A steam-soak production model for thick gravity drainage petroleum reservoirs

Summary This paper deals with the production performance for the steam-soak process as applied to a reservoir where oil is produced by gravity drainage. An improved analytical temperature profile which is simple, less time consuming and comparable to the exact solution is used to compute the viscosity variation inside the reservoir. Based on this temperature profile the continuity equation is solved by finite difference technique to find the oil height as a function of radius and time which in turn gives the flow rate and cumulative oil production. Comparison of the developed model with available field data shows that the model gives better prediction of steam-soak oil recovery than other comparable methods.

---

Ein Modell zur Ausbeute von Rohölfeldern durch Schwerkraftsickerung bei zyklischer Dampfinjektion

Übersicht Behandelt wird das Förderverhalten eines Rohölspeichers bei Dampfinjektion und Schwerkraftsickerströmung. Zur Berechnung der Viskositätsverteilung im Reservoir wird ein vereinfachtes Temperaturfeld, welches das wahre annähert, benutzt. Mit dieser Temperaturverteilung wird die Kontinuitätsgleichung nach der Finite-Differenzen-Methode gelöst und die Ölstandshöhe als Funktion von Radius und Zeit bestimmt. Daraus ergibt sich der Volumenstrom und die kumulierte Fördermenge. Ein Vergleich des hier entwickelten Modells mit Daten eines Ölfeldes zeigt, daß es bessere Vorhersagen liefert als vergleichbare Methoden.

     

New hybrid Cartesian cut cell/enriched multipoint flux approximation approach for modelling and quantification of structural uncertainties in petroleum reservoirs

Efficient and profitable oil production is subject to make reliable predictions about reservoir performance. However, restricted knowledge about reservoir rock and fluid properties and its geometrical structure calls for history matching in which the reservoir model is calibrated to emulate the field observed history. Such an inverse problem yields multiple history‐matched models, which might result in different predictions of reservoir performance. Uncertainty quantification narrows down the model uncertainties and boosts the model reliability for the forecasts of future reservoir behaviour. Conventional approaches of uncertainty quantification ignore large‐scale uncertainties related to reservoir structure, while structural uncertainties can influence the reservoir forecasts more significantly compared with petrophysical uncertainty. Quantification of structural uncertainty has been usually considered impracticable because of the need for global regridding at each step of history matching process. To resolve this obstacle, we develop an efficient methodology based on Cartesian cut cell method that decouples the model from its representation onto the grid and allows uncertain structures to be varied as a part of history matching process. Reduced numerical accuracy due to cell degeneracies in the vicinity of geological structures is adequately compensated with an enhanced scheme of a class of locally conservative flux continuous methods (extended enriched multipoint flux approximation method or extended EMPFA). The robustness and consistency of the proposed hybrid Cartesian cut cell/extended EMPFA approach are demonstrated in terms of true representation of geological structures influence on flow behaviour. Significant improvements in the quality of reservoir recovery forecasts and reservoir volume estimation are presented for synthetic model of uncertain structures. Copyright © 2015 John Wiley & Sons, Ltd.     

Layered piezoelectric medium with interface crack under anti-plane shear

The theory of linear piezoelectricity is applied to solve the anti-plane shear problem of a piezoelectric layer sandwiched by two dissimilar homogeneous materials with a crack at the interface. Both mechanical and electrical loads are applied to the piezoelectric laminate. By the use of Fourier transforms, the mixed boundary value problem is reduced to a singular integral equation which is solved numerically to determine the stress intensity factors for several layered piezoelectric media, and the results are presented in graphical form.     

Flow processes with change of regime in fractured reservoirs

Experimental and industrial observations indicate a strong nonlinear dependence of the parameters of the flow processes in a fractured reservoir on its state of stress. Two problems with change of boundary condition at the well — pressure recovery and transition from constant flow to fixed bottom pressure — are analyzed for such a reservoir. The latter problem may be formulated, for example, so as not to permit closure of the fractures in the bottom zone. For comparison, the cases of linear [1] and nonlinear [2] fractured porous media and a fractured medium [3] are considered, and solutions are obtained in a unified manner using the integral method described in [1]. Nonlinear elastic flow regimes were previously considered in [3–6], where the pressure recovery process was investigated in the linearized formulation. Problems involving a change of well operating regime were examined for a porous reservoir in [7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 67–73, May–June, 1991.     

