# A New Modeling Framework for Geothermal Operational Optimization with Machine Learning (GOOML)

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Sources

#### 2.2. System Frameworks

#### 2.2.1. Historical System

#### 2.2.2. Forecast System

#### 2.3. Component Models

#### 2.3.1. Well Models

#### 2.3.2. Two-Phase Separator Models (“Flash Plants”)

#### 2.3.3. Power Generating Models

#### 2.3.4. General Utility Component Models

#### 2.4. Modeling Assumptions

**Assumption**

**1.**

**Assumption**

**2.**

**Assumption**

**3.**

**Assumption**

**4.**

**Assumption**

**5.**

**Assumption**

**6.**

**Assumption**

**7.**

**Assumption**

**8.**

**Assumption**

**9.**

**Assumption**

**10.**

**Assumption**

**11.**

**Assumption**

**12.**

## 3. Results

#### 3.1. Forecast Model Validation

#### 3.2. Cross-Validation and Extensibility

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Glossary and Abbreviations

AI | artificial intelligence |

as-built | the true physical system including any modifications made during its construction and/or operation as opposed to the nominal system during the design phase |

binary plant | a power plant that transfers geothermal heat to a secondary fluid with a lower boiling point to drive a turbine generator |

capacity factor | the ratio of actual power generated to the theoretical maximum output of a power station |

digital twin | a digital representation of a physical system |

forecast model | a relational data model that uses trained regressions to predict future operational states |

GOOML | Geothermal Operational Optimization with Machine Learning |

hindcast | a forecast model used for validation purposes that is based on some historical data such as known operator actions |

historical model | a relational data model built using historical data |

hybrid data-driven thermodynamics model | in the context of this work, GOOML is a hybrid model that relies heavily on traditional thermodynamics (e.g., fluid properties and conservation equations) but uses data-driven machine learning models to determine the behavior of the system within the thermodynamic operational space |

IP | intermediate pressure |

join junction | a component where two or more flows are joined to one |

LP | low pressure |

mass take | the total mass extracted by a geothermal system |

MAE | mean absolute error calculated as: $\frac{{{\displaystyle \sum}}_{i=1}^{n}abs\left({x}_{G}-{x}_{T}\right)}{n}$ where ${x}_{G}$ is the GOOML predicted value, ${x}_{T}$ is the true historical value, $n$ is the number of observations, and $abs$ is the absolute value operator |

MBE | mean bias error calculated as: $\frac{{{\displaystyle \sum}}_{i=1}^{n}\left({x}_{G}-{x}_{T}\right)}{n}$ where ${x}_{G}$ is the GOOML predicted value, ${x}_{T}$ is the true historical value, and $n$ is the number of observations |

ML | machine learning |

POI | Poihipi power station at the Wairakei Geothermal Field |

RELU | rectified linear unit |

separator/flash plant (FP) | a vessel that separates steam and liquid phases from a two-phase flow input, often involving pressure drop and cyclonic separation |

split junction | a component where input flow is split into two distinct outputs, e.g., steam and liquid in the case of a separator |

steamfield | a network of wells, pipelines, separators, turbine generators, and binary plants used to harness geothermal energy |

TG | a turbine generator system that uses steam to generate electricity |

THI | Te Mihi power station at the Wairakei Geothermal Field |

TFT | tracer flow test—a method to assess energy and flow rate from a geothermal well |

two-phase flow | a thermodynamic state of water where both saturated liquid and steam exist simultaneously |

Willans Line | a highly simplified linear mass-to-power relationship used to represent turbine generator systems |

WRK | Wairakei power station at the Wairakei Geothermal Field |

WHS | well head separator—a small two-phase separator dedicated to a single well, typically mounted directly on the well head itself |

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**Figure 1.**Block diagram of a basic GOOML system network where WHS is a well head separator, FP is a central flash plant, ${\dot{m}}_{x}$ is the mass flow from component $x$, and additional subscripts ${\dot{m}}_{x\_v}$ and ${\dot{m}}_{x\_l}$ represent separated vapor and liquid flow, respectively.

**Figure 2.**Total system mass take, comparing historically measured data versus the nominal forecast model.

**Figure 3.**Total system separated steam flow, comparing historically measured data versus the nominal forecast model (including the neural network flash plant model) and the theoretical flash plant forecast (using steam quality at separation pressure as separation efficiency).

**Figure 4.**Intermediate pressure (

**left**) and low pressure (

**right**) separated steam flow to the Wairakei power station, comparing historically measured data versus the nominal forecast model (including the neural network flash plant model) and the theoretical flash plant forecast (using steam quality at separation pressure as separation efficiency).

**Figure 5.**Intermediate pressure (

**left**) and low pressure (

**right**) separated steam flow to the Te Mihi power station, comparing historically measured data versus the nominal forecast model (including the neural network flash plant model) and the theoretical flash plant forecast (using steam quality at separation pressure as separation efficiency).

**Figure 6.**Total system power generation, comparing historically measured data versus the nominal forecast model (including the turbine generator multi-linear regression model) and the Willans Line turbine generator forecast (using a constant value for turbine generator steam consumption rate).

**Figure 7.**Wairakei (

**left**) and Te Mihi (

**right**) system power generation, comparing historically measured data versus the nominal forecast model (including the turbine generator multi-linear regression model) and the Willans Line turbine generator forecast (using a constant value for turbine generator steam consumption rate).

**Figure 8.**Binary plant power generation, comparing historically measured data versus the nominal forecast model (including the binary plant multi-linear regression model).

**Figure 9.**Poihipi Road separated steam flow (

**left**) and turbine generator power (

**right**), comparing the historically measured data versus the nominal forecast model and the theoretical flash plant and turbine generator models.

