油藏数值模拟中井筒压力梯度的校正方法

有限元法用于油藏数值模拟具有独特的优越性.由于井筒附近流动的特殊性,直接采用数值模拟得到的压力梯度计算油井产量会导致较大的误差.本文分析了数值模拟中井筒压力梯度产生误差的原因,在此基础上提出了计算井筒压力梯度的校正公式.计算结果表明,压力梯度校正公式可显著提高油井产量的计算精度,并能有效地减少井筒附近的网格剖分数量,从而提高了计算效率.

三维油藏数值模拟正反演算法研究

The dynamic prediction of complex reservoir development is one of the important research contents of dynamic analysis of oil and gas development. With the increase development of time, the permeabilities and porosities of reservoirs and the permeability of block reservoir at its boundaries are dynamically changing. How to track the dynamic change of permeability and porosity and make certain the permeability of block reservoir at its boundary is an important practical problem. To study developing dynamic prediction of complex reservoir, the key problem of research of dynamic prediction of complex reservoir development is realizing inversion of permeability and porosity. To realize the inversion, first of all, the fast forward and inverse method of 3-dimension reservoir simulation must be studied. Although the inversion has been widely applied to exploration and logging, it has not been applied to3-dimension reservoir simulation. Therefore, the study of fast forward and inverse method of 3-dimension reservoir simulation is a cutting-edge problem, takes on important realistic signification and application value. In this dissertation, 2-dimension and 3-dimension fluid equations in porous media are discretized by finite difference, obtaining finite difference equations to meet the inner boundary conditions by Peaceman's equations, giving successive over relaxation iteration of 3-dimension fluid equations in porous media and the dimensional analysis. Several equation-solving methods are compared in common use, analyzing its convergence and convergence rate. The alternating direction implicit procedure of 2-dimension has been turned into successive over relaxation iteration of alternating direction implicit procedure of 3-dimension fluid equations in porous media, which possesses the virtues of fast computing speed, needing small memory of computer, good adaptability for heterogeneous media and fast convergence rate. The geological model of channel-sandy reservoir has been generated with the help of stochastic simulation technique, whose cross sections of channel-sandy reservoir are parabolic shapes. This method makes the hard data commendably meet, very suit for geological modeling of containing complex boundary surface reservoir. To verify reliability of the method, theoretical solution and numerical solution are compared by simplifying model of 3-dimension fluid equations in porous media, whose results show that the only difference of the two pressure curves is that the numerical solution is lower than theoretical at the wellbore in the same space. It proves that using finite difference to solve fluid equations in porous media is reliable. As numerical examples of 3-dimension heterogeneous reservoir of the single-well and multi-well, the pressure distributions have been computed respectively, which show the pressure distributions there are clearly difference as difference of the permeabilities is greater than one order of magnitude, otherwise there are no clearly difference. As application, the pressure distribution of the channel-sandy reservoir have been computed, which indicates that the space distribution of pressure strongly relies on the direction of permeability, and is sensitive for space distributions of permeability. In this dissertation, the Peaceman's equations have been modified into solving vertical well problem and horizontal well problem simultaneously. In porous media, a 3D layer reservoir in which contain vertical wells and horizontal wells has been calculated with iteration. For channel-sandy reservoir in which there are also vertical wells and horizontal wells, a 3D transient heterogeneous fluid equation has been discretized. As an example, the space distribution of pressure has been calculated with iteration. The results of examples are accord with the fact, which shows the modification of Peaceman's equation is correct. The problem has been solved in the space where there are vertical and horizontal wells. In the dissertation, the nonuniform grid permeability integration equation upscaling method, the nonuniform grid 2D flow rate upscaling method and the nonuniform grid 3D flow rate upscaling method have been studied respectively. In those methods, they enhance computing speed greatly, but the computing speed of 3D flow rate upscaling method is faster than that of 2D flow rate upscaling method, and the precision of 3D flow rate upscaling method is better than that of 2D flow rate upscaling method. The results also show that the solutions of upscaling method are very approximating to that of fine grid blocks. In this paper, 4 methods of fast adaptive nonuniform grid upscaling method of 3D fluid equations in porous media have been put forward, and applied to calculate 3D heterogeneous reservoir and channel-sandy reservoir, whose computing results show that the solutions of nonuniform adaptive upscaling method of 3D heterogeneous fluid equations in porous media are very approximating to that of fine grid blocks in the regions the permeability or porosity being abnormity and very approximating to that of coarsen grid blocks in the other region, however, the computing speed of adaptive upscaling method is 100 times faster than that of fine grid block method. The formula of sensitivity coefficients are derived from initial boundary value problems of fluid equations in porous media by Green's reciprocity principle. The sensitivity coefficients of wellbore pressure to permeability parameters are given by Peaceman's equation and calculated by means of numerical calculation method of 3D transient anisotropic fluid equation in porous media and verified by direct method. The computing results are in excellent agreement with those obtained by the direct method, which shows feasibility of the method. In the dissertation, the calculating examples are also given for 3D reservoir, channel-sandy reservoir and 3D multi-well reservoir, whose numerical results indicate: around the well hole, the value of the sensitivity coefficients of permeability is very large, the value of the sensitivity coefficients of porosity is very large too, but the sensitivity coefficients of porosity is much less than the sensitivity coefficients of permeability, so that the effect of the sensitivity coefficients of permeability for inversion of reservoir parameters is much greater than that of the sensitivity coefficients of porosity. Because computing the sensitivity coefficients needs to call twice the program of reservoir simulation in one iteration, realizing inversion of reservoir parameters must be sustained by the fast forward method. Using the sensitivity coefficients of permeability and porosity, conditioned on observed valley erosion thickness in wells (hard data), the inversion of the permeabilities and porosities in the homogeneous reservoir, homogeneous reservoir only along the certain direction and block reservoir are implemented by Gauss-Newton method or conjugate gradient method respectively. The results of our examples are very approximating to the real data of permeability and porosity, but the convergence rate of conjugate gradient method is much faster than that of Gauss-Newton method.

