The BS was collected from a biogas plant (Xi’an, China). The BS was stored in a refrigerator at 4°C. The properties of the biogas were as follows: pH: 8.28±0.04, Conductivity: 14.38±1.01 ms/cm, Turbidity: 1554±45.30 NTU, Dissolved organic carbon (DOC): 1543.9±40.87 mg/L, UV254: 15.25333±1.01, Suspend solid (SS): 4.15±0.37 g/L, Zeta potential: −24.77±1.097 mV, Ammonium (NH₄⁺-N): 2167.88±41.03 mg/L, Orthophosphate (PO₄³⁻): 50.91±2.17 mg/L, Alkalinity: 2517.08±27.81 mg CaCO₃/L.

Sodium hydroxide (NaOH) and calcium chloride (CaCl₂) were purchased from Sinopharm Chemical Reagent Co., Ltd and Greagent, respectively.

Based on the response surface methodology results in the Supplementary Material (Fig. S1 and Table S1–S3), the effect of pH on SS removal efficiency was statistically more significant than either CaCl₂ dosage or temperature (p < 0.05), particularly under strongly alkaline conditions (pH > 11) where a steep reduction in SS was observed. Design and modeling details (response surface methodology, RSM; central composite design, CCD) are provided in Text S1 (Supplementary Materials). The interaction term between pH and CaCl₂ approached significance, indicating synergistic effects. Considering the BS characteristics and the requirement to drive complete bicarbonate conversion for calcite formation, pH 12 was selected as the optimal fixed parameter for subsequent batch experiments (Text S2 and Table S3, Supplementary Materials). The experimental groups were established with CaCl₂ supplementation at 10, 20, 30, 40, 50, and 60 mg/L, labeled as 1, 2, 3, 4, 5, and 6, respectively. The control group (labeled 0) was at pH 12 with no CaCl₂ added, and the blank group (labeled −1) was BS without any treatment. Each group was replicated three times to ensure result consistency.

Each jar contained 300 mL BS, with the pH adjusted to 12 using 4 M NaOH solution. Subsequently, various doses of CaCl₂ were added. The mixture was stirred at 300 rpm for 2 minutes to fully dissolve the CaCl₂ (rapid stirring stage), followed by stirring at 100 rpm for 20 minutes to evenly distribute the flocs formed in the solution (mixing stage).

Samples were collected from 1 cm above the bottom of the beaker using a syringe during the rapid mixing stage. A portion was used to measure the floc particle size, while the other portion was analyzed for floc fractions by X-ray diffractometry (XRD) and X-ray photoelectron spectrometry (XPS) after freeze-drying at −50°C. The system’s zeta potential was measured by taking samples during the mixing phase.

The solid-liquid phase was formed by standing for 24 hours after the stirring procedure was completed. Liquid samples were then collected at a point 1 cm below the liquid interface for analysis of pH, conductivity, turbidity, DOC, UV254, alkalinity, and total orthophosphate (PO₄ ³⁻), Fourier Transform Infrared (FTIR) spectroscopy. The precipitated solid was collected and dried at 60°C for observation of morphology and analysis of elemental composition.

pH and conductivity were measured by a pH meter (METTLER TOLEDO, China) equipped with pH and EC electrodes. DOC was obtained by a total organic carbon analyzer (SHIMADZU, Japan). UV254 values were acquired by a UV-visible spectrophotometer (UNICOSQ-4802, China). NH₄⁺-N was measured by the Nessler reagent spectrophotometric method (HJ 535-2009). PO₄³⁻ was determined by the ammonium molybdate spectrophotometric method (GB 11893-89). Alkalinity was measured by potentiometric titration [27]. FTIR spectra were measured by a Fourier infrared spectrometer (Nicolet iS20, Thermo Fisher Scientific, Amercia) with a measurement wavelength of 4000-400 cm⁻¹. XRD spectra were analyzed by an X-ray diffractometer (SmartLab SE, Rigaku, Japan). Surface morphology and elemental composition were obtained by scanning electron microscopy equipped with energy dispersive spectroscopy (SEM-EDS, ZISS, Germany).

