Rate transient analysis methods for water-producing gas wells in tight reservoirs with mobile water

Tight gas reservoirs with mobile water exhibit multi-phase flow and high stress sensitivity.Accurately analyzing the reservoir and well parameters using conventional single-phase rate transient analysis methods proves challenging.This study introduces novel rate transient analysis methods incorporating evaluation processes based on the conventional flowing material balance method and the Blasingame type-curve method to examine fractured gas wells producing water.By positing a gas-water two-phase equivalent homogenous phase that considers characteristics of mobile water,gas,and high stress sensitivity,the conventional single-phase rate transient analysis methods can be applied by integrating the phase's characteristics and defining the phase's normalized parameters and material balance pseudotime.The rate transient analysis methods based on the equivalent homogenous phase can be used to quantitatively assess the parameters of wells and gas reservoirs,such as original gas-in-place,fracture half-length,reservoir permeability,and well drainage radius.This facilitates the analysis of production dynamics of fractured wells and well-controlled areas,subsequently aiding in locating residual gas and guiding the configuration of well patterns.The specific evaluation processes are detailed.Additionally,a numerical simulation mechanism model was constructed to verify the reliability of the developed methods.The methods introduced have been successfully implemented in field water-producing gas wells within tight gas reservoirs containing mobile water.

Well interference evaluation considering complex fracture networks through pressure and rate transient analysis in unconventional reservoirs

Severe well interference through complex fracture networks(CFNs)can be observed among multi-well pads in low permeability reservoirs.The well interference analysis between multi-fractured horizontal wells(MFHWs)is vitally important for reservoir effective development.Well interference has been historically investigated by pressure transient analysis,while it has shown that rate transient analysis has great potential in well interference diagnosis.However,the impact of complex fracture networks(CFNs)on rate transient behavior of parent well and child well in unconventional reservoirs is still not clear.To further investigate,this paper develops an integrated approach combining pressure and rate transient analysis for well interference diagnosis considering CFNs.To perform multi-well simulation considering CFNs,non-intrusive embedded discrete fracture model approach was applied for coupling fracture with reservoir models.The impact of CFN including natural fractures and frac-hits on pressure and rate transient behavior in multi-well system was investigated.On a logelog plot,interference flow and compound linear flow are two new flow regimes caused by nearby producers.When both NFs and frac-hits are present in the reservoir,frac-hits have a greater impact on well#1 which contains frac-hits,and NFs have greater impact on well#3 which does not have frac-hits.For all well producing circumstances,it might be challenging to see divergence during pseudosteady state flow brought on by frac-hits on the logelog plot.Besides,when NFs occur,reservoir depletion becomes noticeable in comparison to frac-hits in pressure distribution.Application of this integrated approach demonstrates that it works well to characterize the well interference among different multi-fractured horizontal wells in a well pad.Better reservoir evaluation can be acquired based on the new features observed in the novel model,demonstrating the practicability of the proposed approach.The findings of this study can help for better evaluating well interference degree in multi-well systems combing PTA and RTA,which can reduce the uncertainty and improve the accuracy of the well interference analysis based on both field pressure and rate data.

Transient analysis of 1D inhomogeneous media by dynamic inhomogeneous finite element method

The dynamic inhomogeneous finite element method is studied for use in the transient analysis of one dimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based on the shape function. In order to research the advantages of this method, it is compared with the general finite element method. A linear bar element is chosen for the discretization tests of material parameters with two fictitious distributions. And, a numerical example is solved to observe the differences in the results between these two methods. Some characteristics of the dynamic inhomogeneous finite element method that demonstrate its advantages are obtained through comparison with the general finite element method. It is found that the method can be used to solve elastic wave motion problems with a large element scale and a large number of iteration steps.

