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Fair Value Measurements - Level 3 fair value measurements (Details) | Sep. 30, 2022 Y $ / shares item | Dec. 31, 2021 $ / shares | Dec. 31, 2021 item | Dec. 31, 2021 Y | Dec. 31, 2021 | Aug. 06, 2021 Y $ / shares | Dec. 31, 2020 $ / shares
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Weighted average exercise price |  |  |  |  |  |  |
Fair Value Measurement Inputs and Valuation Techniques [Line Items] |  |  |  |  |  |  |
Warrants, measurement input | 17.31 | 17.32 |  |  |  |  | 18.39
Weighted average exercise price | AMCI ACQUISITION CORP. II |  |  |  |  |  |  |
Fair Value Measurement Inputs and Valuation Techniques [Line Items] |  |  |  |  |  |  |
Warrants, measurement input | 11.50 | 11.50 |  |  |  | 11.50 |
Expected volatility |  |  |  |  |  |  |
Fair Value Measurement Inputs and Valuation Techniques [Line Items] |  |  |  |  |  |  |
Warrants, measurement input | 0.769 |  |  |  | 0.706 |  | 0.889
Expected volatility | AMCI ACQUISITION CORP. II |  |  |  |  |  |  |
Fair Value Measurement Inputs and Valuation Techniques [Line Items] |  |  |  |  |  |  |
Warrants, measurement input | 0.058 |  | 0.096 |  | 0.096 | 0.113 |
Stock price |  |  |  |  |  |  |
Fair Value Measurement Inputs and Valuation Techniques [Line Items] |  |  |  |  |  |  |
Warrants, measurement input | 15.03 | 13.77 |  |  |  |  | 4.68
Stock price | AMCI ACQUISITION CORP. II |  |  |  |  |  |  |
Fair Value Measurement Inputs and Valuation Techniques [Line Items] |  |  |  |  |  |  |
Warrants, measurement input | 9.79 | 9.66 |  |  |  | 9.66 |
Term |  |  |  |  |  |  |
Fair Value Measurement Inputs and Valuation Techniques [Line Items] |  |  |  |  |  |  |
Warrants, measurement input | 2.3 |  |  |  | 2.8 |  | 2.8
Term | AMCI ACQUISITION CORP. II |  |  |  |  |  |  |
Fair Value Measurement Inputs and Valuation Techniques [Line Items] |  |  |  |  |  |  |
Warrants, measurement input | Y | 5.19 |  |  | 5.75 |  | 6.51 |
Risk-free interest rate |  |  |  |  |  |  |
Fair Value Measurement Inputs and Valuation Techniques [Line Items] |  |  |  |  |  |  |
Warrants, measurement input | 0.029 |  |  |  | 0.008 |  | 0.004
Risk-free interest rate | AMCI ACQUISITION CORP. II |  |  |  |  |  |  |
Fair Value Measurement Inputs and Valuation Techniques [Line Items] |  |  |  |  |  |  |
Warrants, measurement input | 0.0397 |  | 0.0132 |  | 0.0132 | 0.0099 |

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