Effects of confining pressure and pore pressure on multipole borehole acoustic field in fluid-saturated porous media

In-situ stress is a common stress in the exploration and development of oil reservoirs. Therefore, it is of great significance to study the propagation characteristics of borehole acoustic waves in fluid-saturated porous media under stress.Based on the acoustoelastic theory of fluid-saturated porous media, the field equation of fluid-saturated porous media under the conditions of confining pressure and pore pressure and the acoustic field formula of multipole source excitation in open hole are given. The influences of pore pressure and confining pressure on guided waves of multipole borehole acoustic field in fluid-saturated porous media are investigated. The numerical results show that the phase velocity and excitation intensity of guided wave increase significantly under the confining pressure. For a given confining pressure, the phase velocity of the guided wave decreases with pore pressure increasing. The excitation intensity of guided wave increases at low frequency and then decreases at high frequency with pore pressure increasing, except for that of Stoneley wave which decreases in the whole frequency range. These results will help us get an insight into the influences of confining pressure and pore pressure on the acoustic field of multipole source in borehole around fluid-saturated porous media.

Finite Difference Approach on Magnetohydrodynamic Stratified Fluid Flow Past Vertically Accelerated Plate in Porous Media with Viscous Dissipation

This study intends to evaluate the influence of temperature stratification on an unsteady fluid flow past an accelerated vertical plate in the existence of viscous dissipation.It is assumed that the medium under study is a grey,non-scattered fluid that both fascinates and transmits radiation.The leading equations are discretized using the finite differencemethod(FDM).UsingMATLABsoftware,the impacts of flowfactors on flowfields are revealed with particular examples in graphs and a table.In this regard,FDM results show that the velocity and temperature gradients increase with an increase of Eckert number.Furthermore,tables of the data indicate the influence of flow-contributing factors on the skin friction coefficients,and Nusselt numbers.When comparing constant and variable flow regimes,the constant flow regime has greater values for the nondimensional skin friction coefficient.This research is both innovative and fascinating since it has the potential to expand our understanding of fluid dynamics and to improve many different sectors.

Evaluation of gas wettability and its effects on fluid distribution and fluid flow in porous media

The special gas wettability phenomenon of reservoir rocks has been recognized by more and more researchers.It has a significant effect on efficient development of unconventional reservoirs.First,based on the preferentially gas-covered ability and surface free energy changes,definition and evaluation methods have been established.Second,a method for altering rock wettability and its mechanisms have been studied,surface oriented phenomena of functional groups with low surface energy are the fundamental reason for gas wettability alteration of rock.Third,the effect of gas wettability on the surface energy,electrical properties and dilatability are investigated.Last,the effects of gas wettability on capillary pressure,oil/gas/water distribution and flow are investigated with capillary tubes and etchedglass network models.The gas wettability theory of reservoir rocks has been initially established,which provides theoretical support for the efficient production of unconventional reservoirs and has great significance.

Effects of rotation and magnetic field on the nonlinear peristaltic flow of a second-order fluid in an asymmetric channel through a porous medium

In this paper, the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically. The material is represented by the constitutive equations for a second-order fluid. Closed-form solutions under the consideration of long wavelength and low Reynolds number is presented. The analytical expressions for the pressure gradient, pressure rise, friction force, stream function, shear stress, and velocity are obtained in the physical domain. The effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of rotation, magnetic field, and porosity. The results indicate that the effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow are very pronounced in the phenomena.

A New Numerical Solution of Fluid Flow in Stratigraphic Porous Media

A new numerical technique based on a lattice-Boltzmann method is presented for analyzing the fluid flow in stratigraphic porous media near the earth's surface. The results obtained for the relations between porosity, pressure,and velocity satisfy well the requirements of stratigraphic statistics and hence are helpful for a further study of the evolution of fluid flow in stratigraphic media.