Transient analysis and optimization of passive residual heat removal heat exchanger in advanced nuclear power plant

The transient performance and optimization of a passive residual heat removal heat exchanger(PRHR HX)were investigated.First,a calculation method was developed for predicting the heat transfer of the PRHR HX.The calculation results were validated through comparisons with ROSA experimental data.The heat-transfer performance of the AP1000 PRHR HX in the initial period was predicted,and it satisfied the design requirements.Second,the distributions of the heat flux,tube-inside/outside heattransfer coefficients,and heat load for the AP1000 PRHR HX over 2000 s were examined.Third,an optimization study was conducted by adjusting the horizontal length and tube diameter.Their effects on the four main heat-transfer parameters and the heat-transfer area were analyzed.Furthermore,the influence of the initial in-containment refueling water storage tank(IRWST)temperature was investigated using an established simulation procedure.The results indicated that it significantly affected the trends of the IRWST temperature and reactor outlet temperature.Finally,the minimum required flow rates over time to maintain the reactor outlet temperature at the safety line were determined for different start-up times.The trends of the minimum required flow rate and the peak flow rate were analyzed.

A review of pressure transient analysis in reservoirs with natural fractures,vugs and/or caves

A review of the pressure transient analysis of flow in reservoirs having natural fractures,vugs and/or caves is presented to provide an insight into how much knowledge has been acquired about this phenomenon and to highlight the gaps still open for further research.A comparison-based approach is adopted which involved the review of works by several authors and identifying the limiting assumptions,model restrictions and applicability.Pressure transient analysis provides information to aid the identification of important features of reservoirs.It also provides an explanation to complex reservoir pressuredependent variations which have led to improved understanding and optimization of the reservoir dynamics.Pressure transient analysis techniques,however,have limitations as not all its models find application in naturally fractured and vuggy reservoirs as the flow dynamics differ considerably.Pollard’s model presented in 1953 provided the foundation for existing pressure transient analysis in these types of reservoirs,and since then,several authors have modified this basic model and come up with more accurate models to characterize the dynamic pressure behavior in reservoirs with natural fractures,vugs and/or caves,with most having inherent limitations.This paper summarizes what has been done,what knowledge is considered established and the gaps left to be researched on.

Transient analysis on surface heated piezoelectric semiconductor plate lying on rigid substrate

Based on the thermo-electro-elastic coupling theory,the mathematical model for a surface heated piezoelectric semiconductor(PS)plate is developed in the time domain.Applying the direct and inverse Laplace transformations to the established model,the mechanical and electrical responses are investigated.The comparison between the analytical solution and the finite element method(FEM)is conducted,which illustrates the validity of the derivation.The calculated results show that the maximum values of the mechanical and electrical fields appear at the heating surface.Importantly,the perturbation carriers tend to concentrate in the zone near the heating surface under the given boundary conditions.It can also be observed that the heating induced elastic wave leads to jumps for the electric potential and perturbation carrier density at the wavefront.When the thermal relaxation time is introduced,all the field quantities become smaller because of the thermal lagging effect.Meanwhile,it can be found that the thermal relaxation time can describe the smooth variation at the jump position.Besides,for a plate with P-N junction,the effect of the interface position on the electrical response is studied.The effects of the initial carrier density on the electrical properties are discussed in detail.The conclusions in this article can be the guidance for the design of PS devices serving in thermal environment.

Maximizing the Benefit of Rate Transient Analysis for Gas Condensate Reservoirs

In recent years,many trials have been made to use the Rate Transient Analysis(RTA)techniques as a method to describe the gas condensate reservoirs.The problem with using these techniques is the multi-phase behavior of the gas condensate reservoirs.Therefore,the Pressure Transient Analysis(PTA)is commonly used in this case to analyze the reservoir parameters.In this paper,we are going to compare the results of both PTA and RTA of three wells in gas condensate reservoirs.The comparison showed a great match between the results of the two mentioned techniques for the first time using a reference GOR of 75,000 SCF/STB.Therefore,we concluded that we could depend on RTA instead of PTA to spare the cost associated with the PTA in the gas condensate reservoirs.

