Study of the pressure transient behavior of directional wells considering the effect of non-uniform flux distribution

During the production,the fluid in the vicinity of the directional well enters the wellbore with different rates,leading to non-uniform flux distribution along the directional well.However,in all existing studies,it is oversimplified to a uniform flux distribution,which can result in inaccurate results for field applications.Therefore,this paper proposes a semi-analytical model of a directional well based on the assumption of non-uniform flux distribution.Specifically,the direction well is discretized into a carefully chosen series of linear sources,such that the complex well trajectory can be captured and the nonuniform flux distribution along the wellbore can be considered to model the three-dimensional flow behavior.By using the finite difference method,we can obtain the numerical solutions of the transient flow within the wellbore.With the aid of Green's function method,we can obtain the analytical solutions of the transient flow from the matrix to the wellbore.The complete flow behavior of a directional well is perfectly represented by coupling the above two types of transient flow.Subsequently,on the basis of the proposed model,we conduct a comprehensive analysis of the pressure transient behavior of a directional well.The computation results show that the flux variation along the direction well has a significant effect on pressure responses.In addition,the directional well in an infinite reservoir may exhibit the following flow regimes:wellbore afterflow,transition flow,inclined radial flow,elliptical flow,horizontal linear flow,and horizontal radial flow.The horizontal linear flow can be observed only if the formation thickness is much smaller than the well length.Furthermore,a dip region that appears on the pressure derivative curve indicates the three-dimensional flow behavior near the wellbore.

Pressure transient characteristics of non-uniform conductivity fractured wells in viscoelasticity polymer flooding based on oil-water two-phase flow

Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery.In contrast to water,polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening,polymer convection,diffusion,adsorption retention,inaccessible pore volume and reduced effective permeability.Meanwhile,the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution,formation damage,and proppant breakage.In this paper,we present an oil-water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior,and non-uniform fracture characteristics in fractured polymer flooding.The hydraulic fracture is firstly divided into two parts:high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section.A hybrid grid system,including perpendicular bisection(PEBI)and Cartesian grid,is applied to discrete the partial differential flow equations,and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution.The combination of polymer behavior characterizations and numerical flow simulations are applied,resulting in the calculation for the distribution of water saturation,polymer concentration and reservoir pressure.Compared with the polymer flooding well with uniform fracture conductivity,this non-uniform fracture conductivity model exhibits the larger pressure difference,and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section.The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately,and yields fracture half-lengths that better match engineering reality,enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity.The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology,as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.

Influence of confined water on the limit support pressure of tunnel face in weakly water-rich strata

In the process of shield tunneling through soft soil layers,the presence of confined water ahead poses a significant threat to the stability of the tunnel face.Therefore,it is crucial to consider the impact of confined water on the limit support pressure of the tunnel face.This study employed the finite element method(FEM)to analyze the limit support pressure of shield tunnel face instability within a pressurized water-containing layer.Subsequently,a multiple linear regression approach was applied to derive a concise solution formula for the limit support pressure,incorporating various influencing factors.The analysis yields the following conclusions:1)The influence of confined water on the instability mode of the tunnel face in soft soil layers makes the displacement response of the strata not significant when the face is unstable;2)The limit support pressure increases approximately linearly with the pressure head,shield tunnel diameter,and tunnel burial depth.And inversely proportional to the thickness of the impermeable layer,soil cohesion and internal friction angle;3)Through an engineering case study analysis,the results align well with those obtained from traditional theoretical methods,thereby validating the rationality of the equations proposed in this paper.Furthermore,the proposed equations overcome the limitation of traditional theoretical approaches considering the influence of changes in impermeable layer thickness.It can accurately depict the dynamic variation in the required limit support pressure to maintain the stability of the tunnel face during shield tunneling,thus better reflecting engineering reality.

Stress analytical solution for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform distributed pressure

The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common cases.Stress analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is given.The power series method of complex function is used.The stress analytical solution is obtained with the assumption that two layers of a cylinder are fully contacted.The distributions of normal and tangential contact stress along the interface,tangential stress on the inner boundary and stresses in the radial direction at θ=0°,45° and 90°,are obtained.An example indicates that,when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer,the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous materials.In that way,stress concentration at the inner surface can be alleviated and the stress distribution is more uniform.This is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.

