Dynamic production prediction and parameter identification for gas well with vertical fracture

ＮｏｍｅｎｃｌａｔｕｒｅＢ—ｖｏｌｕｍｅｃｏｅｆｆｉｃｉｅｎｔｏｆｆｏｒｍａｔｉｏｎｆｌｕｉｄ ,ｄｉｍｅｎｓｉｏｎｌｅｓｓ ;Ｃｆｔ—ｃｏｍｐｒｅｈｅｎｓｉｖｅｃｏｍｐｒｅｓｓｉｎｇｃｏｅｆｆｉｃｉｅｎｔｏｆｆｌｕｉｄｉｎｆｒａｃｔｕｒｅ ,(ＭＰａ) - 1;Ｃｐ—ｗｅｉｇｈｔｏｆｓｉｎｇｌｅｌａｙｅｒｐｒｏｐｐａｎｔｐｅｒｕｎｉｔｆｒａｃｔｕｒｅａｒｅａ ,ｋｇ/ｍ2 ;Ｃｔ —ｃｏｍｐｒｅｈｅｎｓｉｖｅｃｏｍｐｒｅｓｓｉｎｇｃｏｅｆｆｉｃｉｅｎｔｏｆｆｏｒｍａｔｉｏｎｆｌｕｉｄ ,(ＭＰａ) - 1;ｄＢＨＮ —Ｂｒ…     

Effect of flows between formations and capillary forces on the process of oil displacement in a stratified inhomogeneous bed

The results of a numerical investigation of the process of oil displacement in a stratified inhomogeneous formation on the basis of the two-phase flow model with account for capillary forces are presented. It is shown that in many cases the vertical inhomogeneity of oil reservoirs may not be a cause of nonuniform displacement and the non-recovery of large oil reserves by the time of water breakthrough to the extraction surface. The action of the capillary forces is an additional factor leading to equalization of the water propagation front in the inhomogeneous formation, water breakthrough delay, and intensification of the mass transfer between the layers with different permeabilities. Analysis of the contribution of the interlayer flows to the water flooding of low-permeability formation intervals calls into question the practicability of blocking high-permeability inclusions in the neighborhood of pumping wells.     

Extension of Whittaker equations to non-holonomic mechanical systems

In 1904, using the energy integral Whittaker studied the reduction of a dynamical problem to a problem with fewer degrees of freedom for the holonomic conservative systems and obtained the Whittaker equation^[1].In this article, Whittaker equations are extended to non-holonomic systems and the generalized Whittaker equations are obtained. And then these equations are transformed into Kiel-sen’s form.Finally an example is given.     

An analysis of species separation in a thermogravitational column filled with a porous medium

In the past, the analysis of species separation in a thermogravitational column filled with porous media has been based on strong dependency of thermal and molecular diffusion to dispersion. In this work, we suggest an alternative and show that the dispersion effect is negligible for the conditions in a packed hermogravitational column and that compositional dependency of the thermal diffusion should be accounted for.     

On the existence of self-similar solutions of the equations governing unsteady flow through a porous medium

In this paper the conditions for the existence of self-similar solutions of the equations governing unsteady flows through a porous medium are presented and discussed. The first two sections deal with the case of non-Newtonian fluids of power-law behavior; the third section analyzes the case of non-Darcy gas flows. The boundary and initial conditions occuring currently in a large class of fluid mechanics problems, of practical interest in engineering, are considered.     

Effect of residual oil saturation on the flow through a porous medium in the neighborhood of an injection well

Models of the residual oil saturation and models of its effect on the flow in injection wells are proposed. The threshold nature of the dependence of the residual oil saturation on the capillary number determines a change in the flow regimes in the neighborhood of the injection well. The cases of pure, contaminated, and compressible reservoirs are considered. The dependences of the basic problem parameters on the displacement conditions and the state of the reservoir are obtained, together with formulas for the pressure distribution and well injectivity. The topicality of such a simulation for field calculations is demonstrated.     

Conjugate model for heat and mass transfer of porous wall in the high temperature gas flow

Heat and mass transfer of a porous permeable wall in a high temperature gas dynamical flow is considered. Numerical simulation is conducted on the ground of the conjugate mathematical model which includes filtration and heat transfer equations in a porous body and boundary layer equations on its surface. Such an approach enables one to take into account complex interaction between heat and mass transfer in the gasdynamical flow and in the structure subjected to this flow. The main attention is given to the impact of the intraporous heat transfer intensity on the transpiration cooling efficiency. The project supported by the National Natural Science Foundation of China (19889209) and Russian Foundation for Basic Research (97-02-16943)     

渗流气体滑脱现象与渗透率变化的关系

气体在致密多孔介质中低速渗流时存在着因气体分子碰撞岩壁而引起的滑脱现象，它由介质的孔隙结构和气体分子的平均自由程共同决定。该现象使气测渗透率大于孔隙介质的绝对渗透率。介质中气体的低速渗流为黏滞流与滑脱流组成，各自所占比例与气体分子按自由程的分布有关。理论计算得到了低速气体渗流的气测渗透率Kg与绝对渗透率K0比值的关系式，实验结果与理论分析吻合。     

Influence of Adsorption and Desorption of Gas Micronuclei on the Nature of the Flow of a Gassy Liquid through a Porous Medium

The problem of gassy liquid flow through a porous medium is considered theoretically. Periodic oscillations of the liquid and gas flow rate observed experimentally are attributable to the processes of sorption and desorption of gas micronuclei on the walls of the pore space and their diffusion. In the kinetic equation employed the desorption rate is directly proportional to the adsorbed micronucleus concentration and the seepage rate, and the adsorption rate is directly proportional to the product of the mobile micronucleus concentration and the free site concentration on the pore surfaces. Steady-state solutions of this equation are investigated. It is shown that periodic oscillations of the flow rate can manifest themselves only when the processes of micronuclei adsorption predominate over the desorption processes.     

