# Volumetric Heating Capacity (VHC) Regression Parameters for 48 Refrigerants

### Clarification of CSV File Structure and Terms
The CSV file in this repository contains the following columns:
   Column Name       | Description                                                                                     |
 |-------------------|-------------------------------------------------------------------------------------------------|
 | **Index**         | Name or ASHRAE designation of the refrigerant (e.g., R290, R717).                              |
 | **a, b, c, ..., j** | Coefficients for the **fourth-order Hamilton-Allen polynomial model** (Eq. 9 in the paper). These are used to calculate the **volumetric heating capacity (VHC)** as a function of heat source and sink temperatures. |
 | **NBT in °C**    | **Normal Boiling Temperature** in °C: The temperature at which the refrigerant boils at standard atmospheric pressure (1.013·10⁵ Pa). Defines the **lower temperature limit** for the refrigerant’s operating range. |
 | **T_crit in °C** | **Critical Temperature** in °C: The temperature above which the refrigerant cannot exist as a liquid, regardless of pressure. Defines the **upper temperature limit** for the refrigerant’s operating range. |

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This repository provides the fourth-order Hamilton-Allen regression parameters for calculating the volumetric heating capacity (VHC) of 48 refrigerants as a function of heat source and sink temperatures. The parameters are derived from the study:

Large-Scale Heat Pumps: Development of a Broadly Applicable, Easy-to-Use Heating Capacity Model

Jesper, Mateo; Hoffmann, Chris René; Pag, Felix; Vajen, Klaus; Jordan, Ulrike

Preprint available at: http://dx.doi.org/10.2139/ssrn.5082708

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The regression model enables simple, accurate, and broadly applicable estimates of VHC for large-scale heat pump applications, including district heating and industrial processes. The parameters are validated with a coefficient of determination (R²) exceeding 0.998 for all refrigerants, ensuring high reliability for preliminary design and feasibility studies.

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### Key Features:
- Coefficients for fourth-order Hamilton-Allen polynomial models (Eq. 9 in the paper) for each refrigerant.
  Parameters cover a wide range of operating conditions, defined by heat source and sink temperatures within the constraints outlined in the study.
- Data for 48 refrigerants, including conventional and low-GWP (Global Warming Potential) options.

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### Applications:
- Suitable for preliminary design, feasibility assessments, and comparative analyses of heat pump systems.
- Complements COP (Coefficient of Performance) regression models for complete heat pump modeling.

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### Assumptions and Limitations:
- The model assumes fixed superheating (7 K) and subcooling (1 K).
- Isentropic compressor efficiency is assumed to be ideal for simplicity.
- Errors may arise if real-world conditions deviate significantly from these assumptions (see Section 4.5 of the paper for sensitivity analysis).