Fig. S2 presents the raw SS concentration and turbidity values measured in the liquid phase after 24 h settling across all treatment conditions. The untreated biogas slurry (Group −1) contained 4.15 g/L SS and 1554 NTU turbidity, establishing baseline contamination levels. The corresponding removal efficiencies are quantified in Fig. 1a. Adjusting pH to 12 without CaCl₂ (Group 0) reduced SS by 15.9% (to 3.49 g/L) and turbidity by 10.2% (to 1396 NTU), demonstrating modest removal via metal hydroxide formation. Adding 10 mg/L CaCl₂ enhanced removal to 34.5% SS and 46.8% turbidity, with optimal performance achieved at 20 mg/L CaCl₂ (Group 2): 47.5% SS removal (2.18 g/L) and 46.8% turbidity reduction (826 NTU) (Supplementary Fig. S2). Beyond this dosage, removal plateaued and slightly decreased, consistent with conventional coagulation over-dosing behavior.

To understand the baseline contribution of metal hydroxide precipitation, we analyzed Fe, Mg, and Ca concentrations. pH adjustment to 12 precipitated 68% of iron and 45% of magnesium as hydroxides, which contributed to the 15.9% baseline SS removal through sweep flocculation (Supplementary Fig. S2–S3). However, these hydroxides alone were insufficient for effective solid-liquid separation, necessitating the calcite precipitation mechanism.

As shown in Fig 1b, the sedimentation velocity data explain the dosage-dependent performance. Maximum settling velocity (0.0468 m/h) occurred at 20 mg/L CaCl₂, matching the SS removal optimum. At higher dosages, velocity decreased to 0.0037 m/h (92% reduction), paralleling the decline in removal efficiency. This correlation demonstrates that effective settling is prerequisite for high removal efficiency. At CaCl₂ doses below 20 mg/L, the settling rate increased with increasing dosage, reaching a peak of 0.0468 m/h at 20 mg/L. However, when the dosage increased to 30 mg/L, the settling rate declined to 0.0134 m/h. At higher concentrations, electrostatic forces may have contributed to the formation of a stable suspension, reducing sedimentation efficiency. At CaCl₂ dosages >30 mg/L, settling velocity decreased precipitously to 0.0037 m/h (92% reduction). This restabilization is not due to charge reversal (zeta potential remains negative throughout, Fig. 4i), but rather kinetic stabilization caused by excessive nucleation rates. At high supersaturation, nucleation dominates over crystal growth, producing numerous small calcite particles with low collision efficiency and insufficient sweep volume to capture SS effectively. Consequently, the system remains in stable suspension despite partial surface charge neutralization. As shown in subsequent sections, 20 mg/L CaCl₂ corresponds to the point where calcite nucleation transitions from growth-dominated to nucleation-dominated (Fig. 4g), producing flocs with optimal size and settling velocity. The declining removal efficiency beyond 20 mg/L is not merely a diminishing return—XRD analysis (Section 3.3) reveals that excess Ca²⁺ forms smaller, more numerous crystals (42 μm) with reduced sweep efficiency. Thus, the SS removal optimum is mechanistically linked to crystallization kinetics rather than simple colloidal destabilization.

With the depletion of CO₃²⁻, the ionization reaction of HCO₃⁻ in BS was intensified (Eq. 1). The relative abundance of H⁺ gradually increased, hence the pH of the supernatant gradually decreased and eventually remained near 9.5 (Fig. 1c). Due to the higher CaCl₂ addition, the fraction of Ca²⁺ not involved in calcite precipitation raised the conductivity of BS from 14.38 in group −1 to 84.01 ms/cm in group −6, with a linear increasing trend (Fig. 1c).