Effect of decomposition of a gas hydrate on the gas recovery from a reservoir containing hydrate and gas in the free state

The problem of gas recovery in the process of methane hydrate dissociation in a reservoir saturated with gas-hydrate mixture is considered. The mathematical model of hydrate decomposition into gas and water is generalized to include the negative temperature interval and takes ice formation into account. The solution of the problem is represented in the self-similar approximation. It is shown that there exists a transition hydrate decomposition regime in which water and ice are formed simultaneously. A comparative analysis of the recovery is carried out on the basis of relations derived for the masses of recovered gas in different hydrate dissociation regimes. It is shown that an anomalous increase in the recovered gas volumes is observed in the transition hydrate dissociation regime.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 132–142. Original Russian Text Copyright © 2005 by Tsypkin.     

Large-Scale Streamwise Vortices in the Supersonic Part of a Permeable Nozzle

Large-scale streamwise vortices in the vicinity of a perforated wall in the supersonic part of the nozzle are studied. The governing effect of gas inflow through a perforated wall on origination and parameters of streamwise vortices is experimentally established.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 68–75, September–October, 2005.     

Numerical Simulation of Darcy and Forchheimer Force Distribution in a HBC Fuse

We present the breaking of a short-circuit current in a HBC fuse simulation based on an isentropic non-stationary model in a porous medium for a one dimensional geometry. The fluid flow is affected by the nature of the gas and by the morphology of the silica sand. To model the gas–silica sand interaction, we introduce two classical laws: the Darcy's law due to the viscous interaction and the Forchheimer's law due to the inertial force. Numerical simulations with realistic physical parameters have been performed using a finite volume scheme with a fractional step technique. We show the evolution of Darcy and Forchheimer forces during time and according to the position in the fuse. We place in prominent position the fact that either force is predominant in the fuse according to the time and the position which justifies a numerical treatment to cover all the situations.     

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

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.     

水流损失和热补偿共同作用对增强型地热系统(EGS)产能影响的研究

基于青海共和盆地-3705m地热田实测数据,结合流固耦合传热理论并运用Comsol软件,建立了离散型裂隙岩体流体传热模型。考虑水流损失和热补偿共同作用,模拟得到了开采过程中上、下岩层(盖层和垫层)为绝热不渗透、传热不渗透、渗透传热时,储层(上、下岩层和压裂层)温度场的变化特征,分析了产出流量、水流损失、产出温度、产热速率的变化规律。研究结果表明:采热过程中产出流量始终小于注入流量;产出流量增幅速率先增大后减小,最后趋于稳定,前3a产出流量增幅超过总增幅量的3/4;忽略水流损失,将高估产热速率,采热初期甚至达到考虑水流损失时产热速率的3倍以上;考虑水流损失,产热速率呈先快速上升再趋于稳定后逐渐下降的趋势,最优开采时间为3a^11a;研究上、下岩层对产出温度的影响,仅考虑传热,采热寿命延长5.43%,同时考虑渗流传热时,采热寿命延长2.71%;采热前9a,水流损失占主导作用,即流入上、下岩层水流损失对产热速率的影响高于热补偿效应,开采10a后,热补偿效应占主导作用;同时考虑水流损失和热补偿效应得到的产热速率变化规律与实际工程更为符合,建议选择低渗透能力的上、下岩层延长增强型地热系统(EGS)运行时间。     

A higher resolution edge‐based finite volume method for the simulation of the oil–water displacement in heterogeneous and anisotropic porous media using a modified IMPES method

In this article, we present a higher‐order finite volume method with a ‘Modified Implicit Pressure Explicit Saturation’ (MIMPES) formulation to model the 2D incompressible and immiscible two‐phase flow of oil and water in heterogeneous and anisotropic porous media. We used a median‐dual vertex‐centered finite volume method with an edge‐based data structure to discretize both, the elliptic pressure and the hyperbolic saturation equations. In the classical IMPES approach, first, the pressure equation is solved implicitly from an initial saturation distribution; then, the velocity field is computed explicitly from the pressure field, and finally, the saturation equation is solved explicitly. This saturation field is then used to re‐compute the pressure field, and the process follows until the end of the simulation is reached. Because of the explicit solution of the saturation equation, severe time restrictions are imposed on the simulation. In order to circumvent this problem, an edge‐based implementation of the MIMPES method of Hurtado and co‐workers was developed. In the MIMPES approach, the pressure equation is solved, and the velocity field is computed less frequently than the saturation field, using the fact that, usually, the velocity field varies slowly throughout the simulation. The solution of the pressure equation is performed using a modification of Crumpton's two‐step approach, which was designed to handle material discontinuity properly. The saturation equation is solved explicitly using an edge‐based implementation of a modified second‐order monotonic upstream scheme for conservation laws type method. Some examples are presented in order to validate the proposed formulation. Our results match quite well with others found in literature. Copyright © 2016 John Wiley & Sons, Ltd.