MATHEMATICAL MODEL OF TWO-PHASE FLUID NONLINEAR FLOW IN LOW-PERMEABILITY POROUS MEDIA WITH APPLICATIONS

A mathematical model of two-phase fluid nonlinear flow in the direction of normal of ellipse through low-permeability porous media was established according to a nonlinear flow law expressed in a continuous function with three parameters, a mass conservation law and a concept of turbulent ellipses. A solution to the model was obtained by using a finite difference method and an extrapolation method. Formulas of calculating development index not only before but also after water breaks through an oil well in the condition of two-phase fluid nonlinear flow in the media were derived. An example was discussed. Water saturation distribution was presented. The moving law of drainage front was found. Laws of change of pressure difference with time were recognized. Results show that there is much difference of water saturation distribution between nonlinear flow and linear flow; that drainage front by water moves faster, water breaks through sooner and the index gets worse because of the nonlinear flow; and that dimensionless pressure difference gets larger at the same dimensionless time and difficulty of oil development becomes bigger by the nonlinear flow. Thus, it is necessary that influence of nonlinear flow on development indexes of the oil fields be taken into account. The results provide water-flooding development of the oilfields with scientific basis.

THE TRANSIENT ELLIPTIC FLOW OF POWER-LAW FLUID IN FRACTAL POROUS MEDIA

The steady oil production and pressure distribution formulae of vertically fractured well for power-law non-Newtonian fluid were derived on the basis of the elliptic flow model in fractal reservoirs. The corresponding transient flow in fractal reservoirs was studied by numerical differentiation method: the influence of fractal index to transient pressure of vertically fractured well was analyzed. Finally the approximate analytical solution of transient flow was given by average mass conservation law. The study shows that using elliptic flow method to analyze the flow of vertically fractured well is a simple method.

Effect of absorption boundary layer on nonlinear flow in low permeability porous media

Taking low permeability cores of Daqing oilfield for example,the flow characteristics at low velocity were studied with the self-designed micro-flux measuring instrument.Considering the throat distribution and capillary model,the thickness of fluid boundary layer under different pressure gradients was calculated,and the mechanism and influencing factors of nonlinear percolation were discussed.The results show that the percolation curve of ultra-low rocks is nonlinear,and apparent permeability is not a constant which increases with pressure gradient.The absorption boundary layer decreases with the increase of pressure gradient,and changes significantly especially in low pressure gradient,which is the essence of nonlinear percolation.The absorption boundary layer is also found to be impacted by the surface property of rocks.

ANALYTICAL SOLUTION OF FLOW OF SECOND-ORDER NON-NEWTONIAN FLUIDS THROUGH ANNULAR PIPES

This paper presents an analytical solution to the unsteady flow of the second-order non-Newtonian fluids by the use of intergral transformation method. Based on the numerical results, the effect of non-Newtonian coefficient Hc and other parameters on the flow are analysed. It is shown that the annular flow has a shorter characteristic time than the general pipe flow while the correspondent velocity, average velocity have a ... nailer value for a given Hc. Else, when radii ratio keeps unchanged, the shear stress of inner wall of annular flow will change with the inner radius -compared with the general pipe flow and is always smaller than that of the outer wall.

Law of nonlinear flow in saturated clays and radial consolidation

It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and test ones. Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow. Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius. The interaction is an important reason why nonlinear flow in saturated clays occurs. An exact mathematical model was presented for nonlinear flow in micro-scale pore of saturated clays. Dimension and physical meanings of parameters of it are definite. A new law of nonlinear flow in saturated clays was established. It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one. Darcy law is a special case of the new law. A math- ematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow. Equations of average mass conservation and moving boundary, and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer, a method of steady state in stead of transient state and a method of integral of an equation. Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained. Re- sults show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay. The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases. Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.

LOCAL DISCONTINUOUS GALERKIN METHOD FOR RADIAL POROUS FLOW WITH DISPERSION AND ADSORPTION

Based on the local discontinuous Galerkin methods for time-dependent convection-diffusion systems newly developed by Corkburn and Shu,according to the form of the generalized convection-diffusion equations which model the radial porous flow with dispersion and adsorption,a local discontinuous Galerkin method for radial porous flow with dispersion and adsorption was developed,a high order accurary new scheme for radial porous flow is obtained.The presented method was applied to the numerical tests of two cases of radial porous,i.e., the convection-dispersion flow and the convection-dispersion-adsorption flow,the corresponding parts of the numerical results are in good agreement with the published solutions,so the presented method is reliable.Reckoning of the computational cost also shows that the method is practicable.

