Physics Informed Neural Networks Based on a Capacitance Resistance Model for Reservoirs Under Water Flooding Conditions

In recent years great interest has risen towards surrogate reservoir models based on data-driven methodologies with the purpose of speeding up reservoir management decisions. In this work, a Physics Informed Neural Network (PINN) based on a Capacitance Resistance Model (CRM) has been developed and tested on a synthetic and on a real dataset to predict the production of oil reservoirs under waterflooding conditions. CRMs are simple models based on material balance that estimate the liquid production as a function of injected water and bottom hole pressure. PINNs are Artificial Neural Networks (ANNs) that incorporate prior physical knowledge of the system under study to regularize the network. A PINN based on a CRM is obtained by including the residual of the CRM differential equations in the loss function designed to train the neural network on the historical data. During training, weights and biases of the network and parameters of the physical equations, such as connectivity factors between wells, are updated with the backpropagation algorithm. To investigate the effectiveness of the novel methodology on waterflooded scenarios, two test cases are presented: a small synthetic one and a real mature reservoir. Results obtained with PINN are compared with respect to CRM and ANN alone. In the synthetic case CRM and PINN give slightly better quality history matches and predictions than ANN. The connectivity factors estimated by CRM and PINN are very similar and correctly represent the underlying geology. In the real case PINN gives better quality history matches and predictions than ANN, and both significantly outperform CRM. Even though the CRM formulation is too simple to predict the complex behavior of a real reservoir, the CRM based regularization contributes to improving the PINN predictions quality compared to the purely data-driven ANN model. The connectivity factors estimated by CRM and PINN are not in agreement. However, the latter method provided results closer to our understanding of the flooding process after many years of operations and data analysis. All considered, PINN outperformed both CRM and ANN in terms of predictivity and interpretability, effectively combining strengths from both methodologies. The presented approach does not require the construction of a 3D model since it learns directly from production data, while preserving physical consistency. Moreover, it represents a computationally inexpensive alternative to traditional full-physics reservoir simulations which could have vast applications for problems requiring many forward evaluations, like the optimization of water allocation for mature reservoirs.

Thermal Resistance Model of a Flat Plate Solar Air Collector for Energy Efficiency Prediction

The temperature of a PV panel rises during operation which affects its power output. A PV panel is similar to a flat plate solar collector. This paper presents a simple theoretical heat transfer resistance model and a solution procedure to predict the absorber plate surface temperature of the solar collector. The model consisted of a rectangular cross-section steel duct placed inclined at an angle to the horizontal and exposed to solar radiation. The heat absorbed on the top surface of the plate is transmitted by conduction through the plate and heats the air in the duct. This creates a natural buoyancy effect which induces a natural convection air flow rate. A simple one-dimensional theoretical model of the solar collector with the thermal resistances of the various components is proposed. Simulated results of plate temperature and induced air flow velocity are presented.

A Novel Electro-Thermal Model of Lithium-Ion Batteries Using Power as the Input

Considering that use of measured current as input of a battery model may cause distortion of the model due to low accuracy of the on-board current sensor and that power can be used to indicate energy transmission in an electric vehicle model, the power input internal resistance model is widely used in simulation of whole electric vehicles. However, since no consideration is given to battery polarization and electro-thermal coupling characteristics, the foregoing model cannot be used to describe the internal temperature change of batteries under working conditions. Three contributions are made in the present study: (1) ternary lithium-ion batteries were taken as the research objects and a second-order RC equivalent circuit model with power as the input was established in the present study; (2) A dynamic heat generation rate model suitable for RC equivalent circuits was built based on coupled electrical and thermal characteristics of lithium-ion batteries; (3) An electric model and a two-state equivalent thermal network model were further built and combined by using the heat generation rate model to form a power input electro-thermal model. Parameters of the model so formed were identified offline, and the battery model was verified with respect to accuracy under seven working conditions. The results show that the maximum root mean square error in voltage estimation, current estimation, and surface temperature estimation is 19.38 mV, 9.51 mA, and 0.19 °C respectively, which indicates that the power input electro-thermal model can describe the electrical and thermal dynamic behavior of batteries more accurately and comprehensively than the traditional power input internal resistance model.

The equivalent resistance model of double-layer embroidered conductive lines on nonwoven fabric

To reveal the engineering relationship among the electrical properties of embroidered conductive lines, the electrical properties and arrangements of conductive yarns, it is necessary to establish their equivalent resistance model. Embroidered conductive lines in textiles are usually fabricated by single-layer (conductive and nonconductive yarn used as upper and lower yarn) or double-layer embroidery technology (conductive yarns used as upper and lower yarn). Several researchers have proposed the simple resistance model for single-layer embroidered conductive line based on geometric structure of single conductive yarn in fabric. However, the double-layer conductive line has the contact resistance periodically interlaced by the upper and lower conductive yarns, and it made its equivalent circuit different from that of single-layer conductive line. In this work, a geometric model was built to describe the trace of conductive yarn in fabric, and in combination with Wheatstone Bridge theory, was applied to establish the equivalent resistance models of double-layer conductive lines with a certain width, consisted of various courses. First, the equivalent resistance model of double-layer conductive lines consisting of single course was proposed to calculate the contact resistance. Then, to obtain the electrical resistance of double-layer conductive lines with a certain width, the equivalent resistance model was extended from single course to multiple courses ([Formula: see text]). Finally, to validate the proposed equivalent resistance model, double-layer conductive lines with different embroidery parameters (stitch length and stitch spacing) on nonwoven fabric were fabricated and evaluated. The experimental results revealed that the proposed model accurately predicted the resistances of double-layer conductive lines.