Sliding Mode Control of Hydraulic Pressure in Electro-Hydraulic Brake System Based on the Linearization of Higher-Order Model

The possibility to enhance the stability and robustness of electrohydraulic brake(EHB)systems is considered a subject of great importance in the automotive field.In such a context,the present study focuses on an actuator with a four-way sliding valve and a hydraulic cylinder.A 4-order nonlinear mathematical model is introduced accordingly.Through the linearization of the feedback law of the high order EHB model,a sliding mode control method is proposed for the hydraulic pressure.The hydraulic pressure tracking controls are simulated and analyzed by MATLAB/Simulink soft considering separately different conditions,i.e.,a sine wave,a square wave and a square wave with superimposed sine disturbance.The results show that the proposed strategy can track the target within 0.25 s,and the mean observed error is less than 1.2 bar.Moreover,with such a strategy,faster response and less overshoot are possible,which should be regarded as significant advantages.

Pressure transient analysis of a finite-conductivity multiple fractured horizontal well in linear composite gas reservoirs

Faulted gas reservoirs are very common in reality,where some linear leaky faults divide the gas reservoir into several reservoir regions with distinct physical properties.This kind of gas reservoirs is also known as linear composite(LC)gas reservoirs.Although some analytical/semi-analytical models have been proposed to investigate pressure behaviors of producing wells in LC reservoirs based on the linear composite ideas,almost all of them focus on vertical wells and studies on multiple fractured horizontal wells are rare.After the pressure wave arrives at the leaky fault,pressure behaviors of multiple fractured horizontal wells will be affected by the leaky faults.Understanding the effect of leaky faults on pressure behaviors of multiple fractured horizontal wells is critical to the development design.Therefore,a semi-analytical model of finite-conductivity multiple fractured horizontal(FCMFH)wells in LC gas reservoirs is established based on Laplace-space superposition principle and fracture discrete method.The proposed model is validated against commercial numerical simulator.Type curves are obtained to study pressure characteristics and identify flow regimes.The effects of some parameters on type curves are discussed.The proposed model will have a profound effect on developing analytical/semi-analytical models for other complex well types in LC gas reservoirs.

Preliminary Study on the Linear Relationship between the Internal Pressure Head of Rubber Dam Bags and Real-time Dam Height

The design operating conditions of rubber dams were analyzed,and it is found that the operating conditions are similar to the actual operating conditions of changes in the internal pressure ratio of a specific rubber dam bag in the process of filling and draining. Based on this,the linear relationship curve between the internal pressure head H0 and the real-time dam height H and its approximate analytical formula can be obtained,which can be used as a supplement and correction method for the measurement method of real-time dam height during rubber dam operation,and provides reference for rubber dam project managers.

Preventing Pressure Oscillations Does Not Fix Local Linear Stability Issues of Entropy-Based Split-Form High-Order Schemes

Recently,it was discovered that the entropy-conserving/dissipative high-order split-form discontinuous Galerkin discretizations have robustness issues when trying to solve the sim-ple density wave propagation example for the compressible Euler equations.The issue is related to missing local linear stability,i.e.,the stability of the discretization towards per-turbations added to a stable base flow.This is strongly related to an anti-diffusion mech-anism,that is inherent in entropy-conserving two-point fluxes,which are a key ingredi-ent for the high-order discontinuous Galerkin extension.In this paper,we investigate if pressure equilibrium preservation is a remedy to these recently found local linear stability issues of entropy-conservative/dissipative high-order split-form discontinuous Galerkin methods for the compressible Euler equations.Pressure equilibrium preservation describes the property of a discretization to keep pressure and velocity constant for pure density wave propagation.We present the full theoretical derivation,analysis,and show corresponding numerical results to underline our findings.In addition,we characterize numerical fluxes for the Euler equations that are entropy-conservative,kinetic-energy-preserving,pressure-equilibrium-preserving,and have a density flux that does not depend on the pressure.The source code to reproduce all numerical experiments presented in this article is available online(https://doi.org/10.5281/zenodo.4054366).

Experimental Study on Anchoring Physical Properties of Different Anchoring Lengths Coupled with Temperature and Pressure

Aiming at deep roadway anchorage solids, laboratory similar model tests were used to reveal the mechanical properties of anchorage solids with different anchorage lengths under the coupling effect of temperature and pressure, and SPSS statistical analysis software was used to conduct linear regression analysis of the ultimate anchorage force obtained from the tests. The results show that: through multiple linear regression analysis, the influence degree of temperature and pressure coupling on the ultimate anchorage force is arranged in order of anchoring length > surrounding rock strength > temperature > side pressure coefficient, and the linear regression equation of the model is obtained. Compared with the linear regression equation of simulation results, the model has a high explanatory ability.

