具有井简储集的变形介质双渗模型的压力分析

为更好地研究碳酸盐油藏和低渗油的渗流问题，引入渗透率模数，考虑应力敏感地层中介质的变形，介质的双孔隙度、双渗秀率特征，同时考虑井筒储集的影响，建立新的数学模型。渗透率依赖于孔隙压力变化的流动方程是强非线性的，模型采用Douglas—Jones预估-校正法获得了无限大地层及有界封闭地层的数值解，形成了新的理论图版，并利用这些图版对模型中的有关参数进行了敏感性分析。     

具有井筒储集的变形介质双渗模型的压力分析

为更好地研究碳酸盐油藏和低渗油的渗流问题,引入渗透率模数,考虑应力敏感地层中介质的变形,介质的双孔隙度、双渗秀率特征,同时考虑井筒储集的影响,建立新的数学模型。渗透率依赖于孔隙压力变化的流动方程是强非线性的,模型采用Douglas-Jones预估-校正法获得了无限大地层及有界封闭地层的数值解,形成了新的理论图版,并利用这些图版对模型中的有关参数进行了敏感性分析。     

考虑二次梯度项及动边界的双重介质低渗透油藏流动分析

在传统试井模型的非线性偏微分方程中根据弱可压缩流体的假设,忽略了二次梯度项,对于低渗透油藏这种方法是有疑问的.低渗透问题一个显著的特点就是流体的流动边界随着时间不断向外扩展.为了更好地研究双重介质低渗透油藏中流体的流动问题,考虑了二次梯度项及活动边界的影响,同时考虑了低渗透油藏的非达西渗流特征,建立了双重介质低渗透油藏流动模型.采用Douglas-Jones预估-校正差分方法获得了无限大地层定产量生产时模型的数值解,分别讨论了不同参数变化时压力的变化规律及活动边界随时间的传播规律,还分析了考虑和忽略二次梯度项影响时模型数值解之间的差异随时间的变化规律,做出了典型压力曲线图版,这些结果可用于实际试井分析.     

分形煤层气藏数值模拟研究——Douglas-Jones预估-校正法的应用

传统的煤层气动力学模型多建立在欧几里得基础上,难以描述煤层气孔隙结构的复杂性和形状的不规则性。为此,以分形理论为基础,通过引入煤层基质和裂缝的分形维数来刻画煤层气孔隙结构的复杂性和吸附特性,建立了双重分形介质渗流模型,采用Douglas-Jones预估-校正法对非线性方程组进行离散,获得了无限大地层和有限地层定产量生产时拟稳态吸附模型的差分方程,求得数值解。结果表明,Douglas-Jones预估-校正法可以有效解决这类非线性模型的求解问题,获得无限大地层定产量生产时变形双重分形介质模型的数值解;分析各种分形参数下的煤层压力动态,做出了典型压力曲线图。对无限大地层,初期分形维数对压力影响不大,后期分形维数越小,压力越高。对有限地层,初期分形维数的影响明显,且分形维数越大,压力越低。压力随分形指数的减小量呈现先增大后减小的趋势,在末期压力平稳趋向同一值。     

考虑井储和表皮效应的分形介质煤层气压力动态分析

考虑煤层的双重介质特征和介质的分形特征,建立了考虑井筒储存和表皮效应影响的分形介质煤储层非平衡吸附、非稳态条件下的气体流动数学模型,并分别求得了无限大地层条件下中心一口井定产量生产时无因次井底压力的Laplace空间解析解和实空间上的数值解.给出了无因次井底压力及其导数随分形参数、无因次井筒储存系数以及表皮系数等变化的双对数曲线图.     

分形油藏不稳定渗流问题的精确解

研究了分形油藏无限大地层和有界地层渗流模型，引入了一类有限广义Ｈａｎｋｅｌ变换，利用这种变换和Ｗｅｂｅｒ变换，在井底定流量和定压生产时，对无限大地层及有界地层（包括封闭和定压地层）六种情况，求得了实空间解析解用双参数（ｄｆ，ｄｓ）来刻画分形油藏的分形特性，分析了分形油藏压力动态特征以及分形参数和边界对压力动态的影响     

