On the analytical solution of transient friction in channel flows

The transient friction in channel mean flows is the sum of two contributions,i.e.,the underlying laminar flow(ULF)and the purely turbulent component(PTC),and the contributions are analyzed separately by theoretical experiments.It is found that,the transient friction may be higher or remarkably lower than that in equal-Reynolds number steady-state flows.The universal time constant for plane-parallel laminar flows is reported,and the role of the time constant in a turbulent mean flow is examined.It is shown that the time constant is related to the turbulence's frozen time.Finally,a study of the logarithmic layer during the transient flow is accomplished,which shows that the logarithmic layer is destroyed.

Godunov-type solutions for gas-liquid two-phase transient flows with gas release effects

The gas-liquid two-phase homogenous flow has been extensively investigated without the effect of gas release.However,the dissolved gas will release when internal water pressure drops below saturation pressure during hydraulic transients.This results in inaccuracy or even invalidity of the existing model for homogenous flows,especially for the reproduction of two-phase mass transfer processes.To address this problem,this paper couples the gas release model with conservation equations of homogenous flows,which are numerically solved by the second-order Godunov-type scheme(GTS).Specifically,a virtual-cell method is adopted at system boundaries to achieve the same second-order accuracy as interior cells,which is realized by the monotonic upwind scheme for conservation laws(MUSCL-Hancock scheme).Simulated pressure curves by the proposed model are compared with a series of analytical,numerical and experimental results.It indicates that the proposed model with gas release effects reproduces actual pressure responses most accurately,with minimum relative error and root mean squared error compared with experimental data.Moreover,the gas release leads to dynamic synchronous fluctuations of void fraction,wave speed and pressure head,including the opposite trends of void fraction and pressure,and higher void fraction leading to greater wave speed depression.Furthermore,sensitivity analysis is concluded with recommended Courant number,and different gas release effects in different initial void fractions.Present research increases the basic understanding of two-phase mass transfer processes and their implications for hydraulic transients.

A transient production prediction method for tight condensate gas wells with multiphase flow

Considering the phase behaviors in condensate gas reservoirs and the oil-gas two-phase linear flow and boundary-dominated flow in the reservoir,a method for predicting the relationship between oil saturation and pressure in the full-path of tight condensate gas well is proposed,and a model for predicting the transient production from tight condensate gas wells with multiphase flow is established.The research indicates that the relationship curve between condensate oil saturation and pressure is crucial for calculating the pseudo-pressure.In the early stage of production or in areas far from the wellbore with high reservoir pressure,the condensate oil saturation can be calculated using early-stage production dynamic data through material balance models.In the late stage of production or in areas close to the wellbore with low reservoir pressure,the condensate oil saturation can be calculated using the data of constant composition expansion test.In the middle stages of production or when reservoir pressure is at an intermediate level,the data obtained from the previous two stages can be interpolated to form a complete full-path relationship curve between oil saturation and pressure.Through simulation and field application,the new method is verified to be reliable and practical.It can be applied for prediction of middle-stage and late-stage production of tight condensate gas wells and assessment of single-well recoverable reserves.

A semi-analytical rate-transient analysis model for light oil reservoirs exhibiting reservoir heterogeneity and multiphase flow

Rate-transient analysis(RTA)has been widely applied to extract estimates of reservoir/hydraulic fracture properties.However,the majority of RTA techniques can lead to misdiagnosis of reservoir/fracture information when the reservoir exhibits reservoir heterogeneity and multiphase flow simultaneously.This work proposes a practical-yet-rigorous method to decouple the effects of reservoir heterogeneity and multiphase flow during TLF,and improve the evaluation of reservoir/fracture properties.A new,general,semi-analytical model is proposed that explicitly accounts for multiphase flow,fractalbased reservoir heterogeneity,anomalous diffusion,and pressure-dependent fluid properties.This is achieved by introducing a new Boltzmann-type transformation,the exponent of which includes reservoir heterogeneity and anomalous diffusion.In order to decouple the effects of reservoir heterogeneity and multiphase flow during TLF,the modified Boltzmann variable allows the conversion of three partial differential equations(PDE's)(i.e.,oil,gas and water diffusion equations)into ordinary differential equations(ODE's)that are easily solved using the Runge-Kutta(RK)method.A modified time-power-law plot is also proposed to estimate the reservoir and fracture properties,recognizing that the classical square-root-of-time-plot is no longer valid when various reservoir complexities are exhibited simultaneously.Using the slope of the straight line on the modified time-power-law plot,the linear flow parameter can be estimated with more confidence.Moreover,because of the new Boltzmann-type transformation,reservoir and fracture properties can be derived more efficiently without the need for defining complex pseudo-variable transformations.Using the new semi-analytical model,the effects of multiphase flow,reservoir heterogeneity and anomalous diffusion on rate-decline behavior are evaluated.For the case of approximately constant flowing pressure,multiphase flow impacts initial oil rate,which is a function of oil relative permeability and well flowing pressure.However,multiphase flow has a minor effect on the oil production decline exponent.Reservoir heterogeneity/anomalous diffusion affect both the initial oil production rate and production decline exponent.The production decline exponent constant is a function of reservoir heterogeneity/anomalous diffusion only.The practical significance of this work is the advancement of RTA techniques to allow for more complex reservoir scenarios,leading to more accurate production forecasting and better-informed capital planning.

