A constrained machine learning surrogate model to predict the distribution of water-in-oil emulsions in electrostatic fields.

Accurately describing the evolution of water droplet size distribution in crude oil is fundamental for evaluating the water separation efficiency in dehydration systems. Enhancing the separation of an aqueous phase dispersed in a dielectric oil phase, which has a significantly lower dielectric constant than the dispersed phase, can be achieved by increasing the water droplet size through the application of an electrostatic field in the pipeline. Mathematical models, while being accurate, are computationally expensive. Herein, we introduced a constrained machine learning (ML) surrogate model developed based on a population balance model. This model serves as a practical alternative, facilitating fast and accurate predictions. The constrained ML model, utilizing an extreme gradient boosting (XGBoost) algorithm tuned with a genetic algorithm (GA), incorporates the key parameters of the electrostatic dehydration process, including droplet diameter, voltage, crude oil properties, temperature, and residence time as input variables, with the output being the number of water droplets per unit volume. Furthermore, we modified the objective function of the XGBoost algorithm by incorporating two penalty terms to ensure the model's predictions adhere to physical principles. The constrained model demonstrated accuracy on the test set, with a mean squared error of 0.005 and a coefficient of determination of 0.998. The efficiency of the model was validated through comparison with the experimental data and the results of the population balance mathematical model. The analysis shows that the initial droplet diameter and voltage have the highest influence on the model, which aligns with the observed behaviour in the real-world process.

Modelling droplet size distribution in inline electrostatic coalescers for improved crude oil processing.

Water-in-oil emulsions pose significant challenges in the petroleum and chemical industrial processes, necessitating the coalescence enhancement of dispersed water droplets in emulsified oils. This study develops a mathematical model to predict the evolution of water droplet size distribution in inline electrostatic coalescers (IEC) as a promising means to improve the water separation efficiency of current oil processing systems. The proposed model utilizes the population balance modelling approach to effectively simulate the dynamic and complex processes of coalescence and breakage of droplets in crude oil which directly influence the separation efficiency of the process. The method of classes as an effective mathematical technique is selected to solve the population balance equation (PBE). The accuracy of the model and considered assumptions agree well with experimental data collected from the literature. The results demonstrate the model's ability to accurately simulate droplet coalescence and breakage in emulsified oil while predicting droplet size distribution and water removal efficiency. The electric field strength, residence time, and fluid flow rate significantly influence the coalescence of droplets. At 4 kV and 5 m3/h after 4 s the mean diameter of droplets (D50) and separation efficiency reach the maximum of 94.3% and 432 µm, respectively. The model enables the optimization of operational conditions, resulting in increased performance and reliability of oil-processing systems while reducing the energy consumption and use of chemical demulsifiers. Additionally, utilization of the device in optimized conditions significantly reduces the size and weight of downstream separation equipment, which is particularly advantageous for heavy oils and offshore fields.

Gaussian process regression to determine water content of methane: Application to methane transport modeling.

The uncontrolled release of methane from natural gas wells may pose risks to shallow groundwater resources. Numerical modeling of methane migration from deep hydrocarbon formations towards shallow systems requires knowledge of phase behavior of the water-methane system, usually calculated by classic thermodynamic approaches. This study presents a Gaussian process regression (GPR) model to estimate water content of methane gas using pressure and temperature as input parameters. Bayesian optimization algorithm was implemented to tune hyper-parameters of the GPR model. The GPR predictions were evaluated with experimental data as well as four thermodynamic models. The results revealed that the predictions of the GPR are in good correspondence with experimental data having a MSE value of 3.127 × 10-7 and R2 of 0.981. Furthermore, the analysis showed that the GPR model exhibits an acceptable performance comparing with the well-known thermodynamic models. The GPR predicts the water content of methane over widespread ranges of pressure and temperature with a degree of accuracy needed for typical subsurface engineering applications.

Predicting methane solubility in water and seawater by machine learning algorithms: Application to methane transport modeling.

The upward migration of methane from natural gas wells associated with fracking operations may lead to contamination of groundwater resources and surface leakage. Numerical simulations of methane transport in the subsurface environment require knowledge of methane solubility in the aqueous phase. This study employs machine learning (ML) algorithms to predict methane solubility in aquatic systems for temperatures ranging from 273.15 to 518.3 K and pressures ranging from 1 to 1570 bar. Four regression algorithms including regression tree (RT), boosted regression tree (BRT), least square support vector machine (LSSVM) and Gaussian process regression (GPR) were utilized for predicting methane solubility in pure water and mixed aquatic systems containing Na+, K+, Ca2+, Mg2+, Cl- and SO4-2. The experimental data collected from the literature were used to implement the models. We used Grid search (GS), Random search (RS) and Bayesian optimization (BO) for tuning hyper-parameters of the ML models. Moreover, the predicted values of methane solubility were compared against Spivey et al. (2004) and Duan and Mao (2006) equations of state. The results show that the BRT-BO model is the most rigorous model for the prediction task. The coefficient of determination (R2) between experimental and predicted values is 0.99 and the mean squared error (MSE) is 1.19 × 10-7. The performance of the BRT-BO model is satisfactory, showing an acceptable agreement with experimental data. The comparison results demonstrated the superior performance of the BRT-BO model for predicting methane solubility in aquatic systems over a span of temperature, pressure and ionic strength that occurs in deep marine environments.

Modeling fate and transport of hydraulic fracturing fluid in the presence of abandoned wells.

Hydraulic fracturing in shale/tight gas reservoirs creates fracture network systems that can intersect pre-existing subsurface flow pathways, e.g. fractures, faults or abandoned wells. This way, hydraulic fracturing operations could pose environmental risks to shallow groundwater systems. This paper explores the long-term (> 30 years) flow and transport of fracturing fluids into overburden layers and groundwater aquifers through a leaky abandoned well, using the geological setting of North German Basin as a case study. A three-dimensional model consisting of 15 sedimentary layers with three hydrostratigraphic units representing the hydrocarbon reservoir, overburden, and the aquifer is built. The model considers one perforation location at the first section of the horizontal part of the well, and a discrete hydraulic fracture intersecting an abandoned well. A sensitivity analysis is carried out to quantify and understand the influence of a broad spectrum of field possibilities (reservoir properties, overburden properties, abandoned well properties and its proximity to hydraulic fractures) on the flow of fracturing fluid to shallower permeable strata. The model results suggest the spatial properties of the abandoned well as well as its distance from the hydraulic fracture are the most important factors influencing the vertical flow of fracturing fluid. It is observed that even for various field set-tings, only a limited amount of fracturing fluid can reach the aquifer in a long-term period.