Gravity-Capillary Waves in Layered Fluid

In this work, we analyze the stability of a gravity wave generated on the separation surface of two immiscible liquids inside a moving container and perturbed by a capillary wave. Such a phenomenon is experimentally observed when the amplitude and the frequency of the motion imposed to the container attain certain values. The evolution of the system is described by the variational principle. We assume that the motion of the system is decomposed into two modes: the gravity mode and the capillary mode. With suitable scaling assumptions, it is possible to show that the evolution of the gravity mode is determined by the forcing motion, while the capillary mode is excited by the nonlinear interactions between the capillary and gravity modes. Finally, an analytic dispersion relation is obtained for the pulsation of the capillary mode. This relation is a function of several quantities, all depending on the capillary wave number and the characteristics of the exciting motion.     

Dissociation of gas hydrates coexisting with gas in natural reservoirs

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 84–87, September–October, 1990.     

The Onset of Convection in a Layered Porous Medium with Vertical Throughflow

An analytical investigation of the effect of vertical throughflow on the onset of convection in a composite porous medium consisting of two horizontal layers has been made. The cases of iso-flux and iso-temperature boundaries are both investigated. The critical Rayleigh number depends on a Péclet number $Q$ , a permeability ratio $K_{r}$ , a thermal conductivity ratio $k_{r}$ , and a depth ratio $\delta $ . For the case of small $Q$ an approximate solution is obtained, which shows that in general throughflow has a stabilizing effect whose magnitude may be increased or decreased by the heterogeneity. This solution is supplemented by an asymptotic solution valid for large $Q.$      

Backward Transfer-Matrix Method for Elastic Analysis of Layered Solids with Imperfect Bonding

This paper presents a backward transfer-matrix method for the elastic analysis of layered solids with an imperfect bonding at the layer interfaces. Literature review reveals that the conventional transfer-matrix method has an intrinsic fault which leads to ill-conditioned matrices for thick layers and accumulative numerical errors for a large number of layers and that there are a few publications available in the relevant literature regarding analytical analysis of layered solids by taking into account the effects of imperfectly bonded interfaces. The backward transfer-matrix method adopted in this paper completely overcomes the ill-posedness associated with the conventional transfer-matrix method and fully retains the highest efficiency of the classical transfer-matrix concept for analytical formulation of solutions in layered elastic solids with imperfectly bonded interfaces. Numerical results indicate that there is no problem in the numerical evaluation of the solutions with high accuracy and efficiency, and that the interfacial bonding conditions have a significant effect on the elastic response of layered solids due to external loading. This revised version was published online in August 2006 with corrections to the Cover Date.     

弱界面ZnO-SiO2-Si压电层合结构中的Love波

建立了考虑弱连接界面特性的传递矩阵,基于状态空间法分析了弱界面压电层合结构中Love波的传播特性,揭示了ZnO-SiO2-Si层间的弱界面位置和特性对Love波相速度的影响,研究发现频率较高的第零阶Love波对靠近表面的弱界面更敏感,当频率趋于零和无穷时,弱界面的特性和位置对Love波第零阶的相速度没有影响.第一阶Love波的相速度在截断频率附近受弱界面影响相对显著,当频率趋于无穷时,弱界面的特性和位置对Love波第一阶的相速度影响越来越小.     

层状压电半空间中的螺位错

研究了层状压电半空间中的螺位错与界面的相互作用,应用傅立叶变换的方法,推导了压电层和基体的弹性场和电场,并在此基础上给出了像力的表达式,分析了几何尺寸和材料的相对刚度对像力和界面应力的影响.结果表明:压电效应的存在可以改变位错与界面的相互作用机理;弹性常数的差异对界面应力有较大的影响.     