Dynamic mode decomposition and reconstruction of transient cavitating flows around a Clark-Y hydrofoil

The transient cavitating flow around the Clark-Y hydrofoil is numerically investigated by the dynamic mode decomposition with criterion.Based on the ranking dominant modes,frequencies of the first four modes are in good accordance with those obtained by fast Fourier transform.Furthermore,the cavitating flow field is reconstructed by the first four modes,and the dominant flow features are well captured with the reconstructed error below 12%when compared to the simulated flow field.This paper offers a reference for observing and reconstructing the flow fields,and gives a novel insight into the transient cavitating flow features.

Integrated wellbore-reservoir-geomechanics modeling for enhanced interpretation of distributed fiber-optic strain sensing data in hydraulicfracture analysis

Fiber-optic distributed strain sensing(FO-DSS)has been successful in monitoring strain changes along horizontal wellbores in hydraulically fractured reservoirs.However,the mechanism driving the various FO-DSS responses associated with near-wellbore hydraulic fracture properties is still unclear.To address this knowledge gap,we use coupled wellbore-reservoir-geomechanics simulations to study measured strain-change behavior and infer hydraulic fracture characteristics.The crossflow among fractures is captured through explicit modeling of the transient wellbore flow.In addition,local grid refinement is applied to accurately capture strain changes along the fiber.A Base Case model was designed with four fractures of varying properties,simulating strain change signals when the production well is shut-in for 10 d after 240 d of production and reopened for 2 d.Strain-pressure plots for different fracture clusters were used to gain insights into inferring fracture properties using DSS data.When comparing the model with and without the wellbore,distinct strain change signals were observed,emphasizing the importance of incorporating the wellbore in FO-DSS modeling.The effects of fracture spacing and matrix permeability on strain change signals were thoroughly investigated.The results of our numerical study can improve the understanding of the relation between DSS signals and fracture hydraulic properties,thus maximizing the value of the dataset for fracture diagnostics and characterization.

Application of Computational Fluid Dynamics and Fluid Structure Interaction Techniques for Calculating the 3D Transient Flow of Journal Bearings Coupled with Rotor Systems

Journal bearings are important parts to keep the high dynamic performance of rotor machinery. Some methods have already been proposed to analysis the flow field of journal bearings, and in most of these methods simplified physical model and classic Reynolds equation are always applied. While the application of the general computational fluid dynamics （CFD）-fluid structure interaction （FSI） techniques is more beneficial for analysis of the fluid field in a journal bearing when more detailed solutions are needed. This paper deals with the quasi-coupling calculation of transient fluid dynamics of oil film in journal bearings and rotor dynamics with CFD-FSI techniques. The fluid dynamics of oil film is calculated by applying the so-called ＂dynamic mesh＂ technique. A new mesh movement approacb is presented while the dynamic mesh models provided by FLUENT are not suitable for the transient oil flow in journal bearings. The proposed mesh movement approach is based on the structured mesh. When the joumal moves, the movement distance of every grid in the flow field of bearing can be calculated, and then the update of the volume mesh can be handled automatically by user defined function （UDF）. The journal displacement at each time step is obtained by solving the moving equations of the rotor-bearing system under the known oil film force condition. A case study is carried out to calculate the locus of the journal center and pressure distribution of the journal in order to prove the feasibility of this method. The calculating results indicate that the proposed method can predict the transient flow field of a journal bearing in a rotor-bearing system where more realistic models are involved. The presented calculation method provides a basis for studying the nonlinear dynamic behavior of a general rotor-bearing system.