Enduring effect of permeability texture for enhancing accuracy and reducing uncertainty of reservoir fluid flow through porous media

Modeling reservoir permeability is one of the crucial tasks in reservoir simulation studies.Traditionally,it is done by kriging-based methods.More rigorous modeling of the permeability results in more reliable outputs of the reservoir models.Recently,a new category of geostatistical methods has been used for this purpose,namely multiple point statistics(MPS).By this new category of permeability modeling methods,one is able to predict the heterogeneity of the reservoir permeability as a continuous variable.These methods consider the direction of property variation in addition to the distances of known locations of the property.In this study,the reservoir performance of a modified version of the SPE 10 solution project as a pioneer case is used for investigating the efficiency of these methods and paralleling them with the kriging-based one.In this way,the permeability texture concept is introduced by applying some MPS methods.This study is accomplished in the conditions of real reservoir dimensions and velocities for the whole reservoir life.A continuous training image is used as the input of calculation for the permeability modeling.The results show that the detailed permeability of the reservoir as a continuous variable makes the reservoir simulation show the same fluid front movement and flooding behavior of the reservoir similar to the reference case with the same permeability heterogeneity.Some MPS methods enable the reservoir simulation to reproduce the fluid flow complexities such as bypassing and oil trapping during water flooding similar to the reference case.Accordingly,total oil production is predicted with higher accuracy and lower uncertainty.All studied cases are identical except for the permeability texture.Even histograms and variograms of permeabilities for the studied reservoir are quite similar,but the performance of the reservoir shows that kriging-based method results have slightly less accuracy than some MPS methods.Meanwhile,it results in lower uncertainty in outputs for this water flooding case performance.

MATHEMATICAL MODEL OF TWO-PHASE FLUID NONLINEAR FLOW IN LOW-PERMEABILITY POROUS MEDIA WITH APPLICATIONS

A mathematical model of two-phase fluid nonlinear flow in the direction of normal of ellipse through low-permeability porous media was established according to a nonlinear flow law expressed in a continuous function with three parameters, a mass conservation law and a concept of turbulent ellipses. A solution to the model was obtained by using a finite difference method and an extrapolation method. Formulas of calculating development index not only before but also after water breaks through an oil well in the condition of two-phase fluid nonlinear flow in the media were derived. An example was discussed. Water saturation distribution was presented. The moving law of drainage front was found. Laws of change of pressure difference with time were recognized. Results show that there is much difference of water saturation distribution between nonlinear flow and linear flow; that drainage front by water moves faster, water breaks through sooner and the index gets worse because of the nonlinear flow; and that dimensionless pressure difference gets larger at the same dimensionless time and difficulty of oil development becomes bigger by the nonlinear flow. Thus, it is necessary that influence of nonlinear flow on development indexes of the oil fields be taken into account. The results provide water-flooding development of the oilfields with scientific basis.

Review on the Development of Oil and Gas Flow in Underground Porous Media

Through reviewing the flow theory’s birth and development history in underground porous media and contrasting the mechanics of underground fluids and mechanics of viscous fluids, this paper points out the main factors, which affect the development of the theory on oil and gas porous flow. The development law and development route of the mechanics of fluids in porous media are also summarized in this paper.

Oscillatory squeeze flow through an Oldroyd-B fluid-saturated porous layer

This study deals with the analytical investigation of oscillatory squeeze film flow through a Brinkman viscoelastic Oldroyd-B fluid-saturated porous layer subject to two vertically harmonically oscillatory disks.The validity of the present proposed analytical solutions is first demonstrated for the Newtonian fluids when bothΛ_(1)andΛ_(2)tend to zero by comparison with the previous literature.Results demonstrate that an increase in the elasticity parameterΛ_(1)correlates with a rise in axial velocities,indicating that the relaxation timeΛ_(1)facilitates enhanced squeeze flow.In the case of squeeze film flow in porous layers,low oscillating frequencies exert minimal effects on axial velocities,independent of variations in the viscoelasticity parameterΛ_(1).However,at higher oscillating frequencies,axial velocities escalate with increasing the viscoelasticity parameterΛ_(1).Furthermore,the retardation timeΛ_(2)of the viscoelastic fluid shows no significant effect on the axial velocity,regardless of oscillating frequency changes in both pure fluids and porous layers.

