Using fracture-based continuum modeling of coupled geomechanical-hydrological processes for numerical simulation of hydraulic fracturing

This paper describes numerical simulation of hydraulic fracturing using fracture-based continuum modeling(FBCM)of coupled geomechanical-hydrological processes to evaluate a technique for high-density fracturing and fracture caging.The simulations are innovative because of modeling discrete fractures explicitly in continuum analysis.A key advantage of FBCM is that fracture initiation and propagation are modeled explicitly without changing the domain grid(i.e.no re-meshing).Further,multiple realizations of a preexisting fracture distribution can be analyzed using the same domain grid.The simulated hydraulic fracturing technique consists of pressurizing multiple wells simultaneously:initially without permeating fluids into the rock,to seed fractures uniformly and at high density in the wall rock of the wells;followed by fluid injection to propagate the seeded fracture density hydraulically.FBCM combines the ease of continuum modeling with the potential accuracy of modeling discrete fractures and fracturing explicitly.Fractures are modeled as piecewise planar based on intersections with domain elements;fracture geometry stored as continuum properties is used to calculate parameters needed to model individual fractures;and rock behavior is modeled through tensorial aggregation of the behavior of discrete fractures and unfractured rock.Simulations are presented for previously unfractured rock and for rock with preexisting fractures of horizontal,shallow-dipping,steeply dipping,or vertical orientation.Simulations of a single-well model are used to determine the pattern and spacing for a multiple-well design.The results illustrate high-density fracturing and fracture caging through simultaneous fluid injection in multiple wells:for previously unfractured rock or rock with preexisting shallow-dipping or horizontal fractures,and in situ vertical compressive stress greater than horizontal.If preexisting fractures are steeply dipping or vertical,and considering the same in situ stress condition,well pressurization without fluid permeation appears to be the only practical way to induce new fractures and contain fracturing within the target domain.

COHESIVE ZONE FINITE ELEMENT-BASED MODELING OF HYDRAULIC FRACTURES

Hydraulic fracturing is a powerful technology used to stimulate fluid production from reservoirs. The fully 3-D numerical simulation of the hydraulic fracturing process is of great importance to the efficient application of this technology, but is also a great challenge because of the strong nonlinear coupling between the viscous flow of fluid and fracture propagation. By taking advantage of a cohesive zone method to simulate the fracture process, a finite element model based on the existing pore pressure cohesive finite elements has been established to investigate the propagation of a penny-shaped hydraulic fracture in an infinite elastic medium. The effect of cohesive material parameters and fluid viscosity on the hydraulic fracture behaviour has been investigated. Excellent agreement between the finite element results and analytical solutions for the limiting case where the fracture process is dominated by rock fracture toughness demonstrates the ability of the cohesive zone finite element model in simulating the hydraulic fracture growth for this case.

Nonlinear Mathematical Modeling and Sensitivity Analysis of Hydraulic Drive Unit

The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.

Coupled hydro-thermo-mechanical modeling of hydraulic fracturing in quasi-brittle rocks using BPM-DEM

This paper presents an improved understanding of coupled hydro-thermo-mechanical(HTM) hydraulic fracturing of quasi-brittle rock using the bonded particle model(BPM) within the discrete element method(DEM). BPM has been recently extended by the authors to account for coupled convective econductive heat flow and transport, and to enable full hydro-thermal fluidesolid coupled modeling.The application of the work is on enhanced geothermal systems(EGSs), and hydraulic fracturing of hot dry rock(HDR) is studied in terms of the impact of temperature difference between rock and a flowing fracturing fluid. Micro-mechanical investigation of temperature and fracturing fluid effects on hydraulic fracturing damage in rocks is presented. It was found that fracture is shorter with pronounced secondary microcracking along the main fracture for the case when the convectiveeconductive thermal heat exchange is considered. First, the convection heat exchange during low-viscosity fluid infiltration in permeable rock around the wellbore causes significant rock cooling, where a finger-like fluid infiltration was observed. Second, fluid infiltration inhibits pressure rise during pumping and delays fracture initiation and propagation. Additionally, thermal damage occurs in the whole area around the wellbore due to rock cooling and cold fluid infiltration. The size of a damaged area around the wellbore increases with decreasing fluid dynamic viscosity. Fluid and rock compressibility ratio was found to have significant effect on the fracture propagation velocity.

