaked hulled and split beans (420 g CO 2e /kg) and by 34% for malted, hulled, and split beans cooked in saltwater with 2 g/L of sodium carbonate (368 g CO 2e /kg).

Figure 1 .
Figure 1.Flowchart of the production processes for malting, dehulling, and splitting the cotyledons of Gradoli Purgatory beans.

Figure 2 .
Figure 2. Lateral (a) and front (b) view pictures of the 100 kg pilot-scale malter used in this work.

Figure 2 .
Figure 2. Lateral (a) and front (b) view pictures of the 100 kg pilot-scale malter used in this work.

Figure 4 .
Figure 4. Images of pre-soaked GPBs subjected to the pinch test after cooking for 20 to 75 min.

Figure 4 .
Figure 4. Images of pre-soaked GPBs subjected to the pinch test after cooking for 20 to 75 min.

Figure 6 .
Figure 6.Effect of the molar concentration (C i ) of monovalent cations (•, Na + ; △, K + ) in cooking water on optimal cooking time (OCT) of malted and decorticated Gradoli Purgatory beans.The broken line was plotted using Equation(7).

Figure 7 .
Figure 7. Photos of malted, decorticated, and split GPBs cooked in tap water containing 4 g/L of Na2CO3 for 15 min (a) and submitted to the pinch test (b).

Figure 8
Figure 8 depicts the progression of electric energy (ES) consumed by the induction hob during the cooking of about 750 g of GPBs (pre-soaked in 3 L of tap water for 16 h) at 98 °C, with a water volume of four times the weight of the dried beans.

Figure 7 .
Figure 7. Photos of malted, decorticated, and split GPBs cooked in tap water containing 4 g/L of Na 2 CO 3 for 15 min (a) and submitted to the pinch test (b).

Figure 8
Figure 8 depicts the progression of electric energy (E S ) consumed by the induction hob during the cooking of about 750 g of GPBs (pre-soaked in 3 L of tap water for 16 h) at 98 • C, with a water volume of four times the weight of the dried beans.Therefore, the energy (E S ) consumed by the induction stove can be predicted as follows:E Sc (t) = 0.0333 t C for t C ≤ 12.9 ± 1.3 min(8)

Figure 7 .
Figure 7. Photos of malted, decorticated, and split GPBs cooked in tap water containing 4 g/L of Na2CO3 for 15 min (a) and submitted to the pinch test (b).

Figure 8
Figure 8 depicts the progression of electric energy (ES) consumed by the induction hob during the cooking of about 750 g of GPBs (pre-soaked in 3 L of tap water for 16 h) at 98 °C, with a water volume of four times the weight of the dried beans.

Figure 8 .
Figure 8. Electric energy (ES) consumed by the induction hob to cook about 750 g of GPBs (presoaked in 3 L tap water for 16 h) versus cooking time (tC).The broken lines were plotted using Equation (8) or Equation (9).

Figure 8 .
Figure 8. Electric energy (E S ) consumed by the induction hob to cook about 750 g of GPBs (pre-soaked in 3 L tap water for 16 h) versus cooking time (t C ).The broken lines were plotted using Equation (8) or Equation (9).

Table 4 .
Parameters used to calculate the carbon footprint (CF BC ) associated with cooking 1 kg of dried beans in water, as they (GPB) are either hulled and split (DSGPB) or malted, decorticated, and split (MDSGPB), then cooked in water with different concentrations of sodium or potassium bicarbonate/carbonate.

Table 1 .
Main parameters used to calculate the theoretical energy consumed (E th ) to heat the cooking water (m W0 ) and dried beans (m BD ), with a known dry matter content (x ss ), from room temperature (T 0 ) to the boiling point (T b ): average loss of the Italian electrical grid (η IG) and emission factors for the production and distribution of low-voltage electrical energy in Italy (FE EE ), tap water (FE TW ), and monovalent salts used (FE Si ).

Table 3 .
Empirical least-squares softening coefficients of differently pre-treated GPBs cooked in tap water or salt solutions at different concentrations (c Si ) together with the corresponding coefficients of determinations (r 2 ).
In each column, values with the same letter have no significant difference at p < 0.05.