Alkalinity is critical for maintaining pH stability during the alkaline treatment process and directly determines the available carbonate reservoir for calcite formation. The alkalinity of raw BS (−1 group) was 2517.08 mg CaCO₃/L, HCO₃⁻ deprotonated to form a large amount of CO₃²⁻ after NaOH supplementation, which increased to 7384.77 mg CaCO₃/L (Fig. 1d). At this point, the high concentration of CO₃²⁻ in the solution reacted rapidly with Ca²⁺ to form calcite, and the alkalinity and CO₃²⁻ were also reduced rapidly. The alkalinity was reduced by 69.70% at 10 mg/L CaCl₂ dose, corresponding to a 66.45% reduction in CO₃ ²⁻. Excess Ca²⁺ could increase the ionic strength of the BS, and higher ionic strength implies lower ionic activity coefficients [28], leading to a decrease in the effective concentration of Ca²⁺ and CO₃ ²⁻ involved in the formation of calcite. In addition, Ca²⁺ would not further react with CO₃²⁻ due to the buffering capacity of CO₃²⁻ and HCO₃⁻. Therefore, the decreasing trend of alkalinity and CO₃²⁻ levels off as the dose of CaCl₂ increases.

Typical organic matter in BS, humic substances, is a complex class of mixtures whose types of functional groups are closely related to the types of reducing sugars and amino acids in the matrix, and the solubility increases with the increase of pH [29, 30]. A previous study demonstrated that carboxylate groups, a type of acidic functional group, constitute a significant portion of humic-like substances in BS [31]. As the pH increases, these carboxylate groups undergo deprotonation, transforming into more polar carboxylates. This change enhances their solubility, following the principle that substances with similar polarity tend to dissolve in one another. The variation of DOC is shown in Fig. 2a. The DOC increased from 1543.90 mg/L in the −1 group to 2071 mg/L, reflecting a growth rate of 25.45% as the pH of the biogas slurry was raised to 12. Humic substances can chelate with calcium ions to form complexes that are removed through co-precipitation when calcium ions are introduced into the system [32]. As the dosage of CaCl₂ increased, the DOC concentration dropped to 1,276.60 mg/L, achieving a removal efficiency of 38.36% (Fig. 2a). However, pH adjustment led to an increase in DOC concentration in the BS, resulting in only a 17.31% reduction compared to the −1 group.

UV254, which reacts with unsaturated or aromatic organics in water [33], exhibited a trend similar to DOC, as shown in Fig. 2b. The pH adjustment caused UV254 to increase from 15.25 to 18.85 in the blank group. With the addition of CaCl₂, UV254 decreased significantly, with a 20 mg/L dosage achieving a 40.72% reduction compared to the −1 group. This decrease in UV254 is likely due to the reduction in humic substances.

Fig. 2c and Fig. 2d illustrate the changes in NH₄⁺-N and PO₄³⁻ concentrations across different groups. Overall, the trends for NH₄⁺-N and PO₄³⁻ were consistent with other liquid-phase indicators, demonstrating effective removal. At pH 12, the ionization equilibrium of NH₄⁺ in the BS shifted to the right (Eq. 1), leading to a decrease in NH₄⁺-N from 2167.88 mg/L in group −1 to 1468.77 mg/L in group 0, with a removal rate of 32.25% (Fig. 2c). After the addition of CaCl₂, After the addition of CaCl₂, the experimental groups showed an 14.08–28.3% increase in ammonia-nitrogen removal relative to the −1 group. This improvement is plausibly attributable to the occlusion/entrainment of NH₄⁺ within CaCO₃ precipitates formed via Ca²⁺–carbonate interactions under alkaline conditions.

Theoretically, when the pH of the BS was increased from 8.3 to 12, the dominant phosphate species should have been HPO₄²⁻ and PO₄³⁻, leading to a peak PO₄³⁻ concentration. However, PO₄³⁻ decreased from 50.91 mg/L in group-1 to 43.29 mg/L (Fig. 2d). This discrepancy may be attributed to the method of pH adjustment, which desorption of PO₄³⁻ adsorbed on SS. Under alkaline conditions (pH 12), the BS, which is rich in iron, aluminum, magnesium, and calcium, facilitates the formation of metal hydroxides. These hydroxides exhibit strong adsorption capacity for PO₄³⁻, contributing to its removal from the solution [34–36]. Upon the addition of 10 mg/L CaCl₂, PO₄³⁻ was effectively removed by forming Ca₃(PO₄)₂ (Eq. 3), reducing its concentration to 9.31 mg/L. Complete removal of PO₄³⁻ was achieved by further increasing the CaCl₂ dosage.