Investigation on Mechanisms of Polymer Enhanced Oil Recovery by Nuclear Magnetic Resonance and Microscopic Theoretical Analysis

聚合物泛滥是一种有效技术在水泛滥上提高油恢复。关于为聚合物泛滥提高油恢复的机制有大量讨论。主要焦点是聚合物泛滥是否能增加把效率弄独自一个，或能增加两个打扫效率和排水量效率。我们在场这个问题上的研究。4 个自然核心的油排水量实验证明聚合物泛滥能在水上增加油恢复效率超过 12% 。而且，相片被原子磁性的回声(NMR ) 在水泛滥以后并且在聚合物泛滥以后两个都花方法，它在中间的十字显示出留下的油浸透分发节和中央纵的节。这些相片的分析证明聚合物泛滥罐头增加两个都打扫效率和排水量效率。

Nonlinear Flow Numerical Simulation of an Ultra-Low Permeability Reservoir

非线性的流动数学模型被建立，格子方程被推出。一座非线性的流动水库数字模拟节目被编译。渗透损失系数被用来描述渗透损失。飞行员计算根据实际的域数据被做，它反映水库开发特征。数字模拟节目能更确切基于非线性的流动期望极端低的渗透水库利用的动态特征。[从作者抽象]

Mechanism of gas-water flow at pore-level in aquifer gas storage

By means of the pore-level simulation, the characteristics of gas-water flow and gas-water distribution during the alternative displacement of gas and water were observed directly from etched-glass micromodel. The results show that gas-water distribution styles are divided into continuous phase type and separate phase type. The water lock exists in pore and throat during the process of gas-water displacement, and it reduces the gas flow-rate and has some effects on the recovery efficiency during the operation of gas storage. According to the experimental results of aquifer gas storage in X area, the differences in available extent among reservoirs are significant, and the availability of pore space is 33% 45%.

Nuclear Magnetic Resonance Measurements of Original Water Saturation and Mobile Water Saturation in Low Permeability Sandstone Gas

We use nuclear magnetic resonance （NMR） and centrifugation to measure the original water saturation and mobile water saturation of cores from the Xujiahe low permeability sandstone gas reservoir, and compare the NMR results with the corresponding field data. It is shown that the NMR water saturation after 300psi centrifugation effectively represents the original water saturation measured by weighing fresh cores. There is a good correlation between mobile water saturation and the water production performance of the corresponding gas wells. The critical mobile water saturation whether reservoir produces water of the Xujiahe low permeability sandstone gas is 6%. The higher the mobile water saturation, the greater the water production rate of gas well. This indicates that well＇s water production performance can be forecasted by mobile water saturation of cores.

An overview on nonlinear porous flow in low permeability porous media

This paper gives an overview on nonlinear porous flow in low permeability porous media, reveals the microscopic mechanisms of flows, and clarifies properties of porous flow fluids. It shows that, deviating from Darcy＇s linear law, the porous flow characteristics obey a nonlinear law in a low-permeability porous medium, and the viscosity of the porous flow fluid and the permeability values of water and oil are not constants. Based on these characters, a new porous flow model, which can better describe low permeability reservoir~ is established. This model can describe various patterns of porous flow, as Darcy＇s linear law does. All the parameters involved in the model, having definite physical meanings, can be obtained directly from the experiments.

U-Pb Isotope Geochronology of Syntectonic Granites from Hainan Island,South China:Constraints on Tectonic Evolution of the Eastern Paleo-Tethys Ocean

Since the recognition of the Indosinian orogeny in northern Vietnam,Triassic orogens have been widely identified around the western and southwestern boundaries of the South China block.The paleo-Tethys sutures stretch from west to southeast,from Jinshajiang-Ailaoshan via NE Vietnam to Hainan Island;these sutures exhibit and develop voluminous Permian-early Triassic magmatism and numerous high-strain shear zones.As ophiolites related to the paleo-Tethys are lacking on Hainan Island,the eastward extension of the Indosinian orogeny and subduction and closure time of the paleo-Tethys Ocean on Hainan Island remain controversial.Here,an integrated kinematic and geochronological study has been conducted on two shear zones,called the Xiaomei and Mangsan shear zones.U-Pb zircon dating yields an age of early Triassic(252-251 Myr)for Xiaomei syntectonic granites which formed in the same tectonic setting and presented the similar nanoparticles to the Indosinian granites from Ailaoshan ductile shear zone,including the strawberry-like and flower-like nanoparticles.The NE-trending Mangsan shear zone represented by the gneissic granites with middle Permian ages(264-262 Myr)formed in the same tectonic setting as the Wuzhi-shan granites that were proposed as I-type granites.These middle Permian gneissic granites with arc affinity may represent an arc setting related to the NW subduction of the paleo-Tethys.The analyses reveal that granites with late Triassic ages(235-232 Myr)in the Xiaomei shear zone have the characteristics of A-type granites.The late Triassic extensional events on Hainan Island may be related to the subduction of the paleo-Pacific Plate beneath the East Asian continent.

The Effect of Gas Leaks on Underground Gas Storage Performance During Development and Operation

Underground gas storage is an efficient tool for matching the constant supply of gas to the variable demands of the market.Gas escaping from a storage field may cause environmental and safety problems.We present a physical simulation together with actual field data to evaluate the caprock of underground gas storage in the Jing-Bian area.The effect of gas leaks on the performance of gas storage is analyzed by using the type curves of the injection-withdrawal cycle.

