Evaluation of hydraulic fracturing of horizontal wells in tight reservoirs based on the deep neural network with physical constraints

Accurate diagnosis of fracture geometry and conductivity is of great challenge due to the complex morphology of volumetric fracture network. In this study, a DNN (deep neural network) model was proposed to predict fracture parameters for the evaluation of the fracturing effects. Field experience and the law of fracture volume conservation were incorporated as physical constraints to improve the prediction accuracy due to small amount of data. A combined neural network was adopted to input both static geological and dynamic fracturing data. The structure of the DNN was optimized and the model was validated through k-fold cross-validation. Results indicate that this DNN model is capable of predicting the fracture parameters accurately with a low relative error of under 10% and good generalization ability. The adoptions of the combined neural network, physical constraints, and k-fold cross-validation improve the model performance. Specifically, the root-mean-square error (RMSE) of the model decreases by 71.9% and 56% respectively with the combined neural network as the input model and the consideration of physical constraints. The mean square error (MRE) of fracture parameters reduces by 75% because the k-fold cross-validation improves the rationality of data set dividing. The model based on the DNN with physical constraints proposed in this study provides foundations for the optimization of fracturing design and improves the efficiency of fracture diagnosis in tight oil and gas reservoirs.

Virtual Synchronous Generator Adaptive Control of Energy Storage Power Station Based on Physical Constraints

The virtual synchronous generator(VSG)can simulate synchronous machine’s operation mechanism in the control link of an energy storage converter,so that an electrochemical energy storage power station has the ability to actively support the power grid,from passive regulation to active support.Since energy storage is an important physical basis for realizing the inertia and damping characteristics in VSG control,energy storage constraints of the physical characteristics on the system control parameters are analyzed to provide a basis for the system parameter tuning.In a classic VSG control,its virtual inertia and damping coefficient remain unchanged.When the grid load changes greatly,the constant control strategy most likely result in the grid frequency deviation beyond the stable operation standard limitations.To solve this problem,a comprehensive control strategy considering electrified wire netting demand and energy storage unit state of charge(SOC)is proposed,and an adaptive optimization method of VSG parameters under different SOC is given.The energy storage battery can maintain a safe working state at any time and be smoothly disconnected,which can effectively improve the output frequency performance of energy storage system.Simulation results further demonstrated the effectiveness of the VSG control theoretical analysis.

An Improved Data-Driven Topology Optimization Method Using Feature Pyramid Networks with Physical Constraints

Deep learning for topology optimization has been extensively studied to reduce the cost of calculation in recent years.However,the loss function of the above method is mainly based on pixel-wise errors from the image perspective,which cannot embed the physical knowledge of topology optimization.Therefore,this paper presents an improved deep learning model to alleviate the above difficulty effectively.The feature pyramid network(FPN),a kind of deep learning model,is trained to learn the inherent physical law of topology optimization itself,of which the loss function is composed of pixel-wise errors and physical constraints.Since the calculation of physical constraints requires finite element analysis(FEA)with high calculating costs,the strategy of adjusting the time when physical constraints are added is proposed to achieve the balance between the training cost and the training effect.Then,two classical topology optimization problems are investigated to verify the effectiveness of the proposed method.The results show that the developed model using a small number of samples can quickly obtain the optimization structure without any iteration,which has not only high pixel-wise accuracy but also good physical performance.

Shale oil production predication based on an empirical modelconstrained CNN-LSTM

Accurately predicting the production rate and estimated ultimate recovery(EUR)of shale oil wells is vital for efficient shale oil development.Although numerical simulations provide accurate predictions,their high time,data,and labor demands call for a swifter,yet precise,method.This study introduces the DuongeCNNeLSTM(D-C-L)model,which integrates a convolutional neural network(CNN)with a long short-term memory(LSTM)network and is grounded on the empirical Duong model for physical constraints.Compared to traditional approaches,the D-C-L model demonstrates superior precision,efficiency,and cost-effectiveness in predicting shale oil production.

Improved geologic surface approximation using a multiquadric method with additional constraints

Geologic surface approximation is profoundly affected by the presence, density and location of scattered geologic input data. Many studies have recognized the importance of utilizing varied sources of information when reconstructing a surface. This paper presents an improved geologic surface approximation method using a multiquadric function and borehole data. Additional information, i.e., inequality elevation and dip-strikes data extracted from outcrops or mining faces, is introduced in the form of physical constraints that control local changes in the estimated surface. Commonly accepted hypothesis states that geologic surfaces can be approximated to any desired degree of exactness by the summation of regular, mathematically defined, surfaces: in particular displaced quadric forms. The coefficients of the multiquadric functions are traditionally found by a least squares method. The addition of physical constraints in this work makes such an approach into a non-deterministic polynomial time problem. Hence we propose an objective function that represents the quality of the estimated surface and that includes the additional constraints by incorporation of a penalty function. Maximizing the smoothness of the estimated surface and its fitness to the additional constraints then allows the coefficients of the multiquadric function to be obtained by iterative methods. This method was implemented and demonstrated using data collected from the 81'st coal mining area of the Huaibei Coal Group.