三孔单渗模型数值模拟研究

保留了非线性偏微分方程中的所有项,没有忽略二次梯度项的影响。建立了由基岩、裂缝及溶洞系统组成的三孔单渗模型。采用有限差分的方法获得了无限大地层定产量生产、有界封闭地层定产量生产和有界封闭地层定压生产时的三孔单渗模型的差分方程,用解非线性方程组的Broyder迭代法求得了方程组的数值解。分别讨论了三重介质参数变化时的压力变化规律,并考虑了井筒储集和表皮效应对压力的影响,做出了典型压力曲线图。     

多孔介质非线性渗流问题的摄动解

考虑变形多孔介质渗透参数(渗透率和孔隙度)与孔隙压力呈负指数变化的特点，建立了多孔介质渗流问题的数学模型，采用积分变换方法求出了一维非线性渗流问题的摄动解，并对常数渗透参数和指数渗透参数的渗流问题进行对比分析，计算结果表明：两者之间的差别较大，且渗透参数的变化对于流体渗流中后期过程有着重要的影响，但对渗流早期影响不大，这对于定量研究工程中非线性渗流问题模型参数的相对重要性提供了可靠的理论依据。     

变形三重介质低渗透油藏垂直裂缝井的非线性流动分析

不仅考虑低渗透油藏具有启动压力梯度的渗流特征,还考虑应力敏感地层中介质的变形;发展了Cinco-Ley H.提出的有限导流垂直裂缝井双线性流理论,将流体在垂直裂缝与地层中形成的流动划分为两个区域—垂直裂缝中的线性流区域和变形三重介质低渗透油藏中的非线性流区域;由此建立了变形三重介质低渗透油藏有限导流垂直裂缝井的非线性流...     

裂缝性油藏流固耦合渗流

本文给出了考虑介质变形的双重孔隙介质流固耦合渗流模型,并考虑渗流参数随有效应力而变化的非线性双重孔隙介质流固耦合渗流,在此基础上,本文还推导了双重孔隙介质非线性系数非线性等流固耦合流流计算,并给出了算例。     

The Flow Problem of Fluids Flow in a Fractal Reservoir with Double Porosity

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裂缝性低渗透油藏流固耦合渗流分析

在低渗透油田的开发过程中，油藏流体渗流和储层岩土之间存在明显的耦合作用。本文首先研究给出了低渗裂缝性储层孔渗参数的等效方法，然后将渗流力学和岩土力学相结合，给出了低渗透裂缝性储层流固耦合渗流的数学模型，该模型不仅可以反映基质孔渗参数在开发中的变化，而且更能反映裂缝开度变化所引起的渗透率变化，而这对于低渗透裂缝性油田而言十分重要。最后对一实际井网进行了流固耦合油藏数值模拟，给出了开发过程中孔渗参数的变化及其耦合效应对油田开发的影响．     

On the theory of seepage waves of pressure in a fracture in a porous permeable medium

Seepage pressure waves in fractures in a porous permeable medium are studied. The effects of the reservoir and fracture porosity and permeability, the fracture width, and the rheological properties of the saturating fluid on the perturbation dynamics in the fracture are analyzed. It is shown that in porous permeable reservoirs, fractures are wave channels through which low-frequency fluctuations of borehole pressure propagate. Accurate solutions are obtained which describe the evolution of pressure fields in a fracture with an instantaneous change in the borehole pressure by a constant value. Based on these solutions, dependences of the fluid flow rate on time and interface pressure are determined.     

Assessment of Stimulated Area Growth During High-Pressure Hydraulic Stimulation of Fractured Subsurface Reservoir

Hydraulic stimulation is performed by high-pressure fluid injection, which permanently increases the permeability of a volume of rock, typically transforming it from the microdarcy into the millidarcy range. After a period of stimulation, fluid injection and recovery boreholes are introduced into the stimulated rock volume, and heat is extracted by water circulation. In the present study a simplified mathematical model of non steady-state hydraulic stimulation is proposed and analyzed. Fluid flow is assumed to be radial, injected flow rate constant; and fluid density, rock porosity, and permeability depend on fluid pressure. The conventional boundary of the growing stimulated rock volume is introduced as a surface where the porosity and permeability of the stimulated rock exhibit a sharp decline and remain constant within the undisturbed area. The problem is solved analytically by a modified method of integral correlations. As a result, approximate close-form solutions for pressure distributions in the stimulated and nonstimulated (undisturbed) areas are obtained, and an equation for the moving boundary of the stimulated volume is derived. The correctness of the approximate solution is validated by comparison to an exact self-similar solution of the problem obtained for the particular case when the well’s radius is assumed to be equal to zero.     