Performance assessment of two-dimensional hydraulic models for generation of flood inundation maps in mountain river basins

Hydraulic models for the generation of flood inundation maps are not commonly applied in mountain river basins because of the difficulty in modeling the hydraulic behavior and the complex topography. This paper presents a comparative analysis of the performance of four twodimensional hydraulic models (HEC-RAS 2D, Iber 2D, Flood Modeller 2D, and PCSWMM 2D) with respect to the generation of flood inundation maps. The study area covers a 5-km reach of the Santa B-arbara River located in the Ecuadorian Andes, at 2330 masl, in Gualaceo. The model's performance was evaluated based on the water surface elevation and flood extent, in terms of the mean absolute difference and measure of fit. The analysis revealed that, for a given case, Iber 2D has the best performance in simulating the water level and inundation for flood events with 20- and 50-year return periods, respectively, followed by Flood Modeller 2D, HEC-RAS 2D, and PCSWMM 2D in terms of their performance. Grid resolution, the way in which hydraulic structures are mimicked, the model code, and the default value of the parameters are considered the main sources of prediction uncertainty.

Modelling of an hydraulic excavator using simplifiedrefined instrumental variable(SRIV)algorithm

Instead of establishing mathematical hydraulic system models from physical laws usually done with the problems of complex modelling processes, low reliability and practicality caused by large uncertainties, a novel modelling method for a highly nonlinear system of a hydraulic excavator is presented. Based on the data collected in the excavator＇s arms driving experiments, a data-based excavator dynamic model using Simplified Refined Instrumental Variable （SRIV） identification and estimation algorithms is established. The validity of the proposed data-based model is indirectly demonstrated by the performance of computer simulation and the.real machine motion control exoeriments.

GRAY-BOX" MODELING METHOD AND PARAMETERS IDENTIFICATION FOR LARGE-SCALE HYDRAULIC SYSTEM

Modeling and digital simulation is an effective method to analyze the dynamiccharacteristics of hydraulic system. It is difficult to determine some performance parameters inthe hydraulic system by means of currently used modeling methods. The 'gray-box' modeling method forlarge-scale hydraulic system is introduced. The principle of the method, the submodels of somecomponents and the parameters identification of components or subsystem are researched.

Modeling unsaturated flow in fractured rocks with scaling relationships between hydraulic parameters

Modeling unsaturated flow in fractured rocks is essential in various subsurface engineering applications,but it remains a great challenge due to the difficulties in determining the unsaturated hydraulic properties of rocks that contain various scales of fractures.It is generally accepted that the van Genuchten(VG)model can be applied to fractured rocks,provided that the hydraulic parameters could be representatively determined.In this study,scaling relationships between the VG parameters(a and n)and hydraulic conductivity(K)across 8 orders of magnitude,from 10^(-10)m/s to 10^(-2)m/s,were proposed by statistical analysis of data obtained from 1416 soil samples.The correlations were then generalized to predict the upper bounds of VG parameters for fractured rocks from the K data that could be obtained more easily under field conditions,and were validated against a limited set of data from cores,fractures and fractured rocks available in the literature.The upper bound estimates significantly narrow the ranges of VG parameters,and the representative values of a and n for fractured rocks at the field scale can then be determined with confidence by inverse modeling using groundwater observations in saturated zones.The proposed methodology was applied to saturated-unsaturated flow modeling in the right-bank slope at the Baihetan dam site with a continuum approach,showing that most of the flow behaviors in fractured rocks in this complex hydrogeological condition could be properly reproduced.The proposed method overcomes difficulties in suction measurement in fractured rocks with strong heterogeneity,and provides a feasible way for modeling of saturated-unsaturated flow in fractured rocks with acceptable engineering accuracy.

Reliability modeling of hydraulic system of drum shearer machine

The hydraulic system plays an important role in supplying power and its transition to other working parts of a coal shearer machine. In this paper, the reliability of the hydraulic system of a drum shearer was analyzed. A case study was done in the Tabas Coal Mine in Iran for failure data collection. The results of the statistical analysis show that the time between failures （TBF） data of this system followed the 3-parameters Weibull distribution. There is about a 54% chance that the hydraulic system of the drum shearer will not fail for the first 50 h of operation. The developed model shows that the reliability of the hydraulic system reduces to a zero value after approximately 1 650 hours of operation. The failure rate of this system decreases when time increases. Therefore, corrective maintenance （run-to-t^ailure） was selected as the best maintenance strategy for it.