The BS comprises a complex mixture of substances, including PO₄³⁻, NH₄⁺, soluble microbial products, and significant amounts of SS. Interactions among these substances may occur following the addition of CaCl₂. To investigate the functionally active species, XPS was conducted to analyze the elemental composition of the flocs (Fig. 3a). The XPS analysis revealed the presence of Na, O, N, C, and Cl elements in Group 0, corresponding to binding energies of 1071.08 eV, 532.08 eV, 399.08 eV, 284.08 eV, and 198.08 eV, respectively. The peak at 1071.08 eV represents the Na 1s orbital peak, which exhibited relatively high intensity in Group 0 due to the addition of NaOH for the initial pH adjustment of the BS. The intensity of Na peaks gradually decreased from Groups 3 to 6. Similarly, the Auger peak of Na1s at 497.08 eV followed a consistent trend. Notably, the XPS spectra differed between the groups in terms of the presence of Ca. Experimental groups 3, 4, 5, and 6 exhibited distinct peaks corresponding to the Ca 2s and 2p orbitals at 439.08 eV and 347.08 eV, respectively, due to the presence of CaCl₂.On the other hand, only the Ca 2p orbital peaks were observed in Groups 1 and 2. XPS Surface Composition and Elemental Specificity. The elemental trends observed in XPS spectra (Fig. 3a) reflect matrix displacement and surface enrichment effects rather than simple bulk concentration changes. For Na 1s (1071.08 eV), the signal intensity decreases from 8.2 at% (Group 0) to 2.1 at% (Group 6). Because: The XPS trends indicate true surface restructuring rather than bulk dilution: Once the nucleation threshold is surpassed, calcite grows at the interface to form a CaCO₃-terminated overlayer that both buries Na within the nanometer-scale XPS probe depth and preferentially attenuates its Na 1s signal. In parallel, Ca²⁺ outcompetes Na⁺ for negative surface sites via specific adsorption and ion exchange, shifting the accessible surface composition toward Ca. These combined effects—burial with differential attenuation, Ca-favored substitution, and interface-localized nucleation/growth—produce the observed decrease in Na and increase in Ca, captured by the rising Ca:Na atomic ratio that marks the transition from a Na-dominated surface to a CaCO₃-covered interface. Based on the XPS spectrogram, it can be inferred that the main components in the floc are calcium and sodium salts.

FTIR spectroscopy was employed to analyze the functional groups involved in the formation of flocs (Fig. 3b). The peaks at 3439 cm⁻¹ and 1631 cm⁻¹ were derived from the stretching vibration and bending vibration of adsorbed water or hydroxyl groups deposited on the surface of flocs [37]. Furthermore, peaks at 1449 cm⁻¹, 1056 cm⁻¹, 876 cm⁻¹, and 713 cm⁻¹ corresponded to asymmetric stretching vibration (V3), symmetric stretching vibration (V1), out-of-plane bending vibration (V2), and in-plane bending vibration (V4) for CO₃ ²⁻ [38]. The presence of CO₃ ²⁻ originated from the alkalinity in the BS, with a substantial amount of HCO₃⁻ being fully converted to CO₃²⁻ at a pH of 12. Notably, the asymmetric stretching vibration of CO₃²⁻ started to redshift with the addition of 30 mg/L CaCl₂, which was caused by alteration of the external chemical environment in which CO₃²⁻ was exposed [38]. This spectral phenomenon might be related to the formation of reactive species.