砂砾岩储层流动单元四维模型研究

This article is an important part of "95" technological subject of SINOPEC. It has a large number of difficulties and workloads, and has significant theoretical meanings and practical value. The study area is composed of sandstone & conglomerate reservoir of alluvial fan & fan delta, which belong to Sha3 lower member and Sha4 upper member of lower tertiary of Yong'an Town Oilfield in Dongying Depression. The target stataum develops in the hanging wall of the synsedimentary fault in the scarp zone of Dongying Depression. The frequently intense movements result in the variation of sandstone and conglomerate reservoir and the evolution of the time and space of Sha3 lower member and Sha4 upper member in Yong'an Town Oilfield. As a result, it is difficult for the individual reservoir correlation at the root of fan, which bring about a tackle problem for the exploitation of oilfield. In this background, the research of fluid units will be more difficult. In this article, the new concepts, the new methods, and the new techniques of sedimentology, petroleum geology, reservoir geology, physics of crystal surface, dynamic & static state reservoir description and well logging geology are synthetically applied, and the computer technology are made full uses of, and the identifying, dividing and appraising of the two-formation-type sandstone & conglomerate reservoir fluid units of Sha3 lower member and Sha4 upper member systemically analyzed in Yong'an Town Oilfield, Dongying Depression. For the first time, the single-well model, the section model, the plane model, the nuclear magnetism log model, the microcosmic network model, the 4-D geology model and the simulation model of the two-formation-type reservoir fluid units of the of sandstone & conglomerate reservoir of Sha3 lower member and Sha4 upper member are established, and the formative mechanism and distributing & enrichment laws of oil-gas of the two type of sandstone and conglomerate reservoir fluid units are revealed. This article established the optimizing, identifying, classifying and appraising standard of the two-formation-type reservoir fluid units of the of sandstone and conglomerate reservoir of Sha3 lower member and Sha4 upper member, which settles the substantial foundations for static state model of the fluid units, reveals the macroscopic & microcosmic various laws of geometrical static state of the fluid units, and instructs the oil exploitation. This article established static state model of the two-formation-type sandstone and conglomerate reservoir fluid units by using the multi-subject theories, information and techniques, and reveals the geometrical configuration, special distribution and the oil-gas enrichment laws of the sandstone and conglomerate reservoir fluid units. For the first time, we established the nuclear magnetism log model of the two-formation-type sandstone and conglomerate reservoir of Sha3 lower member and Sha4 upper member, which reveals not only the character and distributing laws of the porosity and permeability, bat also the formation and distribution of the movable fluid. It established six type of microcosmic net model of the two-formation-type sandstone and conglomerate reservoir of Sha3 lower member and Sha4 upper member in the working area by using the advanced theories, such as rock thin section, SEM, image analysis, intrusive mercury, mold, rock C.T. measure & test image etc., which reveals the microcosmic characteristic of porosity & throat, filterate mode and microcosmic oil-gas enrichment laws of the sandstone and conglomerate reservoir. For the first time, it sets up the 4-D model and mathematic model of the sandstone and conglomerate reservoir, which reveals the distributing and evolving laws of macroscopic & microcosmic parameters of the two-formation-type sandstone and conglomerate reservoir and oil-gas in 4-D space. At the same time, it also forecasts the oil-gas distribution and instructs the oilfield exploitation. It established reservoir simulation model, which reveals the filterate character and distributing laws of oil-gas in different porosity & throat net models. This article established the assistant theories and techniques for researching, describing, indicating and forecasting the sandstone and conglomerate reservoir fluid units, and develops the theories and techniques of the land faces faulted basin exploitation geology. In instructing oilfield exploitation, it had won the notable economic & social benefits.

