Wave Field Modeling In Fractured Porous Media And Frequency-dependent AVO Reservoir Parameters Inversion

With the deepening of the degree of oil and gas exploration and development,fractured reservoirs will become more and more important in the worldwide oil andgas exploration and development. The relationship between seismic data and reservoircharacteristics is build with the equivalent medium model for fractured reservoirsmedia. Traditional equivalent medium model do not consider the existence of thepores of the rock, cannot give a reasonable explanation for seismic wave dispersionand attenuation in actual fractured reservoirs, the information about fracture azimuthand fracture density can be got with the use of seismic wave propagation theory infractured reservoirs which is established based on traditional equivalent mediummodel, but the information about fracture geometry (such as fracture size, fractureaperture) can’t be got. However, the information about fracture geometry has animportant effect on reservoir permeability. Therefore，in order to achieve sophisticateddescription of fractured reservoirs, the more perfect equivalent medium model offractured reservoirs media should be used to research issues related to fracturedreservoirs, and then by using the established seismic wave propagation theory toobtain more reservoir information such as the information about fracture geometry, soas to realize the qualitative evaluation of the reservoir and reservoir parametersinversion.In fact, fractured reservoir is a kind of fractured porous media containing fractures,pore space of rocks and fluid. The equivalent medium models for fractured porousmedia can describe the property of the actual fractured reservoirs media moreaccurately. To research wave phenomena and recognize seismic wave propagation law and the response characteristics in fractured porous media through the correspondingequivalent medium model can provide new technical ideas for fractured reservoirprediction, fluid identification and reservoir parameters inversion. This paper analyzesthe characteristics of several common equivalent medium models for fractured porousmedia, the equivalent medium model of Chapman (2003) can give a reasonableexplanation for seismic wave dispersion and attenuation in fractured reservoirs, It hasmore advantages than other models on the description of the property of fracturedreservoirs media, moreover, the existing investigation for some practical applicationsshow that fracture size, fracture density and fracture azimuth can be inverted fromfield observation data with the use of the reservoir parameter inversion methodadvanced based on this model, this model has good application prospect. Therefore,this paper researches the issues related to fractured porous media based on Chapmanmodel, such as the characteristics analysis of seismic wave propagation in fracturedporous media, numerical simulation of wave field, frequency-dependent amplitudeversus offset analysis and reservoir parameter inversion.In order to fully understand seismic wave dispersion, attenuation, azimuthanisotropy and other characteristics in fractured reservoirs, this paper carry outseismic wave propagation characteristics research in fractured porous media based onChapman model. First, begin with frequency domain wave equation for HTI media,the Christoffel equation in the three-dimension HTI media based on Chapman modelis derived by assuming plane harmonic solution of various wave. Then, throughsolving the dispersion relation equation to determine the complex velocity and givethe expressions of phase velocity and quality factor. On this basis, researching theeffect of incidence angle, permeability, fracture size, fracture density and fluid type onseismic wave dispersion and attenuation, and analyzing the azimuth characteristics ofdispersion and attenuation and its influencing factors, meanwhile, through frequency-dependent shear wave splitting and the frequency-dependent property of Thomsenparameters to analyze frequency-dependent anisotropy characteristics of fracturedreservoirs media. The results show that when quasi P wave or quasi SV wave througha fractured porous rock, It will induce fluid flow occurs between fractures and pores result in velocity dispersion and attenuation, as to quasi SH wave, It will not squeezethe fractures and induce fluid flow, thus no velocity dispersion and attenuation.Because of the fractures are aligned in space, then velocity dispersion and attenuationwill show azimuth anisotropy, and then seismic anisotropy and shear wave splittingwill show frequency-dependent. Incidence angle, fracture density, permeability,fracture size and fluid type have important effect on seismic wave dispersion andattenuation. Incidence angle, fracture density, fracture size and fluid type have alsoeffect on the azimuth characteristics of phase velocity and attenuation. Meanwhile,frequency-dependent anisotropy and shear wave splitting will also be affected byfracture density, fracture size and fluid type.In order to reveal seismic wave dispersion, attenuation and frequency-dependentanisotropy caused by wave-induced mesoscopic fluid flow in fractured porous mediafrom the angle of the wave field forward modeling, and then to study the mechanismof seismic wave propagation and seismic response characteristics in fractured porousmedia, this paper advances a time-domain numerical simulation method of wave fieldin fractured porous media based on Chapman model. According to the characteristicsthat the effective stiffness coefficients of Chapman model are complex andfrequency-dependent, by using Zener models to fit the stiffness coefficients, and thencarrying out numerical simulation of wave field by solving the wave equation inviscoelastic anisotropic media which is equivalent to fractured porous media. Thenumerical simulation examples show that the advanced numerical simulation methodsimulates correctly seismic wave propagation characteristics in fractured porousmedia, seismic wave dispersion and attenuation characteristics can be observedclearly from the wave field snapshots, waveform and synthetic seismogram.Seismic wave reflection problem is one of the most basic and most important issues,It is the core issue of the reflection survey. This paper studies reflection problem ofwaves in fractured porous media. By using the Chapman model to describe thefractured porous media, according to the consistency between constitutive equationfor viscoelastic anisotropic media in frequency domain and the HTI media based onChapman model, combining the calculation method of reflection and transmission coefficients of waves in viscoelastic anisotropic media and the Chapman model topresent the calculation method of exact reflection coefficients of seismic waves inHTI media based on Chapman model. Meanwhile, by using the approximate formulasof the reflection coefficients in attenuative anisotropic media to calculate thereflection coefficients in the HTI media based on the Chapman model, two methodshave good consistency within the scope of the approximate formula applicable, whichshow that two methods are both effective. On this basis, analyzing the effects ofimportant reservoir parameters on PP-wave frequency-dependent reflectioncoefficient and further analyzing the frequency-dependent AVO characteristics and thefrequency-dependent AVOZ characteristics of reflected PP-wave, the researches showthat the PP-wave frequency-dependent reflection coefficient is sensitive to variationsof fracture density, fracture size and porosity; frequency-dependent AVOcharacteristics of reflected PP-wave have some connection with the relation of waveimpedance between the overlying formation and underlying formation. Through thecalculations of three model examples, and referring to the classification method forpatchy-saturated gas reservoirs advanced by Ren et al (2009), according tofrequency-dependent property of PP-wave reflection coefficient, classifying fracturedreservoirs into three classification, they are low-frequency dim-out reservoirs,phase-shift reservoirs and low-frequency bright-spot reservoirs. PP-wave reflectioncoefficient and its frequency-dependent characteristics vary with changes in azimuth.As to the studies on fractured reservoirs, fracture size, fracture density, porosityand fracture azimuth are all the key parameters in reservoir identification andevaluation, and the reservoir parameters inversion plays the significant role onqualitative prediction and quantitative description of fractured reservoirs. On the basisof the characteristics that PP-wave frequency-dependent reflection coefficient hasgood sensitivity to the variations of fracture density, fracture size and porosity, thispaper adopts genetic algorithm to carry out reservoir parameter inversion by using thefrequency-dependent AVO or frequency-dependent AVOZ in fractured porous media.In the case of known fracture azimuth, fracture density, fracture size and porosity areinverted by frequency-dependent AVO data. While in the case of unknown fracture azimuth, the fracture azimuth, fracture density, fracture size and porosity are invertedsimultaneously. For the thin fractured reservoir, the thickness of thin lay, fracturedensity, fracture size and porosity are inverted simultaneously. The advanced reservoirparameters inversion method in this paper has a certain stability and noise immunity,provides new techniques for reservoir parameters inversion in fractured reservoirs.