Three-dimensional distinct element modeling of fault reactivation and induced seismicity due to hydraulic fracturing injection and backflow

This paper presents a three-dimensional fully hydro-mechanical coupled distinct element study on fault reactivation and induced seismicity due to hydraulic fracturing injection and subsequent backflow process,based on the geological data in Horn River Basin,Northeast British Columbia,Canada.The modeling results indicate that the maximum magnitude of seismic events appears at the fracturing stage.The increment of fluid volume in the fault determines the cumulative moment and maximum fault slippage,both of which are essentially proportional to the fluid volume.After backflow starts,the fluid near the joint intersection keeps flowing into the critically stressed fault,rather than backflows to the wellbore.Although fault slippage is affected by the changes of both pore pressure and ambient rock stress,their contributions are different at fracturing and backflow stages.At fracturing stage,pore pressure change shows a dominant effect on induced fault slippage.While at backflow stage,because the fault plane is under a critical stress state,any minor disturbance would trigger a fault slippage.The energy analysis indicates that aseismic deformation takes up a majority of the total deformation energy during hydraulic fracturing.A common regularity is found in both fracturing-and backflow-induced seismicity that the cumulative moment and maximum fault slippage are nearly proportional to the injected fluid volume.This study shows some novel insights into interpreting fracturing-and backflowinduced seismicity,and provides useful information for controlling and mitigating seismic hazards due to hydraulic fracturing.

Development of dynamic-mathematical model of hydraulic excavator

This work deals with analysis of dynamic behaviour of hydraulic excavator on the basis of developed dynamic-mathematical model.The mathematical model with maximum five degrees of freedom is extended by new generalized coordinate which represents rotation around transversal main central axis of inertia of undercarriage.The excavator is described by a system of six nonlinear,nonhomogenous differential equations of the second kind.Numerical analysis of the differential equations has been done for BTH-600 hydraulic excavator with moving mechanism with pneumatic wheels.

Modeling and control of hydraulic excavator's arm

In order to find a feasible way to control excavator’s arm and realize autonomous excavation, the dynamic model for the boom of excavator’s arm which was regarded as a planar manipulator with three degrees of freedom was constructed with Lagrange equation. The excavator was retrofitted with electrohydraulic proportional valves, associated sensors (three inclinometers) and a computer control system (the motion controller of EPEC). The full nonlinear mathematic model of electrohydraulic proportional system was achieved. A discontinuous projection based on an adaptive robust controller to approximate the nonlinear gain coefficient of the valve was presented to deal with the nonlinearity of the whole system, the error was dealt with by robust feedback and an adaptive robust controller was designed. The experiment results of the boom motion control show that, using the controller, good performance for tracking can be achieved, and the peak tracking error of boom angles is less than 4°.

Hydraulic model with roughness coefficient updating method based on Kalman filter for channel flood forecast

A real-time channel flood forecast model was developed to simulate channel flow in plain rivers based on the dynamic wave theory. Taking into consideration channel shape differences along the channel, a roughness updating technique was developed using the Kalman filter method to update Manning＇s roughness coefficient at each time step of the calculation processes. Channel shapes were simplified as rectangles, triangles, and parabolas, and the relationships between hydraulic radius and water depth were developed for plain rivers. Based on the relationship between the Froude number and the inertia terms of the momentum equation in the Saint-Venant equations, the relationship between Manning＇s roughness coefficient and water depth was obtained. Using the channel of the Huaihe River from Wangjiaba to Lutaizi stations as a case, to test the performance and rationality of the present flood routing model, the original hydraulic model was compared with the developed model. Results show that the stage hydrographs calculated by the developed flood routing model with the updated Manning＇s roughness coefficient have a good agreement with the observed stage hydrographs. This model performs better than the original hydraulic model.

