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.

Theoretical investigation of micropolar fluid flow between two porous disks

The steady, laminar, incompressible and two dimensional micropolar flow between two porous disks was investigated using optimal homotopy asymptotic method(OHAM) and fourth order Runge–Kutta numerical method. Comparison between OHAM and numerical method shows that OHAM is an exact and high efficient method for solving these kinds of problems. The results are presented to study the velocity and rotation profiles for different physical parameters such as Reynolds number, vortex viscosity parameter, spin gradient viscosity and microinertia density parameter. As an important outcome, the magnitude of the microrotation increases with an increase in the values of injection velocity while it decreases by increasing the values of suction velocity.

Numerical investigations of asymmetric flow of a micropolar fluid between two porous disks

Numerical solution is presented for the two- dimensional flow of a micropolar fluid between two porous coaxial disks of different permeability for a range of Reynolds number Re （-300≤ Re 〈 0） and permeability parameter A （1.0≤A ≤2.0）. The main flow is superimposed by the injection at the surfaces of the two disks. Von Karman＇s similarity transformations are used to reduce the governing equations of motion to a set of non-linear coupled ordinary differential equations （ODEs） in dimensionless form. An algorithm based on the finite difference method is employed to solve these ODEs and Richardson＇s extrapolation is used to obtain higher order accuracy. The results indicate that the parameters Re and A have a strong influence on the velocity and microrotation profiles, shear stresses at the disks and the position of the viscous/shear layer. The micropolar material constants cl, c2, c3 have profound effect on microrotation as compared to their effect on streamwise and axial velocity profiles. The results of micropolar fluids are compared with the results for Newtonian fluids.

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.

Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel

Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a “backward flow” is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.

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.

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.

Examination on the existence of slow wave in fluid saturated porous medium with the optical method

With the shadowgraph method, three ultrasonic pulses in Water, which correspond to the conversion modes of the fast compressional wave, the transverse wave and the slow compressional wave in the sample of Fluid-Saturated Porous Medium (FSPM) respectively,were observed and recorded by CCD camera. The positions of these pulses are cousistent with the computed positions and the time interval between these pulses measured by a transmitterreceiver method.

An explicit finite element method for dynamic analysis in three-medium coupling system and its application

In this paper, an explicit finite element method to analyze the dynamic responses of three-medium coupled systems with any terrain is developed on the basis of the numerical simulation of the continuous conditions on the bounda-ries among fluid saturated porous medium, elastic single-phase medium and ideal fluid medium. This method is a very effective one with the characteristic of high calculating speed and small memory needed because the formulae for this explicit finite element method have the characteristic of decoupling, and which does not need to solve sys-tem of linear equations. The method is applied to analyze the dynamic response of a reservoir with considering the dynamic interactions among water, dam, sediment and basement rock. The vertical displacement at the top point of the dam is calculated and some conclusions are given.

Multi-transmitting formula for attenuating waves

The MTF is extended to case of attenuating incident wave by introducing an attenuation coefficient. The reflection coefficients of this modified MTF and MTF are evaluated and compared when an attenuating wave impinges on the boundary, and the results demonstrate that MTF can be used to absorb slightly attenuating waves and the modified MTF is more capable of absorbing heavily attenuating waves than MTF. The accuracy of modified MTF is also tested by numerical examples of fluid saturated porous media.

THE UPWIND FINITE DIFFERENCE FRACTIONAL STEPS METHOD FOR NONLINEAR COUPLED SYSTEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA

For nonlinear coupled system of multilayer dynamics of fluids in porous media, the second order and first order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward, trod two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in L2 norm are derived to determine the error in the second order approximate solution. This method has already been applied to the numerical simulation of migration-accumulation of oil resources.

MODEL AND METHOD OF WELL TEST ANALYSIS FORWELLS WITH VERTICAL FRACTURE

Based on the flow mechanism of hydraulic fractured wells, through integrating linear-flow model and effective well-radius model, a new model of well test analysis for wells with vertical fracture was established. In the model, wellbore storage, the damage in the wall of fracture and all kinds of boundary conditions are considered. The model is concise in form, has intact curves and computes fast, which may meet the demand of real-time computation and fast responded well test interpretation. A new method to determine effective well radius was presented, and the correlation between effective well radius and the fracture length, fracture conductivity, skin factor of fracture was given. Matching flow rate or pressure tested, the optimization model that identified formation and fracture parameters was set up. The automatic matching method was presented by synthetically using step by step linear least square method and sequential quadratic programming. At last, the application was also discussed. Application shows that all of these results can analyze and evaluate the fracturing treatment quality scientifically and rationally, instruct and modify the design of fracturing and improve fracturing design level.

SPECTRAL METHOD FOR CALCULATING MOVING INTERFACE BETWEEN FLUIDS IN POROUS MEDIUM

In the application of spectral method to the calculation of moving interface between fluids in porous medium there are two difficulties: the spectral calcula- tion of function defined by a singular integral and the numerical quadrature of highly oscillating function. This paper proposes a spectral method for calculating the problem and finds the way to overcome the two difficulties. Example calcula- tions show that the method can describe successfully interfacial motion and, with almost the same order of computational amount, is more accurate and stabler than the corresponding finite difference method.