Transient simulation of a pump-turbine with misaligned guide vanes during turbine model start-up

Experimental studies of a model pump-turbine S-curve characteristics and its improvement by misaligned guide vanes （MGV） were extended to prototype pump turbine through 3-D transient flow simulations. The unsteady Reynolds-averaged Navier-Stokes equations with the SST turbulence model were used to model the transient flow within the entire flow passage of a reversible pump-turbine with and without misaligned guide vanes during turbine model start-up. The unstable S-curve and its improvement by using misaligned guide vane were verified by model test and simulation. The transient flow calculations were used to clarify the variations of pressure pulse and internal flow behavior in the entire flow passage. The use of misaligned guide vanes can eliminate the S-curve characteristics of a pump-turbine, and can significantly increase the pressure pulse amplitude in the entire flow passage and the runner radial forces during start-up. The MGV only decreased the pulse amplitude on the guide vane suction side when the rotating speed was less than 50% rated speed. The hydraulic reason is that the MGV dramatically changed the flow patterns inside the entire flow passage, and destroyed the symmetry of the flow distribution inside the guide vane and runner.

Influence of Blade Thickness on Transient Flow Characteristics of Centrifugal Slurry Pump with Semi-open Impeller

As the critical component, the impellers of the slurry pumps usually have blades of a large thickness. The increasing excretion coefficient of the blades affects the flow in the impeller resulting in a relatively higher hydraulic loss, which is rarely reported. In order to investigate the influence of blade thickness on the transient flow characteristics of a centrifugal slurry pump with a semi-open impeller, transient numerical simulations were carried out on six impellers, of which the meridional blade thickness from the leading edge to trailing edge varied from 5-10 mm, 5-15 mm, 5-20 mm, 10-10 mm, 10-15 mm, and 10-20 mm, respectively. Then, two of the six impellers, namely cases 4 and 6, were manufactured and experimentally tested for hydraulic performance to verify the simulation results. Results of these tests agreed reasonably well with those of the numerical simulation. The results demonstrate that when blade thickness increases, pressure fluctuations at the outlet of the impeller become severe. Moreover, the standard deviation of the relative velocity in the middle portion of the suction sides of the blades decreases and that at the outlet of the impeller increases. Thus, the amplitude of the impeller head pulsation for each case increases. Meanwhile, the distribution of the time-averaged relative flow angle becomes less uniform and decreases at the outlet of the impeller. Hence, as the impeUer blade thickness increases, the pump head drops rapidly and the maximum efficiency point is offset to a lower flow rate condition. As the thickness of blade trailing edge increases by 10 mm, the head of the pump drops by approximately 5 m, which is approximately 10 % of the original pump head. Futhermore, it is for the first time that the time-averaged relative flow angle is being considered for the analysis of transient flow in centrifugal pump. The presented work could be a useful guideline in engineering practice when designing a centrifugal slurry pump with thick impeller blades.

Lagrangian-based investigation of the transient flow structures around a pitching hydrofoil

The objective of this paper is to address the transient flow structures around a pitching hydrofoil by com- bining physical and numerical studies. In order to predict the dynamic behavior of the flow structure effectively, the Lagrangian coherent structures （LCS） defined by the ridges of the finite-time Lyapunov exponent （FTLE） are utilized under the framework of Navier-Stokes flow computations. In the numerical simulations, the k-w shear stress trans- port （SST） turbulence model, coupled with a two-equation F-Reo transition model, is used for the turbulence closure. Results are presented for a NACA66 hydrofoil undergoing slowly and rapidly pitching motions from 0° to 15° then back to 0° at a moderate Reynolds number Re = 7.5 × 105. The results reveal that the transient flow structures can be observed by the LCS method. For the slowly pitching case, it consists of five stages： quasi-steady and laminar, transition from laminar to turbulent, vortex development, large-scale vortex shedding, and reverting to laminar. The observation of LCS and Lagrangian particle tracers elucidates that the trailing edge vortex is nearly attached and stable during the vortex development stage and the interaction between the leading and trailing edge vortex caused by the adverse pres- sure gradient forces the vortexes to shed downstream during the large-scale vortex shedding stage, which corresponds to obvious fluctuations of the hydrodynamic response. For the rapidly pitching case, the inflection is hardly to be observed and the stall is delayed. The vortex formation, interaction, and shedding occurred once instead of being repeated three times, which is responsible for just one fluctuation in the hydrody- namic characteristics. The numerical results also show that the FTLE field has the potential to identify the transient flows, and the LCS can represent the divergence extent of infinite neighboring particles and capture the interface of the vortex region.