A Novel Capacitive Pressure Sensor

A novel capacitive pressure sensor is presented, whose sensing structure is a solid-state capacitor consisting of three square membranes with Al/SiO2/n-type silicon. It was fabricated using pn junction self-stop etching combined with adhesive bonding,and only three masks were used during the process. Sensors with side lengths of 1000,1200,and 1400μm were fabricated,showing sensitivity of 1.8,2.3, and 3.6fF/hPa over the range of 410～ 1010hPa, respectively. The sensi- tivity of the sensor with a side length of 1500μm is 4. 6fF/hPa,the nonlinearity is 6. 4% ,and the max hysteresis is 3.6%. The results show that permittivity change plays an important part in the capacitance change.

NON-UNIFORM LINEAR ARRAY CONFIGURATION FOR MIMO RADAR

Array configuration of multiple-input multiple-output （MIMO） radar with non-uniform linear array （NLA） is proposed. Unlike a standard phased-array radar where NLA is used to generate thinner beam patterns, in MIMO radar the property of NLA is exploited to get more distinct virtual array elements so as to improve pa- rameter identifiability, which means the maximum number of targets that can be uniquely identified by the radar. A class of NLA called minimum redundancy linear array （MRLA） is employed and a new method to construct large MRLAs is descrihed. The numerical results verify that compared to uniform linear array （ULA） MIMO radars, NLA MIMO radars can retain the same parameter identifiability with fewer physical antennas and achieve larger aperture length and lower Cramer-Rao bound with the same number of the physical antennas.

High temperature and high pressure rheological properties of high-density water-based drilling fluids for deep wells

To maintain tight control over rheological properties of high-density water-based drilling fluids, it is essential to understand the factors influencing the theology of water-based drilling fluids. This paper examines temperature effects on the rheological properties of two types of high-density water-based drilling fluids （fresh water-based and brine-based） under high temperature and high pressure （HTHP） with a Fann 50SL rheometer. On the basis of the water-based drilling fluid systems formulated in laboratory, this paper mainly describes the influences of different types and concentration of clay, the content of a colloid stabilizer named GHJ-1 and fluid density on the rheological parameters such as viscosity and shear stress. In addition, the effects of aging temperature and aging time of the drilling fluid on these parameters were also examined. Clay content and proportions for different densities of brine-based fluids were recommended to effectively regulate the rheological properties. Four theological models, the Bingham, power law, Casson and H-B models, were employed to fit the rheological parameters. It turns out that the H-B model was the best one to describe the rheological properties of the high-density drilling fluid under HTHP conditions and power law model produced the worst fit. In addition, a new mathematical model that describes the apparent viscosity as a function of temperature and pressure was established and has been applied on site.

Discrepancy of blood pressure between the brachial artery and radial artery

BACKGROUND:In this study,we attempted to find the relations between blood pressure(BP)measured on the brachial artery(bBP) and BP assessed on the radial artery(rBP) in the right arm.METHODS:Three hundred and fifteen patients were enrolled in this study.Those who had peripheral vascular disease,wounds of arm skin or subcutaneous tissue infection were excluded.After a 15-minute equilibration and stabilization period after inducation of anesthesia,three bBP and rBP records were obtained sequentially using an oscillometric device with an adult cuff and infant cuff,respectively.Order for each BP was randomized.RESULTS:The bBP was significantly lower than the rBP(P<0.05).The difference between the two values varied from 13 to 18 mmHg in systolic BP(SBP),diastolic BP(DBP) and mean blood pressure(MAP) respectively.And the rBP was positively correlated with the bBP(r=0.872,0.754,0.765;P<0.001,<0.001,<0.001;SBP,DBP,MAP,respectively).CONCLUSION:The bBP value can be evaluated by the noninvasive measurements of rBP using an appropriate cuff in clinical practice.

Temperature Compensation Algorithm for Hydraulic System Pressure Control

In this paper the control mechanism of solenoid valve is analyzed,which shows the solenoid valve control is actually the control of coil current.The response characteristic of coil current is related to coil inductance and resistance.The coil resistance is influenced greatly by the ambient temperature and the self-heating of coil,which affects the control precision of coil current.First,considering the heat dissipation mode of coil,the coil temperature model is established from the perspective of heat conduction,and a temperature compensation algorithm for hydraulic system pressure control is put forward.Then the hardware-in-the-loop testbed is set up by using the dSPACE platform,carrying out wheel cylinder pressurization tests with inlet valve fully opened at-40℃ and 20℃,and testing the actual pressure of wheel cylinder with the target pressures at-40℃ and 6 000 kPa/s(pressurization rate).The results show that the pressure control temperature compensation algorithm proposed in this paper accurately corrects the influence of resistance temperature drift on the response accuracy of wheel cylinder pressure.After the correction,the pressure difference is less than 500 kPa,which can meet the control accuracy requirements of solenoid valve,enriching the linear control characteristic of solenoid valve.