Explosion Dynamics in Saturated Rocks and Solids

Non-elastic pore deformations and crack propagations are the principal causes of dynamic damage in rocks and soils. In the case of downhole blasting from wellbores, these two mechanisms compete with each other. Therefore, to carry out a mechanical analysis of rock blasting, a sufficiently complete model that takes these various mechanisms into account has to be developed. To address this issue, this paper proposes the use of an elastic–plastic model, which includes a yield condition with a non-associated plastic flow rule, the effects of pore fluid saturation, and a brittle failure criterion under extension. The results presented in this paper describe underground explosions with spherical motion (cavity growth under the internal pressure of detonated gases without leakage into the formation), typical for oil or water reservoirs. The governing equations are written in a Cartesian system of coordinates for the case of spatial dynamic medium deformation. For this case, Cartesian coordinates are more convenient than spherical coordinates because they avoid numerical difficulties connected with the non-divergent terms of the non-linear form of the Biot–Frenkel equations. The numerical method uses the Wilkins approach, which has been generalized for the model described in this paper. The dilatancy of the material during plastic deformation is neglected for simplicity. The numerical results show that, when using typical parameters for relatively “soft” porous skeleton, the plastic flow overcomes the brittle failure. An extension zone only appears near the cavity. The results also show the presence of the two Biot P-waves. The second Biot wave, however, is only seen in the case of an extremely high permeability rock. Furthermore, in the case of the first Biot wave, the saturating liquid and the solid skeleton particles are moving with different velocities in a 100 darcy rock and with the same velocity in a 0.01 darcy rock. Calculated radial particle velocities as a function of the scaled radius are close to measured velocities in rigid dense media but are larger than measured ones in clays. It is suggested that the difference is due to different levels of water saturation, assumed full saturation in the calculation, partial saturation in the experiments.     

A Computational Approach to Determine Average Reservoir Pressure in a Coalbed Methane (CBM) Well Flowing Under Dominant Matrix Shrinkage Effect

Desorption of gas from coal matrix alters the pore volume of fracture network. Consequently, cleat porosity and permeability of reservoir changes as pressure depletes. The method of standard pressure analysis calculations produces incorrect results in the case of coalbed methane reservoirs producing under dominant matrix shrinkage effect. The change in cleat porosity and permeability due to shrinkage of coal matrix following gas desorption with pressure depletion invalidates the underlying assumptions made in the derivation of diffusivity equation. Consequently, equations of pseudo-steady state commonly used in conventional reservoirs no longer remain valid as the porosity and permeability values change with pressure depletion. In this paper, effort has been made to describe pseudo-steady-state flow in coalbed methane reservoirs in the form of a new equation that accounts for pressure dependency of cleat porosity and permeability due to shrinkage of coal matrix. The concept of Al-Hussainy et al. (1966) has been extended to define a new pseudo-pressure function which assimilates within itself the pressure dependence of porosity and permeability Palmer and Mansoori (1998). Equation has been used to relate the cleat porosity with pressure. The equation-based computational method suggested in this paper finds its usefulness in estimating average reservoir pressure for any known flowing bottom hole pressure and thus reducing the frequency of future pressure buildup tests. The new equation is also useful in predicting reservoir pressure under the situation when coal matrix shrinks below desorption pressure. The equation used in the computational method has been validated with the help of numerical simulator CMG-GEM.     

Effect of yield stress on the flow of a Casson fluid in a homogeneous porous medium bounded by a circular tube

The effect of yield stress on the flow characteristics of a Casson fluid in a homogeneous porous medium bounded by a circular tube is investigated by employing the Brinkman model to account for the Darcy resistance offered by the porous medium. The non-linear coupled implicit system of differential equations governing the flow is first transformed into suitable integral equations and are solved numerically. Analytical solution is obtained for a Newtonian fluid in the case of constant permeability, and the numerical solution is verified with that of the analytic solution. The effect of yield stress of the fluid and permeability of the porous medium on shear stress and velocity distributions, plug flow radius and flow rate are examined. The minimum pressure gradient required to start the flow is found to be independent of the permeability of the porous medium and is equal to the yield stress of the fluid.