Analytical solutions for dynamic pressures of coupling fluid-solid-porous medium due to P wave incidence

Wave reflection and refraction in layered media is a topic closely related to seismology,acoustics,geophysics and earthquake engineering.Analytical solutions for wave reflection and refraction coefficients in multi-layered media subjected to P wave incidence from the elastic half-space are derived in terms of displacement potentials.The system is composed of ideal fluid,porous medium,and underlying elastic solid.By numerical examples,the effects of porous medium and the incident wave angle on the dynamic pressures of ideal fluid are analyzed.The results show that the existence of the porous medium,especially in the partially saturated case,may significantly affect the dynamic pressures of the overlying fluid.

Analytical solution of a double moving boundary problem for nonlinear flows in one-dimensional semi-infinite long porous media with low permeability

Based on Huang＇s accurate tri-sectional nonlin- ear kinematic equation （1997）, a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external mov- ing boundary, which are different from the classical Stefan problem in heat conduction： The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transfor- mation, the nonlinear partial differential equation （PDE） sys- tem is transformed into a linear PDE system. Then an ana- lytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact an- alytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensi- tive effects of the dimensionless variable on the dimension- less pressure distribution and dimensionless pressure gradi- ent distribution become more serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensi- tive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient （TPG） has a great effect on the external moving boundary but has little effect on the internal moving boundary.

Flow characteristics and regime transition of aqueous foams in porous media over a wide range of quality,velocity,and surfactant concentration

Aqueous foam is broadly applicable to enhanced oil recovery(EOR).The rheology of foam as a function of foam quality,gas and liquid velocities,and surfactant concentration constitute the foundation of its application.The great variations of the above factors can affect the effectiveness of N2 foam in EOR continuously in complex formations,which is rarely involved in previous relevant studies.This paper presents an experimental study of foam flow in porous media by injecting pre-generated N2 foam into a sand pack under the conditions of considering a wide range of gas and liquid velocities and surfactant concentrations.The results show that in a wide range of gas and liquid velocities,the pressure gradient contours are L-shaped near the coordinate axes,but V-shaped in other regions.And the surfactant concentration is a strong factor influencing the trend of pressure gradient contours.Foam flow resistance is very sensitive to the surfactant concentration in both the high-and low-foam quality regime,especially when the surfactant concentration is less than CMC.The foam quality is an important variable to the flow resistance obtained.There exists a transition point from low-to high-quality regime in a particular flow system,where has the maximum flow resistance,the corresponding foam quality is called transition foam quality,which increases as the surfactant concentration increases.The results can add to our knowledge base of foam rheology in porous media,and can provide a strong basis for the field application of foams.

A lattice Boltzmann exploration of two-phase displacement in 2D porous media under various pressure boundary conditions

While experimental designs developed in recent decades have contributed to research on dynamic nonequilibrium effects in transient two-phase flow in porous media,this problem has been seldom investigated using direct numerical simulation(DNS).Only a few studies have sought to numerically solve Navier—Stokes equations with level-set(LS)or volume-of-fluid(VoF)methods,each of which has constraints in terms of meniscus dynamics for various flow velocities in the control volume(CV)domain.The Shan—Chen multiphase multicomponent lattice Boltzmann method(SC-LBM)has a fundamental mechanism to separate immiscible fluid phases in the density domain without these limitations.Therefore,this study applied it to explore two-phase displacement in a single representative elementary volume(REV)of two-dimensional(2D)porous media.As a continuation of a previous investigation into one-step inflow/outflow in 2D porous media,this work seeks to identify dynamic nonequilibrium effects on capillary pressure—saturation relationship(P_(c)—S)for quasi-steady-state flow and multistep inflow/outflow under various pressure boundary conditions.The simulation outcomes show that P_(c),S and specific interfacial area(a_(nw))had multistep-wise dynamic effects corresponding to the multistep-wise pressure boundary conditions.With finer adjustments to the increase in pressure over more steps,dynamic nonequilibrium effects were significantly alleviated and even finally disappeared to achieve quasisteady-state inflow/outflow conditions.Furthermore,triangular wave-formed pressure boundary conditions were applied in different periods to investigate dynamic nonequilibrium effects for hysteretical Pc—S.The results showed overshoot and undershoot of P_(c)to S in loops of the nonequilibrium hysteresis.In addition,the flow regimes of multistep-wise dynamic effects were analyzed in terms of Reynolds and capillary numbers(Re and Ca).The analysis of REV-scale flow regimes showed higher Re(1<Re<10)for more significant dynamic nonequilibrium effects.This indicates that inertia is critical for transient twophase flow in porous media under dynamic nonequilibrium conditions.