Estimation of earth pressure against retaining walls with different limited displacement modes based on elastic theory

The earth pressure acting on retaining walls due to creep and consolidation is under limited equilibrium conditions(limited displacement). Linear elastic constitutive theory can be applied to determine earth pressure distribution along retaining walls under limited displacement condition. In addition,tangent modulus in Duncan-Chang nonlinear elastic model was introduced to reflect the variations of soil modulus with confining pressure, and boundary strains were derived from Rankine active earth pressure, Rankine passive earth pressure, static earth pressure and principal stress direction deflection.According to the above four boundary strains, earth pressure on retaining walls was divided into five state zones. By comparing the calculation results obtained from the equations proposed in this paper with those of experimental tests, the following conclusions can be drawn: earth pressure distribution was always nonlinear along retaining walls for translation displacement(T mode), rotation displacement around wall base(RB mode), and translation + rotation displacement around wall base(RBT mode). Also,calculated earth pressure distributions along with the depth of wall were found to be consistent with measured values under three displacement modes.Additionally, a parametric study was carried out to evaluate the effects of internal friction angle and backfill soil cohesion on earth pressure. It could be seen from the above series of studies that the earth pressure equations derived in this work could be well applied in practical engineering in designing retaining walls.

Large-scale edge waves generated by a moving atmospheric pressure

Long waves generated by a moving atmospheric pressure distribution, associated with a storm, in coastal region are investigated numerically. For simplicity the moving atmospheric pressure is assumed to be moving only in the alongshore direction and the beach slope is assumed to be a constant in the on-offshore direction. By solving the linear shallow water equations we obtain numerical solutions for a wide range of physical parameters, including storm size （2a）, storm speed （U）, and beach slope （a）. Based on the numerical results, it is determined that edge wave packets are generated if the storm speed is equal to or greater than the critical velocity, Ucr, which is defined as the phase speed of the fundamental edge wave mode whose wavelength is scaled by the width of the storm size. The length and the location of the positively moving edge wave packet is roughly Ut/2 〈 y 〈 Ut, where y is in the alongshore direction and t is the time. Once the edge wave packet is generated, the wavelength is the same as that of the fundamental edge wave mode corresponding to the storm speed and is independent of the storm size, which can, however, affect the wave amplitude. When the storm speed is less than the critical velocity, the primary surface signature is a depression directly correlated to the atmospheric pressure distribution.

Assessing the Association between Heart Attack, High Blood Pressure, and Heart Disease Mortality Rates and Particulate Matter and Socioeconomic Status Using Multivariate Geostatistical Model

This study addresses the public concerns of potential adverse health effects from ambient fine particulate matter as well as socioeconomic factors. Heart attack, high blood pressure, and heart disease mortality rates were investigated against fine particulate matter and socioeconomic status, for all counties in the United States in 2013. Multivariate multiple regressions as well as multivariate geostatistical predictions show that these are significant factors towards assessing the causal inferences between exposure to air pollution and socioeconomic status and the three mortality rates.

Dynamic calibration method of capacitive pressure measuring device

This paper presents working principle,structure and a dynamic calibration method of capacitive pressure measuring device.Using this method,placing calibrated capacitive electronic pressure measuring device and three standard sensors in simulation chamber pressure generator is proper and the data generated by them are analyzed and compared.This calibration method realizes dynamic calibration of capacitive electronic pressure measuring device under actual working pressure;pressure signal and frequency spectrum are analyzed.The experimental results show that simulation chamber pressure calibration method is feasible.

Radial Basis Approximations Based BEMD for Enhancement of Non-Uniform Illumination Images

An image can be degraded due to many environmental factors like foggy or hazy weather,low light conditions,extra light conditions etc.Image captured under the poor light conditions is generally known as non-uniform illumination image.Non-uniform illumination hides some important information present in an image during the image capture Also,it degrades the visual quality of image which generates the need for enhancement of such images.Various techniques have been present in literature for the enhancement of such type of images.In this paper,a novel architecture has been proposed for enhancement of poor illumination images which uses radial basis approximations based BEMD(Bi-dimensional Empirical Mode Decomposition).The enhancement algorithm is applied on intensity and saturation components of image.Firstly,intensity component has been decomposed into various bi-dimensional intrinsic mode function and residue by using sifting algorithm.Secondly,some linear transformations techniques have been applied on various bidimensional intrinsic modes obtained and residue and further on joining the transformed modes with residue,enhanced intensity component is obtained.Saturation part of an image is then enhanced in accordance to the enhanced intensity component.Final enhanced image can be obtained by joining the hue,enhanced intensity and enhanced saturation parts of the given image.The proposed algorithm will not only give the visual pleasant image but maintains the naturalness of image also.