Theoretical Model of Dynamic Bulk Modulus for Aerated Hydraulic Fluid

Existing models of bulk modulus for aerated hydraulic fluids primarily focus on the effects of pressure and air fraction,whereas the effect of temperature on bulk modulus is disregarded.Based on the lumped parameter method and the full cavitation model,combined with the improved Henry’s law and the air polytropic course equation,a theoretical model of dynamic bulk modulus for an aerated hydraulic fluid is derived.The effects of system pressure,air fraction,and temperature on bulk modulus are investigated using the controlled variable method.The results show that the dynamic bulk modulus of the aerated hydraulic fluid is inconsistent during the compression process.At the same pressure point,the dynamic bulk modulus during expansion is higher than that during compression.Under the same initial air faction and pressure changing period,a higher temperature results in a lower dynamic bulk modulus.When the pressure is lower,the dynamic bulk modulus of each temperature point is more similar to each other.By comparing the theoretical results with the actual dynamic bulk modulus of the Shell Tellus S ISO32 standard air-containing oil,the goodness-of-fit between the theoretical model and experimental value at three temperatures is 0.9726,0.9732,and 0.9675,which validates the theoretical model.In this study,a calculation model of dynamic bulk modulus that considers temperature factors is proposed.It predicts the dynamic bulk modulus of aerated hydraulic fluids at different temperatures and provides a theoretical basis for improving the analytical model of bulk modulus.

Numerical Modelling of Proppant Transport in Hydraulic Fractures

The distribution of proppant injected in hydraulic fractures significantly affects the fracture conductivity and well performance.The proppant transport in thin fracturing fluid used during hydraulic fracturing in the unconventional reservoirs is considerably different from fracturing fluids in the conventional reservoir due to the very low viscosity and quick deposition of the proppants.This paper presents the development of a three-dimensional Computational Fluid Dynamics(CFD)modelling technique for the prediction of proppant-fluid multiphase flow in hydraulic fractures.The proposed model also simulates the fluid leak-off behaviour from the fracture wall.The Euler-Granular and CFD-Discrete Element Method(CFD-DEM)multiphase modelling approach has been applied,and the equations defining the fluid-proppant and inter-proppant interaction have been solved using the finite volume technique.The proppant transport in hydraulic fractures has been studied comprehensively,and the computational modelling results of proppant distribution and other flow properties are in good agreement with the published experimental study.The parametric study is performed to investigate the effect of variation in proppant size,fluid viscosity and fracture width on the proppant transport.Smaller proppants can be injected early,followed by larger proppants to maintain high propping efficiency.This study has enhanced the understanding of the complex flow phenomenon between proppant and fracturing fluid and can play a vital role in hydraulic fracturing design.

APPLICATION OF ARCHITECTURE- BASED NEURAL NETWORKS IN MODELING AND PARAMETER OPTIMIZATION OF HYDRAULIC BUMPER

The dynamic working process of 52SFZ-140-207B type of hydraulic bumper isanalyzed. The modeling method using architecture-based neural networks is introduced. Using thismodeling method, the dynamic model of the hydraulic bumper is established; Based on this model thestructural parameters of the hydraulic bumper are optimized with Genetic algorithm. The result showsthat the performance of the dynamic model is close to that of the hydraulic bumper, and the dynamicperformance of the hydraulic bumper is improved through parameter optimization.

Unraveling the hydraulic properties of loess for landslide prediction:A study on variations in loess landslides in Lanzhou,Dingxi,and Tianshui,China

Loess has distinctive characteristics,leading to frequent landslide disasters and posing serious threats to the lives and properties of local re sidents.The involvement of water repre sents a critical factor in inducing loess landslides.This study focuses on three neighboring cities sequentially situated on the Loess Plateau along the direction of aeolian deposition of loess,namely Lanzhou,Dingxi,and Tianshui,which are densely populated and prone to landslide disasters.The variations in hydraulic properties,including water retention capacity and permeability,are investigated through Soil Water Characteristic Curve(SWCC)test and hydraulic conductivity test.The experimental findings revealed that Tianshui loess exhibited the highest water retention capacity,followed by Dingxi loess,while Lanzhou loess demonstrated the lowest water retention capacity.Contrastingly,the results for the saturated permeability coefficient were found to be the opposite:Tianshui loess showed the lowest permeability,whereas Lanzhou loess displayed the highest permeability.These results are supported and analyzed by scanning electron microscopy(SEM)observation.In addition,the water retention capacity is mathematically expressed using the van Genuchten model and extended to predict unsaturated hydraulic properties of loess.The experimental results exhibit a strong accordance with one another and align with the regional distribution patterns of disasters.