Uncertainty Propagation in Layered Unsaturated Soils

This study analyzes the wetting front migration in layered unsaturated soils which have uncertain hydraulic properties. A Monte Carlo scheme was used to propagate the uncertainty of hydraulic parameters. RANUF, a computer program, was developed to solve the one-dimensional, pressure-based form of Richards' equation and to implement the Monte Carlo scheme.Uncertainty propagation was investigated for two-layered soils of various alternating fine over coarse or coarse over fine layer configurations and of various nonrandomized and/or randomized layer arrangements. The effects of changing initial and boundary conditions were also investigated. Randomness was introduced via the saturated hydraulic conductivity, K _s, which was assumed to be distributed lognormally with a coefficient of variation of about 10 percent.It was found that in layered soils the mean profiles (i.e., water content and pressure head) remained essentially unchanged regardless of which layer (or layers) was (or were) randomized; however, the variance profiles were affected. Also, higher uniform initial water content tended to inhibit uncertainty, but higher supply rates did not show any characteristic trend for uncertainty behavior.     

Pulse testing of wells in reservoirs with a nonlinear seepage law

Non-steady-state flows through porous media generated by pulse excitation are studied for flows following obeying a law with a limiting pressure gradient. The phenomena of approach to the steady-state and steady-state hysteresis due to the limiting pressure gradient are investigated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 104–110, May–June, 1998. The study was supported by the Russian Foundation for Basic Research (project No. 96-01-0748).     

层状磁电复合材料界面共线裂纹平面问题分析

本文研究了面内电磁势载荷作用下双层压电压磁复合材料中共线界面裂纹问题．考虑了压电材料的导磁性质和压磁材料的介电性质,引入了界面电位移和磁感强度的连续性条件．利用Fourier 变换得到一组第二类Cauchy 型奇异积分方程．进一步导出了相应问题的应力强度因子、电位移强度因子和磁感强度强度因子的表达式,给出了应力强度因子的数值结果．结果表明电磁载荷会导致界面裂纹尖端I、II 混合型应力奇异性,同时还伴随着电位移和磁感强度的奇异性．比较了双裂纹左右端的应力强度因子,发现在面内极化方向上施加面内磁势载荷时共线裂纹内侧尖端区域的两个法向应力场发生互相干涉增强．     

Layered Thermohaline Convection in Hypersaline Geothermal Systems

Thermohaline convection occurs in hypersaline geothermal systems due to thermal and salinity effects on liquid density. Because of its importance in oceanography, thermohaline convection in viscous liquids has received more attention than thermohaline convection in porous media. The fingered and layered convection patterns observed in viscous liquid thermohaline convection have been hypothesized to occur also in porous media. However, the extension of convective dynamics from viscous liquid systems to porous media systems is complicated by the presence of the solid matrix in porous media. The solid grains cause thermal retardation, hydrodynamic dispersion, and permeability effects. We present simulations of thermohaline convection in model systems based on the Salton Sea Geothermal System, California, that serve to point out the general dynamics of porous media thermohaline convection in the diffusive regime, and the effects of porosity and permeability, in particular. We use the TOUGH2 simulator with residual formulation and fully coupled solution technique for solving the strongly coupled equations governing thermohaline convection in porous media. We incorporate a model for brine density that takes into account the effects of NaCl and CaCl2. Simulations show that in forced convection, the increased pore velocity and thermal retardation in low-porosity regions enhances brine transport relative to heat transport. In thermohaline convection, the heat and brine transport are strongly coupled and enhanced transport of brine over heat cannot occur because buoyancy caused by heat and brine together drive the flow. Random permeability heterogeneity has a limited effect if the scale of flow is much larger than the scale of permeability heterogeneity. For the system studied here, layered thermohaline convection persists for more than one million years for a variety of initial conditions. Our simulations suggest that layered thermohaline convection is possible in hypersaline geothermal systems provided the vertical permeability is smaller than the horizontal permeability, as is likely in sedimentary basins such as the Salton Trough. Layered thermohaline convection can explain many of the observations made at the Salton Sea Geothermal System over the years.     

压电层合圆杆中的几何非线性波

利用有限变形理论,导出了描述压电层合杆中几何非线性波的传播方程.在端部作用有限振幅位移函数的边界条件下,用逐步近似法对位移函数进行了假设,推导出了一维压电杆中位移函数与电势函数之间的关系式,并应用变动参数法求解了变换得到的非齐次波动方程,得到了位移和电势的响应.数值分析表明:初始频率的改变对位移和电势的非线性特性影响不大;而初始振幅的增加会使非线性波形畸变特性明显增强.