An isogeometric approach to static and transient analysis of fluid-infiltrated porous metal foam piezoelectric nanoplates with flexoelectric effects and variable nonlocal parameters

In this work,a novel refined higher-order shear deformation plate theory is integrated with nonlocal elasticity theory for analyzing the free vibration,bending,and transient behaviors of fluid-infiltrated porous metal foam piezoelectric nanoplates resting on Pasternak elastic foundation with flexoelectric effects.Isogeometric analysis(IGA)and the Navier solution are applied to the problem.The innovation in the present study is that the influence of the in-plane variation of the nonlocal parameter on the free and forced vibration of the piezoelectric nanoplates is investigated for the first time.The nonlocal parameter and material characteristics are assumed to be material-dependent and vary gradually over the thickness of structures.Based on Hamilton’s principle,equations of motion are built,then the IGA approach combined with the Navier solution is used to analyze the static and dynamic response of the nanoplate.Lastly,we investigate the effects of the porosity coefficients,flexoelectric parameters,elastic stiffness,thickness,and variation of the nonlocal parameters on the mechanical behaviors of the rectangular and elliptical piezoelectric nanoplates.

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.

Preliminary safety analysis for heavy water-moderated molten salt reactor

The heavy water-moderated molten salt reactor(HWMSR)is a newly proposed reactor concept,in which heavy water is adopted as the moderator and molten salt dissolved with fissile and fertile elements is used as the fuel.Issues arising from graphite in traditional molten salt reactors,including the positive temperature coefficient and management of highly radio-active spent graphite waste,can be addressed using the HWMSR.Until now,research on the HWMSR has been centered on the core design and nuclear fuel cycle to explore the viability of the HWMSR and its advantages in fuel utilization.However,the core safety of the HWMSR has not been extensively studied.Therefore,we evaluate typical accidents in a small modular HWMSR,including fuel salt inlet temperature overcooling and overheating accidents,fuel salt inlet flow rate decrease,heavy water inlet temperature overcooling accidents,and heavy water inlet mass flow rate decrease accidents,based on a neutronics and thermal-hydraulics coupled code.The results demonstrated that the core maintained safety during the investigated accidents.

A Transient-Pressure-Based Numerical Approach for Interlayer Identification in Sand Reservoirs

Almost all sandstone reservoirs contain interlayers. The identification and characterization of these interlayers iscritical for minimizing the uncertainty associated with oilfield development and improving oil and gas recovery.Identifying interlayers outside wells using identification methods based on logging data and machine learning isdifficult and seismic-based identification techniques are expensive. Herein, a numerical model based on seepageand well-testing theories is introduced to identify interlayers using transient pressure data. The proposed modelrelies on the open-source MATLAB Reservoir Simulation Toolbox. The effects of the interlayer thickness, position,and width on the pressure response are thoroughly investigated. A procedure for inverting interlayer parametersin the reservoir using the bottom-hole pressure is also proposed. This method uses only transient pressuredata during well testing and can effectively identify the interlayer distribution near the wellbore at an extremelylow cost. The reliability of the model is verified using effective oilfield examples.

PRESSURE TRANSIENT ANALYSIS OF HETEROGENOUS RESERVOIRS WITH IMPERMEABILITY BARRIER USING PERTURBATION BOUNDARY ELEMENT METHOD

The transient flow mathematical model of arbitrary shaped heterogeneous reservoirs with impermeability barrier is proposed in this paper. In order to establish this model, the perturbation method is employed and the solution of model is expanded into a series in powers of perturbation parameter. By using the Boundary Element Method (BEM) and Duhamel principle, wellbore pressure with effects of skins and wellbore storage is obtained. The type curves are plotted and analyzed considering effects of heterogeneity, arbitrary shape and impermeable barriers. Finally, the results obtained by perturbation boundary element method is compared with the analytical solution and is available for the transient pressure analysis of arbitrary shaped reservoirs.

Dual-porosity model of rate transient analysis for horizontal well in tight gas reservoirs with consideration of threshold pressure gradient

Most researches of the threshold pressure gradient in tight gas reservoirs are experimental and mainly focus on the transient pressure response, without paying much attention to the transient rate decline. This paper establishes a dual-porosity rate transient decline model for the horizontal well with consideration of the threshold pressure gradient, which represents the non-Darcy flow in a fracture system. The solution is obtained by employing the Laplace transform and the orthogonal transform. The bi-logarithmic type curves of the dimensionless production rate and derivative are plotted by the Stehfest numerical inversion method. Seven different flow regimes are identified and the effects of the influence factors such as the threshold pressure gradient, the elastic storativity ratio, and the cross flow coefficient are discussed. The presented research could interpret the production behavior more accurately and effectively for tight gas reservoirs.