Implications for fault reactivation and seismicity induced by hydraulic fracturing

Evaluating the physical mechanisms that link hydraulic fracturing(HF) operations to induced earthquakes and the anticipated form of the resulting events is significant in informing subsurface fluid injection operations. Current understanding supports the overriding role of the effective stress magnitude in triggering earthquakes, while the impact of change rate of effective stress has not been systematically addressed. In this work, a modified critical stiffness was brought up to investigate the likelihood, impact,and mitigation of induced seismicity during and after hydraulic fracturing by developing a poroelastic model based on rate-and-state fraction law and linear stability analysis. In the new criterion, the change rate of effective stress was considered a key variable to explore the evolution of this criterion and hence the likelihood of instability slip of fault. A coupled fluid flow-deformation model was used to represent the entire hydraulic fracturing process in COMSOL Multiphysics. The possibility of triggering an earthquake throughout the entire hydraulic fracturing process, from fracturing to cessation, was investigated considering different fault locations, orientations, and positions along the fault. The competition between the effects of the magnitude and change rate of effective stress was notable at each fracturing stage. The effective stress magnitude is a significant controlling factor during fracturing events, with the change rate dominating when fracturing is suddenly started or stopped. Instability dominates when the magnitude of the effective stress increases(constant injection at each fracturing stage) and the change rate of effective stress decreases(the injection process is suddenly stopped). Fracturing with a high injection rate, a fault adjacent to the hydraulic fracturing location and the position of the junction between the reservoir and fault are important to reduce the Coulomb failure stress(CFS) and enhance the critical stiffness as the significant disturbance of stresses at these positions in the coupled process. Therefore,notable attention should be given to the injection rate during fracturing, fault position, and position along faults as important considerations to help reduce the potential for induced seismicity. Our model was verified and confirmed using the case of the Longmaxi Formation in the Sichuan Basin, China, in which the reported microseismic data were correlated with high critical stiffness values. This work supplies new thoughts of the seismic risk associated with HF engineering.

MODELING AND EXPERIMENTAL STUDY OF A PASSIVE HYDRAULIC ENGINE MOUNT WITH INERTIA AND DIRECT-DECOUPLER

To investigate the dynamic characteristics and damping theory of the passive hydraulic engine mount （PHEM）, numerical prediction is performed through lumped parameter model. System parameters, including volume compliance of the decoupler chamber, effective piston area, fluid inertia and resistance of inertia track and direct-decoupler, are identified by means of experiments and finite element method （FEM）. Dynamic behaviors are tested with elastomer test system for purpose of validating PHEM. With incorporation of inertia track and direct-decoupler, PHEM behaves effective and efficient vibration isolation in range of both low and high frequencies. The comparison of the numerical results with the experimental observations shows that the present PHEM achieves fairly good performance for the engine vibration isolation.

Development of River Rating Curves for Simple to Complex Hydraulic Structure Based on Calibrated HEC-RAS Hydraulic Model, in Kwale, Coastal Kenya

Accurate and reliable river flow information is critical to planning and management for sustainable water resources utilization. Most of engineering activities related to hydrologic designs, flood, drought, reservoirs and their operations are heavily dependent on the river flow information derived from river rating curve. The rating curve for a given river section is normally developed from a set of direct stage-discharge measurements for different periods. This involves considerable labour, risk and resources, and presupposes a complex and extensive measuring survey. Extrapolating the rating curve beyond the measured range, as common in many cases, is fraught with errors and uncertainties, due to the complex hydraulic behaviour of the surface water profile in transition from section, channel, downstream and flood plain controls which are often poorly understood with direct measurements. Hydraulic modeling has recently emerged as one of the more promising methods to efficiently develop accurate rating curves for a river section with simple or complex hydraulic structures and conditions. This paper explores the use of a Hydraulic Engineering Center-River Analysis System (HEC-RAS) model to review and develop river rating curves for three hydrometric stations on two rivers in Kwale, coastal Kenya. The HEC-RAS models were set up based on topographical (cross section and longitudinal) survey data for the reaches and engineering drawings for the hydraulic structures commonly used as section controls for flow measurement. The model was calibrated under unsteady state conditions against measured stage-discharge data which were captured using a Velocity Current Meter (Valeport) and an Acoustic Doppler Current Profiler (ADCP) for both low and high flow. The rating curves were extracted from model results and the uncertainty associated with each rating curve analyzed. The results obtained by the HEC-RAS model were satisfactory and deemed acceptable for predicting discharge across the stage range at each river section.