MHD Fluctuating Flow of Non-Newtonian Fluid through a Porous Medium Bounded by an Infinite Porous Plate

In present paper, an investigation has been made on the fluctuating flow of a non-Newtonian second grade fluid through a porous medium over a semi-infinite porous plate in presence of a transverse magnetic field B0. The governing equations have been solved analytically and the expressions for the velocity and stress fields are obtained. The free stream velocity U(t) fluctuates in time about a non-zero constant mean. The effects of the permeability parameter K and magnetic field parameter M on velocity field have been analyzed quantitatively with the help of figures. It is noticed that the velocity field asymptotically approaches free stream velocity as it goes far away from the plate.

Volumetric lattice Boltzmann method for pore-scale mass diffusionadvection process in geopolymer porous structures

Porous materials present significant advantages for absorbing radioactive isotopes in nuclear waste streams.To improve absorption efficiency in nuclear waste treatment,a thorough understanding of the diffusion-advection process within porous structures is essential for material design.In this study,we present advancements in the volumetric lattice Boltzmann method(VLBM)for modeling and simulating pore-scale diffusion-advection of radioactive isotopes within geopolymer porous structures.These structures are created using the phase field method(PFM)to precisely control pore architectures.In our VLBM approach,we introduce a concentration field of an isotope seamlessly coupled with the velocity field and solve it by the time evolution of its particle population function.To address the computational intensity inherent in the coupled lattice Boltzmann equations for velocity and concentration fields,we implement graphics processing unit(GPU)parallelization.Validation of the developed model involves examining the flow and diffusion fields in porous structures.Remarkably,good agreement is observed for both the velocity field from VLBM and multiphysics object-oriented simulation environment(MOOSE),and the concentration field from VLBM and the finite difference method(FDM).Furthermore,we investigate the effects of background flow,species diffusivity,and porosity on the diffusion-advection behavior by varying the background flow velocity,diffusion coefficient,and pore volume fraction,respectively.Notably,all three parameters exert an influence on the diffusion-advection process.Increased background flow and diffusivity markedly accelerate the process due to increased advection intensity and enhanced diffusion capability,respectively.Conversely,increasing the porosity has a less significant effect,causing a slight slowdown of the diffusion-advection process due to the expanded pore volume.This comprehensive parametric study provides valuable insights into the kinetics of isotope uptake in porous structures,facilitating the development of porous materials for nuclear waste treatment applications.

A fractal approach to low velocity non-Darcy flow in a low permeability porous medium

In this paper, the mechanism for fluid flow at low velocity in a porous medium is analyzed based on plastic flow of oil in a reservoir and the fractal approach. The analytical expressions for flow rate and velocity of non-Newtonian fluid flow in the low permeability porous medium are derived, and the threshold pressure gradient （TPG） is also obtained. It is notable that the TPG （J） and permeability （K） of the porous medium analytically exhibit the scaling behavior J ~ K-D＇r/（l＋Or）, where DT is the fractal dimension for tortuous capillaries. The fractal characteristics of tortuosity for capillaries should be considered in analysis of non-Darcy flow in a low permeability porous medium. The model predictions of TPG show good agreement with those obtained by the available expression and experimental data. The proposed model may be conducible to a better understanding of the mechanism for nonlinear flow in the low permeability porous medium.