古潜山油藏非均质三维地质建模

The discovery of the highly productive Renqiu buried hill reservoir in Bohai Bay Basin in 1975 started the high tide of finding buried hill reservoirs in China and their research. As the advance of E&P technologies, the study of buried hill reservoir in China had a qualitative leap. The reservoir description and some other aspects of development have reached or approached to the international leading level. However, some core techniques for reservoir study such as structure & faulting system study, formation prediction and connection study and heterogeneous model's construction could not completely carry out the quantitative or accurate reservoir description, e. g. the areal distribution of porosity, permeability and oil saturation. Especially, the modeling for reservoir simulation is still wandering in the stage of simplicity. The inaccurate understanding of geology could not derive 3D heterogeneous geological model that can reveal the actual underground situation thus could not design practical and feasible oilfield development plan. Therefore, the problems of low oil recovery rate, low recovery factor and poor development effectiveness have not been solved. The poor connection of the reservoir determined that waterflooding could not get good development effect and the production had to depend on the reservoir elastic energy, and this will bring big difficulty for development modification and improvement of oil recovery. This study formed a series of techniques for heterogeneous model research that can be used to construct heterogeneous model consistent with the reservoir geology. Thus the development effectiveness, success ratio of drilling and percent of producing reserves can be enhanced. This study can make the development of buried hill reservoir be of high recovery rate and high effect. The achievements of this study are as follows: 1. Evaluated the resources, summarized the geological characteristics and carried out the reservoir classification of the buried hill reservoirs in Shengli petroliferous area; 2. Established the markers for stratigraphical correlation and formed the correlation method for complex buried hill reservoirs; 3. Analyzed the structural features of the buried hill reservoirs, finished the structure interpretation and study of faulting system using synthetic seismograms, horizontal slices and coherent analysis, and clarified structural development history of the buried hill reservoirs in Shengli petroliferous area; 4. Determined the 3 classes and 7 types of pore space and the main pore space type, the logging response characteristics and the FMI logging identified difference between artificial and natural fractures by the comprehensive usage of core analysis, other lab analyses, conventional logging, FMI logging and CMR logging; 5. Determined the factors controlled the growth of the fractures, vugs and cavities, proposed the main formation prediction method for buried hill reservoir and analyzed their technical principium and applicability, and formed the seismic method and process for buried hill reservoir description; 6. Established the reserve calculation method for buried hill reservoirs, i. e. the reserves of fractures and matrix are calculated separately; the recoverable reserves are calculated by decline method and are classified by the SPE criteria; 7. Studied restraining barriers and the sealing of the faults thus clarified the oil-bearing formations of the buried hill reservoirs, and verified the multiple reservoir forming theory; 8. Formed reasonable procedure of buried hill reservoir study; 9. Formed the 3 D modeling technology for buried hill reservoirs; 10. Studied a number of buried hill blocks on the aspects of reservoir description, reservoir engineering and development plan optimization based on the above research and the profit and social effect are remarkable.

油藏数值模拟中的网格粗化和细化技术研究

The grid is a foundation of reservoir description and reservoir simulation. The scale of grid size is vital influence for the precision of reservoir simulation the gridding of reservoir parameters require reasonable interpolation method with computing quickly and accurately. The improved distant weighted interpolation method has many properties, such as logical data points selection, exact interpolation, less calculation and simply programming, and its application can improve the precision of reservoir description and reservoir simulation. The Fractal geologic statistics describes scientifically the distribution law of various geological properties in reservoir. The Fractal interpolation method is applied in grid interpolation of reservoir parameters, and the result more accorded with the geological property and configuration of reservoir, and improved the rationality and quality of interpolation calculation. Incorporating the improved distant weighted interpolation method with Fractal interpolation method during mathematical model of grid-upscaling and grid-downscaling, the softwares of GROUGH(grid-upscaling) and GFINE (grid-downscaling) were developed aiming at the questions of grid-upscaling and grid-downscaling in reservoir description and reservoir simulation. The softwares of GROUGH and GFINE initial applied in the research of fined and large-scale reservoir simulation. It obtained fined distribution of remaining oil applying grid-upscaling and grid-downscaling technique in fined reservoir simulation of Es21-2 Shengtuo oilfield, and provided strongly and scientific basis for integral and comprehensive adjustment. It's a giant tertiary oil recovery pilot area in the alkaline/surfactant/polymer flooding pilot area of west district of Gudao oilfield, and first realized fined reservoir simulation of chemical flooding using grid-upscaling and grid-downscaling technique. It has wide applied foreground and significant research value aiming at the technique of grid-upscaling and grid-downscaling in reservoir description and reservoir simulation.