Differences and relations of objectives, constraints, and decision parameters in the optimization of individual heat exchangers and thermal systems

Performance improvement of heat exchangers and the corresponding thermal systems benefits energy conservation, which is a multi-parameters, multi-objectives and multi-levels optimization problem. However, the optimized results of heat exchangers with improper decision parameters or objectives do not contribute and even against thermal system performance improvement. After deducing the inherent overall relations between the decision parameters and designing requirements for a typical heat exchanger network and by applying the Lagrange multiplier method, several different optimization equation sets are derived, the solutions of which offer the optimal decision parameters corresponding to different specific optimization objectives, respectively. Comparison of the optimized results clarifies that it should take the whole system, rather than individual heat exchangers, into account to optimize the fluid heat capacity rates and the heat transfer areas to minimize the total heat transfer area, the total heat capacity rate or the total entropy generation rate, while increasing the heat transfer coefficients of individual heat exchangers with different given heat capacity rates benefits the system performance. Besides, different objectives result in different optimization results due to their different intentions, and thus the optimization objectives should be chosen reasonably based on practical applications, where the inherent overall physical constraints of decision parameters are necessary and essential to be built in advance.

ELECTROWEAK MODEL AND CONSTRAINTS ON NEW PHYSICS

Revised November 2013 by J. Erler （U. Mexico） and A. Freit＆s （Pittsburgh U.）.10.1 Introduction 10.2 Renormalization and radiative corrections

Optimal interface surface determination for multi-axis freeform surface machining with both roughing and finishing

In the current practice of multi-axis machining of freeform surfaces, the interface surface between the roughing and finishing process is simply an offset surface of the nominal surface. While there have already been attempts at minimizing the machining time by considering the kinematic capacities of the machine tool and/or the physical constraints such as the cutting force, they all target independently at either the finishing or the roughing process alone and are based on the simple premise of an offset interface surface. Conceivably, since the total machining time should count that of both roughing and finishing process and both of them crucially depend on the interface surface, it is natural to ask if, under the same kinematic capacities and the same physical constraints, there is a nontrivial interface surface whose corresponding total machining time will be the minimum among all the possible（infinite） choices of interface surfaces, and this is the motivation behind the work of this paper. Specifically, with respect to the specific type of iso-planar milling for both roughing and finishing, we present a practical algorithm for determining such an optimal interface surface for an arbitrary freeform surface. While the algorithm is proposed for iso-planar milling, it can be easily adapted to other types of milling strategy such as contour milling. Both computer simulation and physical cutting experiments of the proposed method have convincingly demonstrated its advantages over the traditional simple offset method.

Integrated guidance and control for damping augmented system via convex optimization

In this paper,an integrated guidance and control approach is presented to improve the performance of the missile interception.The approach includes damping augmented system with attitude rate feedback to decrease the oscillation during the homing phase for missiles with low damping.In addition,physical constraints,which can affect the performance of the missile interception,such as acceleration limit,seeker’s look angle,and look angle rate constraints are considered.The integrated guidance and control problem is formulated as a convex quadratic optimization problem with equality and inequality constraints,and the solution is obtained by a primal–dual interior point method.The performance of the proposed method is verified through several numerical examples.

Implementation of the direct demodulation method for natural gamma ray spectral logging

Spectrum analysis of natural gamma ray spectral logging （SGR） data is a critical part of surface informa- tion processing systems. Due to the low resolution, which is an inherent weakness of SGR, and the low signal-to-noise ratio problem of logging measurements, SGR is usually treated with a low confidence level. The Direct Demodulation （DD） method is an advanced technique to solve modulation equations interactively under physical constraints. It has higher sensitivity and spatial resolution than the traditional methods and can effectively suppress the logging noise. Based on standard count rate spectral data obtained from the China Offshore Oil Logging Company SGR Calibration Facility, this paper presents the application of the DD method to gamma-ray logging. The results are compared with four traditional algorithmic methods, showing that the DD method is a credible choice, with higher sensitivity and higher spatial resolution in gamma-ray log interpretation. The Point-Spread-Function of the Shengli Oil Logging Company＇s natural gamma ray spectroscopy instrument is obtained for the first time. The quantities of various radionuclides in their calibration pits are also obtained. The DD method was applied successfully to gamma-ray logging, offering a new option for SGR logging algorithm selection.