On the transient models of the VITAS code:applications to the C5G7-TD pin-resolved benchmark problem

This article describes the transient models of the neutronics code VITAS that are used for solving time-dependent,pinresolved neutron transport equations.VITAS uses the stiffness confinement method(SCM)for temporal discretization to transform the transient equation into the corresponding transient eigenvalue problem(TEVP).To solve the pin-resolved TEVP,VITAS uses a heterogeneous variational nodal method(VNM).The spatial flux is approximated at each Cartesian node using finite elements in the x-y plane and orthogonal polynomials along the z-axis.Angular discretization utilizes the even-parity integral approach at the nodes and spherical harmonic expansions at the interfaces.To further lower the computational cost,a predictor–corrector quasi-static SCM(PCQ-SCM)was developed.Within the VNM framework,computational models for the adjoint neutron flux and kinetic parameters are presented.The direct-SCM and PCQ-SCM were implemented in VITAS and verified using the two-dimensional(2D)and three-dimensional(3D)exercises on the OECD/NEA C5G7-TD benchmark.In the 2D and 3D problems,the discrepancy between the direct-SCM solver’s results and those reported by MPACT and PANDAS-MOC was under 0.97%and 1.57%,respectively.In addition,numerical studies comparing the PCQ-SCM solver to the direct-SCM solver demonstrated that the PCQ-SCM enabled substantially larger time steps,thereby reducing the computational cost 100-fold,without compromising numerical accuracy.

Transient Squeal Analysis of a Non Steady State Manoeuvre

Brake squeal is one of the main NVH （vibration harshness） challenges in the brake development of passenger cars. The conflict of goals in the development process and the late testability leads to the need of a deeper basic understanding of the squeal phenomenon and definition of design rules. On the other hand, brake squeal is still a very interesting field of research also for the universities because of its combination of different fundamentals, such as friction and stability behaviour of systems with local nonlinearities. Major nonlinearities of the brake system are the joints, especially the contact areas formed by the oscillating brake pad and the caliper. The state-of-the-art calculation method, which still is the ＂complex eigenvalue analysis＂, linearizes these joints, hence, neglecting its nonlinear influence in the stability analysis. Vehicle and bench experiments show that special driving manoeuvres like parking, where the brake pad often leaves the steady state, are likely causing brake squeal. The system in these manoeuvres sometimes behaves opposed to the linearized stability analysis, indicating a limit cycle beyond the Hopf point. Therefore, these states must be investigated more closely. This paper investigates the nonlinear influence of the pad caliper joint in a fixed brake caliper, also called abutment. Bench tests with pressure foils at the abutment of the brake caliper and mode shape analysis were done and a simple FE （finite element） model for a transient simulation is proposed. It is shown that the joint activity varies with driving manoeuvres, leading to different stability behaviours and limiting cycle amplitudes.

A Transient Multidimensional CFD Approach to the Analysis of a Control Valve Using Non-Newtonian Fluids

In this paper the flow through a control directional valve is studied by means of a CFD （computational fluid-dynamics） analysis under transient operating conditions. The mesh motion is resolved on a time basis as a function of the external actuation system In the analysis, an open source fluid-dynamics code is used and both cavitation and turbulence are accounted for in the modeling. Moreover, the numerical model of the working fluid is modified in order to account also for the non-Newtonian fluids. The effects of the shear rate on the shear stress are accounted for both by using experimental measurements and correlations available in literature, such as the Herschel-Bulkley model. The analysis determines the performance of the control directional valve under different operating conditions when using either Newtonian or non-Newtonian fluids. In particular, the discharge coefficient, the recirculating regions, the flow acceleration angle and the pressure and velocity fields are investigated.

Transient Temperature Analysis for Industrial AC Arc Furnace Bottom

Heat losses from the furnaces depend on the design and size. The surface heat loss from the bottom of an industrial AC electric arc furnace (EAF) possesses an important fraction of overall losses. So in this study the transient temperature variation at the bottom of the EAF was investigated. The transient temperature analysis was carried out using MATLAB computer program. T=T(r, t) for different bottom lining layers was depicted.

