# Development of a Distributed Mathematical Model and Control System for Reducing Pollution Risk in Mineral Water Aquifer Systems

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## Abstract

**:**

## 1. Introduction

## 2. Problem Statement

- Possibility of considering the spatial distribution of the object (field);
- Modeling a complex of interconnected hydrogeological objects;
- Ability to control the parameters of the operating mode of a group of hydrogeological objects.

## 3. Methods

#### 3.1. Method Description

- First group. Deposits with a simple geological structure containing large or medium-sized bodies of minerals, which can be characterized by the stable thickness and internal structure, consistent quality of minerals and uniform distribution of the main valuable components.
- Second group. Deposits with a complex geological structure containing large and medium-sized bodies with disturbed bedding, which can be characterized by unstable thickness and uneven distribution of the main valuable components.
- Third group. Deposits with a very complex geological structure containing medium and small-sized bodies of minerals with intensively disturbed occurrence, which can be characterized by very variable thickness and internal structure, and a very uneven distribution of the main valuable components.
- Fourth group. Deposits with a small, less often medium-sized bodies containing extremely disturbed bedding, which can be characterized by sharp variability of thickness and internal structure, extremely uneven quality of the mineral [18].

- Delphi 7 software package;
- Software package for modeling hydrodynamic processes developed up to GOST R 57,700.2;
- Software package for modeling parameters of an open-loop control system developed up to GOST 24.104-85;
- A software package for modeling the parameters of a closed-loop control system developed up to GOST 24.104-85;
- A software package for modeling the spatial heterogeneity of the field strata hydrogeological structure developed up to GOST R 57,700.2 [21].

- Hydrogeological conditions (lithological structure of water-bearing soils, feeding characteristics and conditions at the boundaries of the tested layer);
- Groundwater regime (features of the pressure fluctuations nature—levels and the influence on these fluctuations of various disturbing sources, including technogenic);
- Technological conditions for testing, the data of which are used to check the accuracy of modeling (fluctuations in flow rate and pressure during pumping) [28].

#### 3.2. Development of the “Reservoir” Layout

- DBGrid (for the “temperature” table displaying);
- DBNavigator (for table entries managing);
- ADOConnection (for the communication with the database);
- ADOQwery;
- ComPortDriver;
- Timer;
- DataSource.

## 4. Development of an Experimental Reservoir’s Distributed Mathematical Model

- The proposed method takes into account the interstratal interactions of aquifer;
- The proposed method gives a possibility of a three-dimensional model of the field mathematical description;
- The proposed method provides a sufficiently high accuracy of the hydrodynamic processes’ reflection for a given experiment;
- The proposed method was successfully tested at one of the fields in the region under consideration [3].

## 5. Results

#### 5.1. Method Effectiveness Analysis

#### 5.2. Control System Synthesis Results

#### 5.3. Experimental Reservoir’s Distributed Mathematical Model Result Analysis

## 6. Conclusions

- Application of sensitivity analysis methods to assess the impact of changes in the initial parameters of the model on the output characteristics.
- Adaptation and scaling of the developed modeling methods for solving problems of the oil and gas industry.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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Water Name | Mineralization g/dm ^{3} | Main Ionic Composition | Bioactive Agents | |||||
---|---|---|---|---|---|---|---|---|

Anions, mg/dm^{3} | Cations, mg/dm^{3} | |||||||

HCO_{3}^{−} | SO_{4}^{2−} | Cl^{−} | Ca^{2+} | Mg^{2+} | (Na^{+} + K^{+}) | |||

Narzan | 2.0–3.5 | 1000–1700 | 250–500 | 50–200 | 200–500 | 50–150 | 50–250 | CO_{2}1000–2500 |

Dolomitic Narzan | 4.0–4.5 | 2000–2300 | 600–800 | 250–350 | 650–700 | 100–180 | 300–400 | CO_{2}2000–2300 |

Sulphatic Narzan | 5.0–5.5 | 2300–2500 | 1400–1600 | <50 | 700–800 | 200–400 | 200–300 | CO_{2}2000–2300 |

Essentuki 4 | 7.0–10.0 | 3400–4800 | <25 | 1300–2000 | <150 | <100 | 2000–3000 | H_{3}BO_{3}30–60, CO _{2}500–1800 |

Essentuki 17 | 10.0–14.0 | 5000–7200 | <150 | 1200–2200 | <150 | <150 | 2700–3900 | H_{3}BO_{3}30–80, CO _{2}500–1200 |

LX, m | LY, m | LZ, m | ∂, t s. | S1 | S2 | S3 | S4 | S5 | S6 |
---|---|---|---|---|---|---|---|---|---|

0.03 | 0.03 | 0.01 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |

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**MDPI and ACS Style**

Martirosyan, A.V.; Ilyushin, Y.V.; Afanaseva, O.V.
Development of a Distributed Mathematical Model and Control System for Reducing Pollution Risk in Mineral Water Aquifer Systems. *Water* **2022**, *14*, 151.
https://doi.org/10.3390/w14020151

**AMA Style**

Martirosyan AV, Ilyushin YV, Afanaseva OV.
Development of a Distributed Mathematical Model and Control System for Reducing Pollution Risk in Mineral Water Aquifer Systems. *Water*. 2022; 14(2):151.
https://doi.org/10.3390/w14020151

**Chicago/Turabian Style**

Martirosyan, Alexander V., Yury V. Ilyushin, and Olga V. Afanaseva.
2022. "Development of a Distributed Mathematical Model and Control System for Reducing Pollution Risk in Mineral Water Aquifer Systems" *Water* 14, no. 2: 151.
https://doi.org/10.3390/w14020151