Analytical Solution for Time-dependent Flow of a Third Grade Fluid Induced Due to Impulsive Motion of a Flat Porous Plate

The aim of the present communication is to discuss the analytical solution for the unsteady flow of a third grade fluid which occupies the space y 〉 0 over an infinite porous plate. The flow is generated due to the motion of the plate in its own plane with an impulsive velocity V（t）. Translational symmetries in variables t and y are utilized to reduce the governing non-linear partial differential equation into an ordinary differential equation. The reduced problem is then solved using homotopy analysis method（HAM）. Graphs representing the solution are plotted and discussed and proper conclusions are drawn.

A STUDY ON TRANSIENT FLUID FLOW OF HORIZONTAL WELLS IN DUAL-PERMEABILITY MEDIA

To adopt horizontal wells in dual media reservoirs, a good understanding of the related fluid flows is necessary. Most of the recent studies focus on dual porosity media instead of dual permeability media. In this article, through both integral transformation and sink-source superposition, a new Laplace-domain solution is obtained for the slightly-compressible fluid flow in the 3-D dual-permeability media in which the horizontal well is operating in a constant rate of production. Major asymptotic characteristics of diagnosis curves of dimensionless downhole pressure are analyzed by the limited analysis. Effects of parameters of dual-permeability media including mobility ratio k, storativity ratio ω and inter-porosity flow parameter k on the downhote pressure are studied by using the Laplace numerical inversion. The new solution obtained in this article includes and improves the previous results and then can be used as a basis for either pressure transient analysis or formation behavior evaluation for the typical reservoir with horizontal wells.

Scaled particle theory for bulk and confined fluids： A review

More than half a century after its first formulation by Reiss, Frisch and Lebowitz in 1959, scaled particle theory(SPT) has proven its immense usefulness and has become one of the most successful theories in liquid physics. In recent years, we have strived to extend SPT to fluids confined in a variety of random porous matrices. In this article, we present a timely review of these developments. We have endeavored to present a formulation that is pedagogically more accessible than those presented in various original papers, and we hope this benefits newcomers in their research work. We also use more consistent notations for different cases. In addition, we discuss issues that have been scarcely considered in the literature, e.g., the one-fluid structure of SPT due to the isomorphism between the equation of state for a multicomponent fluid and that for a one-component fluid or the pure-confinement scaling relation that provides a connection between a confined and a bulk fluid.

Evaluation and development of a predictive model for conjugate phase change heat transfer of energy storage system partially filled with porous media

The present study proposes a predictive model to explore the effect of partially filled porous media on the con-jugate heat transfer characteristic of phase change material(PCM)with interfacial coupling conditions between pure fluid region and porous region.The enthalpy-porosity method,local thermal non-equilibrium model and Darcy-Forchheimer law are comprehensively considered to describe the convective heat transfer process in porous media.The modified model is then validated by benchmark data provided by particle image velocimetry(PIV)ex-periments.The phase change behavior,heat transfer efficiency and energy storage performance are numerically investigated for different partial porous filling strategies in terms of filling content,position,height of porous foam and inclination angles of cavity.The results indicate that due to the resistance in porous region,the shear stress exerted by the main vortex(natural convection)in pure fluid region and the momentum transferred,a secondary vortex phenomenon appears in the porous region near the fluid/porous interface.Moreover,such dis-continuity of permeability and fluid-to-porous thermal conductivity results in the cusp of phase change interface at the horizontal fluid/porous boundary.Among four partial porous filling cases,the lower porous filling one has more desirable heat transfer performance,and the 3/4H lower porous filling configuration is the best solution for optimization of the latent heat thermal energy storage(LHTES)systems.For tilted cavity,the increase of inclination angle positively affects the heat transfer efficiency as well as the energy storage rate of the LHTES system,where the performance of 3/4H lower porous filling configuration is further highlighted.

A NUMERICAL SIMULATION OF CHANNEL RESERVOIRS CONTAINING VERTICAL AND HORIZONTAL WELLS

In this article, the bounding surfaces of channels were modeled by Bayesian stochastic simulation, which is a boundary-valued problem with observed valley erosion thickness at the locations of wells （hard data）. In this study, it was assumed that the cross-section of the channel shows a parabolic shape, and the case that the vertical well and the horizontal well are located in the channel was considered. Peaceman＇s equations were modified to simultaneously solve both the vertical well problem and the horizontal well problem. In porous media, a 3D fluid equation was solved with iteration in the spatial domain, which had channels, vertical wells, and horizontal wells. As an example, the spatial distributions of pressure were calculated for channel reservoirs containing vertical and horizontal wells.

Evaluation of Pressure Boundary Conditions for Permeability Calculations Using the Lattice-Boltzmann Method

Lattice-Boltzmann(LB)simulations are a common tool to numerically estimate the permeability of porous media.For valuable results,the porous structure has to be well resolved resulting in a large computational effort as well as high memory demands.In order to estimate the permeability of realistic samples,it is of importance to not only implement very efficient codes,but also to choose the most appropriate simulation setup to achieve accurate results.With the focus on accuracy and computational effort,we present a comparison between different methods to apply an effective pressure gradient,efficient boundary conditions,as well as two LB implementations based on pore-matrix and pore-list data structures.