Transient thermal analysis as measurement method for IC package structural integrity

Practices of IC package reliability testing are reviewed briefly, and the application of transient thermal analysis is examined in great depth. For the design of light sources based on light emitting diode （LED） efficient and accurate reliability testing is required to realize the potential lifetimes of 105 h. Transient thermal analysis is a standard method to determine the transient thermal impedance of semiconductor devices, e.g. power electronics and LEDs. The temperature of the semiconductor junctions is assessed by time-resolved measurement of their forward voltage （Vf）. The thermal path in the IC package is resolved by the transient technique in the time domain. This enables analyzing the structural integrity of the semiconductor package. However, to evaluate thermal resistance, one must also measure the dissipated energy of the device （i.e., the thermal load） and the k-factor. This is time consuming, and measurement errors reduce the accuracy. To overcome these limitations, an innovative approach, the relative thermal resistance method, was developed to reduce the measurement effort, increase accuracy and enable automatic data evaluation. This new way of evaluating data simplifies the thermal transient analysis by eliminating measurement of the k-factor and thermal load, i.e. measurement of the lumen flux for LEDs, by normalizing the transient Vf data. This is especially advantageous for reliability testing where changes in the thermal path, like cracks and delaminations, can be determined without measuring the k-factor and thermal load. Different failure modes can be separated in the time domain. The sensitivity of the method is demonstrated by its application to high- power white InGaN LEDs. For detailed analysis and identification of the failure mode of the LED packages, the transient signals are simulated by time-resolved finite element （FE） simulations. Using the new approach, the transient thermal analysis is enhanced to a powerful tool for reliability investigation of semiconductor packages in accelerated lifetime tests and for inline inspection. This enables automatic data analysis of the transient thermal data required for processing a large amount of data in production and reliability testing. Based on the method, the integrity of LED packages can be tested by inline, outgoing inspection and the lifetime prediction of the products is improved.

An Optimal DF Based Method for Transient Stability Analysis

The effect of energy on the natural environment has become increasingly severe as human consumption of fossil energy has increased.The capacity of the synchronous generators to keep working without losing synchronization when the system is exposed to severe faults such as short circuits is referred to as the power system’s transient stability.As the power system’s safe and stable operation and mechanism of action become more complicated,higher demands for accurate and rapid power system transient stability analysis are made.Current methods for analyzing transient stability are less accurate because they do not account formisclassification of unstable samples.As a result,this paper proposes a novel approach for analyzing transient stability.The key concept is to use deep forest(DF)and a neighborhood rough reduction approach together.Using the neighborhood rough sets,the original feature space is obtained by creating many optimal feature subsets at various granularity levels.Then,by deploying the DF cascade structure,the mapping connection between the transient stability state and the features is reinforced.The weighted voting technique is used in the learning process to increase the classification accuracy of unstable samples.When contrasted to current methods,simulation results indicate that the proposed approach outperforms them.

An analysis method of injection and production dynamic transient flow in a gas field storage facility

A dynamic transient flow analysis method considering complex factors such as the cyclic injection and production history in a gas field storage facility was established in view of the limitations of the existing methods for transient flow analysis and the characteristics of the injection-production operation of strongly heterogeneous gas reservoirs, and the corresponding theoretical charts were drawn. In addition, an injection-production dynamic transient flow analysis model named "three points and two stages" suitable for an underground gas storage(UGS) well with alternate working conditions was proposed. The "three points" refer to three time points during cyclic injection and production, namely, the starting point of gas injection for UGS construction, the beginning and ending points of the injection-production analysis stage;and the "two stages" refer to historical flow stage and injection-production analysis stage. The study shows that the dimensionless pseudo-pressure and dimensionless pseudo-pressure integral curves of UGS well flex downward in the early stage of the injection and production process, and the dimensionless pseudo-pressure integral derivative curve is convex during the gas production period and concave during the gas injection period, and the curves under different flow histories have atypical features. The new method present in this paper can analyze transient flow of UGS accurately. The application of this method to typical wells in Hutubi gas storage shows that the new method can fit the pressure history accurately, and obtain reliable parameters and results.