Transient fluid flow in the Binbei district of the Songliao Basin, China Evidence from apatite fission track thermochronology

The Songliao Basin is famous for the Daqing Oilfield, the biggest in China. However, no economic hydrocarbon reservoir has been found in the northeastern Binbei district. Its thermal history, which is of great importance for hydrocarbon generation and migration, is studied with apatite fission track （AFT） thermochronology. Samples with depositional ages of the late Cretaceous （-108-73 Ma） are analyzed. The AFT ages of the samples from reservoir rock （depositional age 〉 76.1 Ma） fall between the late Cretaceous （724-5 Ma） and the early Eocene （414-3 Ma） period, indicating their total annealing after deposition. In contrast, two samples from the main seals of the Qingshankou （depositional age 〉 89.3 Ma） and the Nenjiang Formation （depositional age 〉 73.0 Ma） are not annealed or partially annealed （AFT ages of 974-9 Ma and 704-4 Ma, respectively）. Because the maximum burial temperature （〈90 ℃） evidenced by low vitrinite reflectance （Ro〈0.7） is not high enough to account for the AFT total annealing （110-120 ℃）, the transient thermal effect arising from the syntectonic fluid flow between the late Cretaceous and the early Eocene is proposed. Transient thermal effects from fluid flow explains the indicated temperature discrepancies between the AFT thermometer and the Ro thermometer because the transient thermal effect from the fluid flow with a temperature high enough （110-120 ℃） to anneal the AFT thermometer does not last long enough （104-105 yrs.） for an enhancement of the Ro （minimum 106- 107 yrs. under the same temperature）. This indicates that dating thermal effect from fluid flow might be a new means to reconstruct the tectonic history. It also answers why the samples from the main seals are not annealed because the seals will prohibit fluid flow and supply good thermal insulation. The large-scale fluid flow in the Binbei district calls for a new idea to direct the hydrocarbon exploration.

Simulations of the Transient Flow Generated from a Started Flat Plate

Transient operations are commonly founded in fluid machineries such as the starting, stopping, and variations of rotor speeds, etc. Flow generated from a started fiat plate is of fundamental importance. Experiments have been done to observe the flow evolution in current researches. And in order to explore the flow in more detailed scale, some vortex methods with high resolution and other numerical methods were developed to solve various related problems by some researchers. But the promotion of vortex method to engineering application is rare due to its complexity and difficulty in specifying the boundary conditions. In order to build up a method of numerical study for such problems, a simplified model is built up with a flat plate. The development of two-dimensional viscous incompressible flow generated from an impulsively started and uniformly accelerated infinitesimally thin flat plate is simulated numerically. A dynamic mesh（DM） method based on the spring analogue and local remeshing is applied to realize the mesh motion caused by the started plate. Researches show that the mesh quality will decline under large grid shear force during the updating process. To conquer this problem, a region near the plate is separated to guarantee the mesh quality at location of interest which is the innovation of the present paper. All computations at least cover a period during which the plate translates 6 times its length. The simulated instantaneous velocity profiles, flow structures and drag coefficients under several Reynolds numbers （20 ≤ Re ≤ 126） and accelerations （20 m/s2≤ a ≤ 152 m/s2） are presented and compared with existing results in literatures. Comparisons are found to be satisfactory, confirming the validity of the current proposed method（region separated DM）. The proposed DM method is firstly used to study the transient flow generated from a started flat plate and can be used in further study of transient characteristics during transient operations of turbo machineries.

Numerical simulation of transient flow in horizontal drainage systems

A numerical simulation model based on the characteristic-based finite-difference method with a time-line interpolation scheme was developed for predicting transient free surface flow in horizontal drainage systems. The fundamental accuracy of the numerical model was first clarified by comparison with the experimental results for a single drainage pipe. Boundary conditions for junctions and bends, which are often encountered in drainage systems, were studied both experimentally and numerically. The numerical model was applied to an actual drainage system. Comparison with a full-scale model experiment indicates that the model can be used to accurately predict flow characteristics in actual drainage networks.