The crystalline phases that existed in the flocs were determined from the XRD (Fig. 3c). In Group -1, no identifiable crystal structure was observed. However, in Group 0, distinct diffraction peaks were observed at 2θ angles of 31.69°, 45.45°, and 56.48°, corresponding to the crystal planes (200), (220), and (222) of sodium chloride (NaCl) respectively (PDF#05-0628). Additionally, peaks at 30.15°, 35.24°, and 37.99° were identified as the crystal planes (002), (310), and (112) of sodium carbonate (Na₂CO₃) (PDF#37-0451). All experimental groups exhibited consistent XRD patterns, with recognizable diffraction peaks characteristic of NaCl. Furthermore, the presence of calcite-type calcium carbonate was indicated by peaks at 29.4°, 47.51°, and 48.50°, corresponding to the crystallographic planes (104), (018), and (116), respectively (PDF#47-1743). The XRD results clarify the flocculation pattern and mechanism: Salt-only systems provide limited, weak entrapment, whereas calcite furnishes dense, crystalline “ballast” with chemically heterogeneous surfaces that promote heterogeneous nucleation, particulate capture, and phosphate co-precipitation. Peak broadening at higher Ca doses indicates a shift toward nucleation-dominated regimes that yield smaller crystallites and slower settling, explaining the performance optimum at intermediate dosage and the decline when excessive nucleation produces undersized calcite particles.

Fig. 4a-f illustrates the morphological characteristics of flocs formed with varying calcium chloride additions. SEM reveals a clear morphological progression: Untreated samples show diffuse amorphous aggregates; at pH 12 without CaCl₂, sparse angular Na-salt microcrystals yield loose, porous clusters; with CaCl₂, faceted calcite dominates, interlocking into compact, dense flocs with stepped surfaces. Floc mean size increases with calcite particle size within an optimal range (enhanced bridging and rigidity), but at excessive Ca, nucleation produces numerous fine crystallites that weaken interlocking, causing floc size to plateau or decline. This morphology–size linkage explains the observed improvement in settling up to a dosage optimum, followed by diminished gains [39].

Fig. 4g shows the average particle size of calcite produced during the mixing phase. As the CaCl₂ dosage increased from 10 mg/L to 60 mg/L, the calcite particle size exhibited a three-stage trend. At 10 mg/L CaCl₂, flocs had an average particle size of 77.05 μm. When the dosage increased to 20–30 mg/L, the size decreased to 53.55–52.61 μm. Beyond 30 mg/L, the particle size stabilized around 42 μm up to a dosage of 50 mg/L, with no significant reduction observed at higher dosages. This behavior is attributed to the time-dependent dissolution of CaCl₂. When solid CaCl₂ was introduced into the system, the dissolved portion reacted with PO₄³⁻ and CO₃²⁻ to form water-insoluble precipitates. During magnetic stirring, these precipitates are fragmented by the shear forces, and the process repeats with the remaining undissolved CaCl₂. At the microscopic level, classical crystallization theory suggests that in solutions with high supersaturation of calcium ions, nucleation is the dominant process. In contrast, in solutions with low supersaturation, crystal growth is more prevalent [40]. When the CaCl₂ dose is low, the concentration of Ca²⁺ remains low, which slows down nucleation. This allows existing crystal nuclei to grow fully. As the CaCl₂ dose increases, the Ca²⁺ concentration rises, resulting in higher supersaturation. This accelerates nucleation, leading to the formation of many small crystal nuclei in a short period. However, the increased number of nuclei quickly consumes the available Ca²⁺ and CO₃²⁻, limiting the growth of individual crystals and ultimately resulting in the formation of smaller particles. Generally, larger floc sizes are associated with higher SS capture and improved settling performance [41]. However, in this study, the size of calcite flocs decreased as the CaCl₂ dosage increased, while the SS removal efficiency showed the opposite trend. This seemingly paradoxical result can be explained by the fact that Ca²⁺ on the surface of calcite particles attracts negatively charged SS during the ongoing dissolution of CaCl₂ with CO₃²⁻ to form calcite. Fig. 4h exhibits the specific surface area of the active species calcite. The maximum specific surface area of calcite was measured at 25.05 m²/g, with a noticeable decrease as the dose of CaCl₂ increased. This observation suggests that the removal of suspended solids is primarily driven by precipitation rather than adsorption.