Sensitivity Analysis of Dimensionless Parameters for Physical Simulation of Water-Flooding Reservoir

A numerical approach to optimize dimensionless parameters of water-flooding porous media flows is proposed based on the analysis of the sensitivity factor defined as the variation ration of a target function with respect to the variation of dimensionless parameters. A complete set of scaling criteria for water-flooding reservoir of five-spot well pattern case is derived from the 3-D governing equations, involving the gravitational force, the capillary force and the compressibility of water, oil and rock. By using this approach, we have estimated the influences of each dimensionless parameter on experimental results and thus sorted out the dominant ones with larger sensitivity factors ranging from10-4to10-0 .

A coupled model for multiphase fluid flow and sedimentation deformation in oil reservoir and its numerical simulation

A mathematical model for coupled multiphase fluid flow and sedimentation deformation is developed based on fluid-solid interaction mechanism. A finite difference-finite element numerical approach is presented. The results of an example show that the fluid-solid coupled effect has great influence on multiphase fluid flow and reservoir recovery performances, and the coupled model has practical significance for oilfield development.

Simulation of Natural Gas Production in Hydrate Reservoirs

This paper simulates a one-dimensional physical model of natural gas production from hydrate dissociation in a reservoir by depressurization. According to the principles of solid hydrate decomposition in stratum and flow of natural gas in porous medium, the pressure governing equations for both gas zone and hydrate zone are set up based on the physical production model. Using the approximation reported by N. N. Verigin et al. (1980), the nonlinear governing equations are simplified and the self-similar solutions are obtained. Through calculation, for different reservoir parameters, the distribution characters of pressure are analyzed. The decline trend of natural gas production rate with time is also studied. The simulation results show that production of natural gas from a hydrate reservoir is very sensitive to several reservoir parameters, such as wellbore pressure and stratum porosity and permeability.

The Experimental and Numerical Studies on Gas Production from Hydrate Reservoir by Depressurization

A set of experimental system to study hydrate dissociation in porous media is built and some experiments on hydrate dissociation by depressurization are carried out. A mathematical model is developed to simulate the hydrate dissociation by depressurization in hydrate-bearing porous media. The model can be used to analyze the effects of the flow of multiphase fluids, the kinetic process and endothermic process of hydrate dissociation, ice-water phase equilibrium, the variation of permeability, convection and conduction on the hydrate dissociation, and gas and water productions. The numerical results agree well with the experimental results, which validate our mathematical model. For a 3-D hydrate reservoir of Class 3, the evolutions of pressure, temperature, and saturations are elucidated and the effects of some main parameters on gas and water rates are analyzed. Numerical results show that gas can be produced effectively from hydrate reservoir in the first stage of depressurization. Then, methods such as thermal stimulation or inhibitor injection should be considered due to the energy deficiency of formation energy. The numerical results for 3-D hydrate reservoir of Class 1 show that the overlying gas hydrate zone can apparently enhance gas rate and prolong life span of gas reservoir.

Energy conversion in shape memory alloy heat engine - Part II: Simulation

In this paper, a theoretical model proposed in Part I (Zhu et al., 2001a) is used to simulate the behavior of a twin crank NiTi SMA spring based heat engine, which has been experimentally studied by Iwanaga et al. (1988). The simulation results are compared favorably with the measurements. It is found that (1) output torque and heat efficiency decrease as rotation speed increase; (2) both output torque and output power increase with the increase of hot water temperature; (3) at high rotation speed, higher water temperature improves the heat efficiency. On the contrary, at low rotation speed, lower water temperature is more efficient; (4) the effects of initial spring length may not be monotonic as reported. According to the simulation, output torque, output power and heat efficiency increase with the decrease of spring length only in the low rotation speed case. At high rotation speed, the result might be on the contrary.

Molecular dynamics simulation of the role of dislocations in microcrack healing

The molecular dynamics method is used to simulate microcrack healing during heating or/and under compressive stress. A centre microcrack in Cu crystal would be sealed under compressive stress or by heating. The role of compressive stress and heating in crack healing was additive. During microcrack healing, dislocation generation and motion occurred. When there were pre-existing dislocations around the microcrack, the critical temperature or compressive stress necessary for microcrack healing would decrease, and, the higher the number of dislocations, the lower the critical temperature or compressive stress. The critical temperature necessary for microcrack healing depended upon the orientation of the crack plane. For example, the critical temperature for the crack along the (001) plane was the lowest, i.e. 770K.