THE TRANSIENT ELLIPTIC FLOW OF POWER-LAW FLUID IN FRACTAL POROUS MEDIA

The steady oil production and pressure distribution formulae of vertically fractured well for power-law non-Newtonian fluid were derived on the basis of the elliptic flow model in fractal reservoirs. The corresponding transient flow in fractal reservoirs was studied by numerical differentiation method: the influence of fractal index to transient pressure of vertically fractured well was analyzed. Finally the approximate analytical solution of transient flow was given by average mass conservation law. The study shows that using elliptic flow method to analyze the flow of vertically fractured well is a simple method.

RULE OF TRANSIENT PHREATIC FLOW SUBJECTED TO VERTICAL AND HORIZONTAL SEEPAGE

In a semi-infinite aquifer bounded by a channel, a transient flow model is constructed for phreatic water subjected to vertical and horizontal seepage. Based on the first linearized Boussinesq equation, the analytical solution of the model is obtained by Laplace transform. Having proven the transformation between the analytical solution and some relevant classic formulas, suitable condition for each of these formulas is demonstrated. On the base of the solution, the variation of transient flow process caused by the variables, such as vertical infiltration intensity, fluctuation range of river stage, aquifer parameters such as transmissivity and specific yield, and the distance from calculating point to channel boundary, are analyzed quantitatively one by one. Lagging effect will happen to the time, when phreatic water gets its maximum fluctuation velocity, response to the varying of the variables stated above. The condition for some variables to form equivalent lagging effect is demonstrated. Corresponding to the mathematical charac teristics of the analytical solution, the physical implication and the fluctuation rule of groundwater level are discussed.

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.

Calculation of the Water Distribution Networks Based on the Theory of Slow Transient Flow

Urban water supply network is a modern urban survival and development of the infrastructure of a city,and its normal running conditions have important significance. The actual hydraulic process in the variableload water distribution networks can be treated as the slow transient flow which belongs to the unsteady flow. This paper analyzes the multi-loops network slow transient model based on graph theory,and the link flow matrix is treated as the variables of the discrete solution model to simulate the process of the slow transient flow in the network. With the simulation of hydraulic regime in an actual pipe network,the changing laws of the flow in the pipes,nodal hydraulic heads and other hydraulic factors with the passage of time are obtained. Since the transient processes offer much more information than a steady process,the slow transient theory is not only practical on analyzing the hydraulic condition of the network,but also on identifying hydraulic resistance coefficients of pipes and detecting the leakage in networks.

SECOND-MOMENT CLOSURE FOR MODELLING THE NEAR-WALL TURBULENCE IN 3D MEAN FLOWS

A second-moment closure for the near-wall turbulence is proposed. The limiting behaviour of this closure near a wall is consistent with that of the exact Reynolds-stress transport equations, and it converts asymptotically into a high- Reynolds-number closure remote from the wall. The closure is applied to a pressure- driven 3D transient channel flow. The predicted results are in fair agreement with the DNS data.

Numerical simulation on rotordynamic characteristics of annular seal under uniform and non-uniform flows

Currently, the flow field of annular seals disturbed by the circular whirl motion of rotors is usually solved using computational fluid dynamics(CFD) to evaluate the five rotordynamic coefficients. The simulations are based on the traditional quasi-steady method. In this work, an improved quasi-steady method along with the transient method was presented to compute the rotordynamic coefficients of a long seal. By comparisons with experimental data, the shortcomings of quasi-steady methods have been identified. Then, the effects of non-uniform incoming flow on seal dynamic coefficients were studied by transient simulations. Results indicate that the long seal has large cross stiffness k and direct mass M which are not good for rotor stability, while the transient method is more suitable for the long seal for its excellent performance in predicting M. When the incoming flow is non-uniform, the stiffness coefficients vary with the eccentric directions. Based on the rotordynamic coefficients under uniform incoming flow, the linearized fluid force formulas, which can consider the effects of non-uniform incoming flow, have been presented and can well explain the varying-stiffness phenomenon.

CALCULATION ON TWO-PHASE FLOW TRANSIENTS AND THEIR EXPERIMENTAL RESEARCH

From basic equations of gas-liquid, solid-liquid, solid-gas two-phase flow,the calculating method on flow transients of two-phase flow is developed by means of characteristicmethod. As one example, a gas-liquid flow transient is calculated and it agrees well with theexperimental result. It is shown that the method is satisfactory for engineering demand.