Zeta potential is a key parameter that indicates the stability of colloidal dispersion systems. It measures the degree of repulsion between like-charged particles in a colloidal system. Systems with zeta potentials below 5 mV are prone to aggregation, while those with values above 10 mV tend to be more stable [42]. The zeta potentials and corresponding pH values for various CaCl₂ systems are shown in Fig. 4i. CaCl₂ significantly influences both the zeta potential and pH of the system. In the −1 group, the pH of the BS was 8.28, corresponding to a zeta potential of −24.77 mV, indicating electrostatic stability [43]. This suggests that SS was difficult to remove by gravity. After adjusting the pH with NaOH, the dissociation and deprotonation of hydroxyl groups on the particle surfaces were enhanced [41], causing the zeta potential to increase to −39.03 mV in Group 0.

When CaCl₂ dissolves, it dissociates into Ca²⁺ and Cl⁻, which interact with the negative charges on the colloidal particles, neutralizing some of these surface charges. As more CaCl₂ was added, the electric double layer was compressed, reducing the potential difference between the particle surface and the surrounding solution [44]. This leads to a decrease in the zeta potential and a corresponding drop in pH. For instance, in Group 6, the pH decreased from 12 to 10.34, and the zeta potential dropped from −39.03 mV to −7.66 mV (Fig. 4i). The increase in ionic strength, due to the higher CaCl₂ concentration, also contributes to the reduction in zeta potential through charge shielding effects [45, 46].

In terms of zeta potential, adjusting the pH increased the zeta potential of the BS system, thereby enhancing its stability. This is notable because, typically, Ca²⁺ tends to destabilize colloidal particles by reducing the zeta potential. However, although the addition of CaCl₂ alone did not lead to calcite precipitation, it still similarly contributed to system destabilization. This highlights the necessity of pH adjustment for the formation of calcite precipitation, as calcium chloride alone, despite its contribution, was insufficient to trigger the precipitation.

Alkaline precipitation relies on four synergistic mechanisms: Alkalinity-activated carbonate, chargedensity–driven Ca²⁺ adsorption that partially neutralizes SS and promotes flocculation, optimal CaCl₂–enabled shift to heterogeneous nucleation on SS, and coprecipitation of phosphate, ammonium, and humics. Collectively, these underpin high efficiency at low CaCl₂ dosage and provide an integrated route for SS and nutrient removal (Fig. 3d).

Control tests (Fig. S4) confirm that pH elevation is essential: CaCl₂ alone did not induce settling. The alkaline calcium route requires significant basification of the tested biogas slurry (BS) using NaOH (13.3 g/L; Text S3, Supplementary Materials), followed by CaCl₂, driven by its high inherent alkalinity (2517 mg CaCO₃/L). This elevates concerns about feasibility and neutralization costs. A full cost assessment shows reagent costs appear low at 2.07 CNY/m³, but rise to 2.45 CNY/m³ when discharge neutralization is included (Table S4).

Sensitivity analysis (Table S5) indicates costs remain competitive at 11–14 g/L NaOH (2.20–2.55 CNY/m³), outperforming highdose PAM (4.00 CNY/m³) and comparable to PAC/PAM (2.15 CNY/m³), while achieving 15% higher SS removal. For BS with alkalinity >3000 mg/L, alkali costs may exceed 3.00 CNY/m³, warranting sitespecific assessment.

Costreduction measures include: Replacing NaOH with CaO (0.08 CNY/g) to cut alkali cost by ~60% while supplying Ca²⁺; CO₂ prestripping (air stripping at pH ~10) to reduce base demand by 25–30%; and integrating with streams that already require pH adjustment. Where discharge limits mandate pH 6–9, include acid neutralization (~0.38 CNY/m³) in lifecycle costs.

The process lowers toxic coagulant use but produces ~2.17 kg/m³ wet sludge. Its calciterich matrix (68.3% CaCO₃) differs from metalhydroxide sludges and enables valorization: 4.8 wt% P (as Ca₃(PO₄)₂) and 2.1 wt% N support slow release fertilizer use; alternative pathways include P recovery, agricultural amendment, or construction materials. If reuse is infeasible, landfill remains an option. Heavy metals and ARGs must be evaluated to ensure safe, sitespecific reuse.