**Figure 10.**Results from a flash plant modeling cross-validation experiment where models were trained only with two-phase input mass flow less than 1900 tonne/h. The top plot shows the two-phase mass flow through FP16IP+ with the training data limitation. The bottom plot shows the historical separated steam flow compared to predictions by a baseline model trained on all data, the cross-validation (xval) model, and a theoretical model.

Component | Common Historical Data | Forecast Model | Model Input Features |
---|---|---|---|

Single-Phase Well | Pressure, temperature, mass flow | Linear extrapolation with decline | Pressure, temperature, mass flow |

Two-Phase Well | Pressure, mass flow (TFT estimate), enthalpy (TFT estimate) | TFT deliverability curves with decline | Pressure |

Separator (Flash Plant) | Output steam pressure, output steam mass flow, output liquid mass flow | Feed-forward neural network, theoretical (thermodynamic-based) | Input mass flow, input enthalpy, input pressure, input steam quality, input velocity, residence time, steam quality at separation pressure, theoretical pressure drop, cyclone design number |

Turbine Generator | Heat sink temperature, power | Multi-linear regression, Willans Line, theoretical (Carnot-based) | Input mass flow, input enthalpy flow, heat sink temperature, temperature differential |

Binary Plant | Heat sink temperature, power | Multi-linear regression, theoretical (Carnot-based) | Input enthalpy flow, temperature differential, upstream flow contribution fractions |

Join Junctions | N/A | N/A | N/A |

Split Junctions | N/A | N/A | N/A |

**Table 2.**Comparison of results of steamfield model components in the GOOML environment based on mean bias error (MBE) and mean absolute error (MAE) between historical and forecast data. Relative error values are calculated with respect to the mean historical value.

Metric | Model | MAE | MAE (%) | MBE | MBE (%) |
---|---|---|---|---|---|

Total System Mass Take (1000 kg/h) | Nominal Forecast | 783 | 8.1 | −328.4 | −3.4 |

Total Separated Steam (1000 kg/h) | Nominal Forecast | 133 | 5.2 | −76.8 | −3.0 |

Total Separated Steam (1000 kg/h) | Theoretical FP | 314.2 | 12.3 | −297 | −11.6 |

WRK IP Steam (1000 kg/h) | Nominal Forecast | 47.5 | 6.1 | 10.9 | 1.4 |

WRK IP Steam (1000 kg/h) | Theoretical FP | 70.7 | 9.1 | 45.4 | 5.8 |

WRK LP Steam (1000 kg/h) | Nominal Forecast | 29.3 | 12.6 | −16 | −6.9 |

WRK LP Steam (1000 kg/h) | Theoretical FP | 142.8 | 61.3 | −142.8 | −61.3 |

THI IP Steam (1000 kg/h) | Nominal Forecast | 62.5 | 6.8 | −54.2 | −5.9 |

THI IP Steam (1000 kg/h) | Theoretical FP | 166.6 | 18.2 | −163.8 | −17.9 |

THI LP Steam (1000 kg/h) | Nominal Forecast | 38.3 | 10.5 | −20.2 | −5.5 |

THI LP Steam (1000 kg/h) | Theoretical FP | 34.6 | 9.5 | 25.2 | 6.9 |

POI Steam (1000 kg/h) | Nominal Forecast | 52.3 | 16.4 | −49.8 | −15.6 |

POI Steam (1000 kg/h) | Theoretical FP | 81.1 | 25.4 | −80.7 | −25.3 |

Total System Power (Gross MWe) | Nominal Forecast | 16.6 | 5.0 | −12.8 | −3.9 |

Total System Power (Gross MWe) | Willans Line TG | 28.5 | 8.6 | −27.4 | −8.3 |

WRK Power (Gross MWe) | Nominal Forecast | 4.8 | 4.2 | −0.3 | −0.3 |

WRK Power (Gross MWe) | Willans Line TG | 6.8 | 5.9 | −5.4 | −4.7 |

THI Power (Gross MWe) | Nominal Forecast | 16.7 | 10.4 | −14 | −8.7 |

THI Power (Gross MWe) | Willans Line TG | 15.9 | 9.9 | −13.5 | −8.4 |

POI Power (Gross MWe) | Nominal Forecast | 2.7 | 6.1 | 0.4 | 1.0 |

POI Power (Gross MWe) | Willans Line TG | 9.8 | 21.9 | −9.6 | −21.5 |

Binary Plant Power (Gross MWe) | Nominal Forecast | 1.3 | 11.8 | 1.1 | 10.0 |

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**MDPI and ACS Style**

Buster, G.; Siratovich, P.; Taverna, N.; Rossol, M.; Weers, J.; Blair, A.; Huggins, J.; Siega, C.; Mannington, W.; Urgel, A.;
et al. A New Modeling Framework for Geothermal Operational Optimization with Machine Learning (GOOML). *Energies* **2021**, *14*, 6852.
https://doi.org/10.3390/en14206852

**AMA Style**

Buster G, Siratovich P, Taverna N, Rossol M, Weers J, Blair A, Huggins J, Siega C, Mannington W, Urgel A,
et al. A New Modeling Framework for Geothermal Operational Optimization with Machine Learning (GOOML). *Energies*. 2021; 14(20):6852.
https://doi.org/10.3390/en14206852

**Chicago/Turabian Style**

Buster, Grant, Paul Siratovich, Nicole Taverna, Michael Rossol, Jon Weers, Andrea Blair, Jay Huggins, Christine Siega, Warren Mannington, Alex Urgel,
and et al. 2021. "A New Modeling Framework for Geothermal Operational Optimization with Machine Learning (GOOML)" *Energies* 14, no. 20: 6852.
https://doi.org/10.3390/en14206852