NEW STUDYING OF LATTICE BOLTZMANN METHOD FOR TWO-PHASE DRIVEN IN POROUS MEDIA

By using the interaction of particles, such as the physical principle of the same attract each other and the different repulse each other, a new model of Lattice Boltzmann to simulate the two-phase driven in porous media was discussed. The result shows effectively for the problem of two-phase driven in porous media. Furthermore, the method economizes on computer time, has less fluctuation on boundary surface and takes no average measure.

Experimental evaluation on well pattern adaptability of ultra-low permeability reservoir using sandstone flat model

As for ultra-low permeability reservoir,the adaptability of common nine-spot well pattern is studied through large-scale flat models made by micro-fractured natural sandstone outcrops.Combined with non-linear porous flow characteristics,the concept of dimensionless pressure sweep efficiency and deliverability index are put forward to evaluate the physical models' well pattern adaptability.Through experiments,the models' pressure distribution is measured and on which basis,the pressure gradient fields are drawn and the porous flow regions of these models are divided into dead oil region,non-linear porous flow region,and quasi-linear porous flow region with the help of twin-core non-linear porous flow curve.The results indicate that rectangular well pattern in fracture reservoirs has the best adaptability,while the worst is inverted nine-spot equilateral well pattern.With the increase of drawdown pressure,dead oil region decreases,pressure sweep efficiency and deliverability index increase; meantime,the deliverability index of rectangular well pattern has much more rational increase.Under the same drawdown pressure,the rectangular well pattern has the largest pressure sweep efficiency.

SENSITIVITY COEFFICIENTS OF SINGLE-PHASE FLOW IN LOW-PERMEABILITY HETEROGENEOUS RESERVOIRS

Theoretical equations for computing sensitivity coefficients of wellbore pressures to estimate the reservoir parameters in low-permeability reservoirs conditioning to non-Darcy flow data at low velocity were obtained. It is shown by a lot of numerical calculations that the wellbore pressures are much more sensitive to permeability very near the well than to permeability a few gridblocks away from the well. When an initial pressure gradient existent sensitivity coefficients in the region are closer to the active well than to the observation well. Sensitivity coefficients of observation well at the line between the active well and the observation well are influenced greatly by the initial pressure gradient.

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.

Geophysical and Production Data History Matching Based on Ensemble Smoother with Multiple Data Assimilation

The Ensemble Kalman Filter(EnKF),as the most popular sequential data assimilation algorithm for history matching,has the intrinsic problem of high computational cost and the potential inconsistency of state variables updated at each loop of data assimilation and its corresponding reservoir simulated result.This problem forbids the reservoir engineers to make the best use of the 4D seismic data,which provides valuable information about the fluid change inside the reservoir.Moreover,only matching the production data in the past is not enough to accurately forecast the future,and the development plan based on the false forecast is very likely to be suboptimal.To solve this problem,we developed a workflow for geophysical and production data history matching by modifying ensemble smoother with multiple data assimilation(ESMDA).In this work,we derived the mathematical expressions of ESMDA and discussed its scope of applications.The geophysical data we used is P-wave impedance,which is typically included in a basic seismic interpretation,and it directly reflects the saturation change in the reservoir.Full resolution of the seismic data is not necessary,we subsampled the P-wave impedance data to further reduce the computational cost.With our case studies on a benchmark synthetic reservoir model,we also showed the supremacy of matching both geophysical and production data,than the traditional reservoir history matching merely on the production data:the overall percentage error of the observed data is halved,and the variances of the updated forecasts are reduced by two orders of the magnitude.

Water coning mechanism in Tarim fractured sandstone gas reservoirs

The problem of water coning into the Tarim fractured sandstone gas reservoirs becomes one of the major concerns in terms of productivity, increased operating costs and environmental effects. Water coning is a phenomenon caused by the imbalance between gravity and viscous forces around the completion interval. There are several controllable and uncontrollable parameters influencing this problem. In order to simulate the key parameters affecting the water coning phenomenon, a model was developed to represent a single well with an underlying aquifer using the fractured sandstone gas reservoir data of the A-Well in Dina gas fields.The parametric study was performed by varying six properties individually over a representative range. The results show that matrix permeability, well penetration(especially fracture permeability), vertical-to-horizontal permeability ratio, aquifer size and gas production rate have considerable effect on water coning in the fractured gas reservoirs. Thus, investigation of the effective parameters is necessary to understand the mechanism of water coning phenomenon. Simulation of the problem helps to optimize the conditions in which the breakthrough of water coning is delayed.

DYNAMIC PRODUCTION PREDICTION AND PARAMETER IDENTIFICATION FOR GAS WELL WITH VERTICAL FRACTURE

In order to devoid the hard work and factitious error in selecting charts while analyzing and interpreting hydraulic fracturing fracture parameters, on the basis of the non-Darcy flow factor, this paper put out the non-Darcy flow mathematical model of real gas in the formation and fracture, established the production history automatic matching model to identify fracture parameters, and offered the numerical solutions of those models, which took the variation of fracture conductivity in production process. These results offered a precise and reliable method to understand formation, analyze and evaluate the fracturing treatment quality of gas well.