Numerical Simulation Of Dual Laterolog In Carbonate Fractured Reservoir

Fracture is not only the fluid storage space, but also critical seepage channel of low permeability reservoir’s fluid.Due to the hard texture of carbonate,at the same time,the carbonate of itself is vulnerable to rock weathering and groundwater dissolution,which provides a basic condition for the formation of fractures.Therefore, fractures are mainly developed in the carbonate reservoir.Nowadays it seems that many of the world’s oilfields are fractured carbonate reservoir zone,such as Augila oilfield of Libya, Auk and Argyll oil field of North Sea, Egyptian Zeit Bay oil field and so on.In China,such as Tarim, Sichuan and other areas has found oil and gas resources of carbonate rocks.In view of the considerable amount, it should obtain more attention and study.In dense carbonate,the cracks are the main reservoir space and seepage channels,the carbonate may be oil and gas reservoir due to the existence of fractures,therefore study fractured carbonate become more and more important.The finite element method is a widely used numerical analysis methods,due to the advantage of the mesh division and boundary conditions,making it suitable for the numerical simulation of the dual lateral logging instrument response.The principle is that a large number of subregion substitute for the entire solution region,so that the simple interpolation function with undetermined coefficients can be used in the subregion.Therefore,the boundary value problem of the infinite degrees of freedom turn into the problem with limited degrees of freedom. The whole process includes the following basic steps:(1) The division of solving region;(2) The selection of interpolation functions;(3) The formation of the equations;(4) The solving of equations.In the conventional logging, dual laterolog is one of the logging methods which is more sensitive to crack, so taking advantage of a good corresponding relationship between the degree of fracture development and the change of resistivity,combined with the dual lateral logging method,based on the complex geological conditions of fractured carbonate reservoirs,then by means of the finite element method for fractured carbonate reservoir numerical simulation in order to study resistivity response law of fractured carbonate formation.Starting from dual lateral logging principle,based on the potential of steady flow electric field satisfies the Laplace equation,combined with the variational principle, simplified the bilateral logging solving region in the cylindrical coordinate system to two-dimensional1/2(or1/4) meridian plane,using the finite element method to solve the potential value of the corresponding strata, at last,counts the deep and shallow bilateral apparent resistivity values. I n this paper,the main contents and results:1.The selection of thedual laterral logging electrodes coefficient KMaking use of the finite element method to calculate apparent resistivity, and the selection of thedual laterral logging electrodes coefficient K will also affect the accuracy of calculated apparent resistivity,based on our uniform stratum1/4plane mesh and reasonably dealing with infinity boundary conditions,calculate the electrodes coefficient, in this paper,the deep and shallow electrodes coefficient KLLd, KLLs respectively are0.773andl.523, which the value of results and related references is basically the same.To solve the the electrodes coefficient can be calculated with the same steps forward to respond to the dual laterolog.2. Simulation of a single fractureFractured reservoirs in carbonate rocks have some characteristics,which are a wide variety of types of reservoir and powerful heterogeneity,so makes the simulation become difficult, in order to facilitate the research and theoretical analysis, the assumptions of stratigraphic model as follows:(1) Strata with rotational symmetry. i.e. Deal with the problem can be transformed into two-dimensional meridional plane.(2).The intrusion of fracture is unlimited. i.e. Liquid filled in the fractures and wellbore is blessed with similar physical properties.(3) Fracture model is flat-shaped.The relationships of deep and shallow lateral resistivity in fractured carbonate reservoirs and mud resistivity, the angle of the fracture, the fracture opening and fracturte length are simulated,and the conclusions of the simulation as follows:(1) The apparent resistivity-mud resistivityWhen the matrix resistivity of this model is Rb=10000Ω·m,fracture apertures and mud resistivity are different, the simulated results as follows:when the mud resistivity is less than100Ω·m, with the mud resistivity increases, the apparent resistivity increases, whereas, the magnitude of increase is relatively small;when mud resistivity increase from100Ω·m to1000Ω·m, the apparent resistivity increases obviously, the mud resistivity has a great impact on apparent resistivity Meanwhile,with the increase of the fracture aperture, the magnitude of the apparent resistivity increases gradually smaller.(2) Deep, shallow lateral resistivity-fracture apertureWhen the matrix resistivity and the length of fractures is the same,mud resistivity is different, the simulated results:the whole trend is apparent resistivity decreases with the increase of the fracture aperture.However, when the fracture aperture is very big,the changes of the mud resistivity have a small impact on the apparent resistivity,so fracture aperture is too large, which possess small actual value for studying.Meanwhile, the relationship between deep, shallow lateral conductivity and fracture aperture is linear, with the increase of the fracture aperture,the difference between deep lateral conductivity and shallow lateral conductivity become more and more large,and there was a linear relationship, which is consistent with the rule that the matrix conductivity Cband mud resistivity Cm are constant, deep, shallow lateral conductivity difference△C∞d.(3) Deep, shallow lateral resistivity-fracture lengthMatrix resistivity Rb=10000Ω·m,fracture aperture d=1000μm, the change of the fracture length from0.5m to10m,deep, shallow lateral resistivity is significantly reduced, when the fracture length is greater than20m, deep, shallow lateral resistivity basically was always linear, the amplitude difference is essentially the same; at the same time, the smaller the mud resistivity,the smaller deep, shallow resistivity, which is just verify the front of the mud resistivity impact on the deep,shallow lateral resistivity in fractured formation.(4) Deep, shallow lateral resistivity-fracture dipMatrix resistivity, mud resistivity and the fracture length are constant, fracture aperture is not the same, when the fracture dip angle is smaller than a certain angle(known as the critical angle), shallow lateral resistivity Rlls greater than the deep lateral resistivity Rlld,i.e.negative difference, and with the increase of dip, negative difference gradually decreases; when fractures of inclination greater than the critical angle, the deep lateral resistivity Rlld is greater than the shallow lateral resistivity Rlls, namely the positive difference, and with the increase of inclination, the difference gradually become larger. When the fracture apertures are different,the relationship between changes of fracture dip and resistivity comply with the above laws.Given different bedrock resistivity Rb, the smaller matrix resistivity, the smaller the critical angle.The results of simulation and the relevant references are basically the same, so that the simulation results are correct,which is proved. Owing to the sake of modeling and meshing, the fracture simulated in this paper is too large, it is necessary to further improve and perfect. It suggested that the studies of fractures in carbonate reservoir should further simulate the rules of variation of bilateral resistivity in the situation that with multiple fractures and minimize fractures, in order to further more understanding fractured carbonate reservoir, and it is more valuable.