Grouting diffusion of chemical fluid flow in soil with fractal characteristics

The chemical fluid property and the capillary structure of soil are important factors that affect grouting diffusion. Ignoring either factor will produce large errors in understanding the inherent laws of the diffusion process. Based on fractal geometry and the constitutive equation of Herschel-Bulkley fluid, an analytical model for Herschel-Bulkley fluid flowing in a porous geo-material with fractal characteristics is derived. The proposed model provides a theoretical basis for grouting design and helps to understand the chemical fluid flow in soil in real environments. The results indicate that the predictions from the proposed model show good consistency with the literature data and application results. Grouting pressure decreases with increasing diffusion distance. Under the condition that the chemical fluid flows the same distance, the grouting pressure undergoes almost no change at first and then decreases nonlinearly with increasing tortuosity dimension. With increasing rheological index, the pressure difference first decreases linearly, then presents a trend of nonlinear decrease, and then decreases linearly again. The pressure difference gradually increases with increasing viscosity and yield stress of the chemical fluid. The decreasing trend of the grouting pressure difference is non-linear and rapid for porosity Φ>0.4, while there is a linear and slow decrease in pressure difference for high porosity.

Interstitial fluid flow:simulation of mechanical environment of cells in the interosseous membrane

In vitro experiments have shown that subtle fluid flow environment plays a significant role in living biological tissues, while there is no in vivo practical dynamical measurement of the interstitial fluid flow velocity. On the basis of a new finding that capillaries and collagen fibrils in the interosseous membrane form a parallel array, we set up a porous media model simulating the flow field with FLUENT software, studied the shear stress on interstitial cells＇ surface due to the interstitial fluid flow, and analyzed the effect of flow on protein space distribution around the ceils. The numerical simulation results show that the parallel nature of capillaries could lead to directional interstitial fluid flow in the direction of capillaries. Interstitial fluid flow would induce shear stress on the membrane of interstitial cells, up to 30 Pa or so, which reaches or exceeds the threshold values of cells＇ biological response observed in vitro. Interstitial fluid flow would induce nonuniform spacial distribution of secretion protein of mast cells. Shear tress on cells could be affected by capillary parameters such as the distance between the adjacent capillaries, blood pressure and the permeability coefficient of capillary＇s wall. The interstitial pressure and the interstitial porosity could also affect the shear stress on cells. In conclusion, numerical simulation provides an effective way for in vivo dynamic interstitial velocity research, helps to set up the vivid subtle interstitial flow environment of cells, and is beneficial to understanding the physiological functions of interstitial fluid flow.

Micromechanics-Based Elastic Fields of Closed-Cell Porous Media

Fluid-filled closed-cell porous media could exhibit distinctive features which are influenced by initial fluid pressures inside the cavities.Based on the equivalent farfield method,micromechanics-based solutions for the local elastic fields of porous media saturated with pressurized fluid are formulated in this paper.In the present micromechanics model,three configurations are introduced to characterize the different state the closed-cell porous media.The fluid-filled cavity is assumed to be a compressible elastic solid with a zero shear modulus,and the pressures in closed pores are represented by eigenstrains introduced in fluid domains.With the assumption of spheroidal fluidfilled pores,the local stress and strain fields in solid matrix of porous media are derived by using the Exterior-Point Eshelby tensors,which are dependent of the Poisson’s ratio of solid matrix and the locations of the investigated material points outside the spheroidal fluid domain.The reliability and accuracy of the analytical elastic solutions are verified by a classical example.Moreover,for finite volume fraction of the fluid inclusions,the local elastic fields of the porous media subjected to the initial fluid pressure and external load are obtained.The results show that the present micromechanics model provides an effective approach to characterize the local elastic fields of the materials with closed-cell fluid-filled pores.

THE TRANSIENT TWO-DIMENSIONAL FLOW THROUGH DOUBLE POROUS MEDIA

This paper presents the analytical solutions in Laplace domain for two-dimensional nonsteady flow of slightly compressible liquid in porous media with double porosity by using the methods of integral transforms and variables separation. The effects of the ratio of storativities to , interporosity flow parameter on the pressure behaviors for a vertically fractured well with infinite conductivity are investigated by using the method of numerical inversion. The new log-log diagnosis graph of the pressures is given and analysed.