Extending LMR for anisotropic unconventional reservoirs

Transcription

1 Extending LMR for anisotropi unonventional reservoirs Maro A. Perez Apahe Canada Ltd Summary It has beome inreasingly advantageous to haraterize rok in unonventional reservoirs within an anisotropi framework. Previous work has shown that anisotropy is linked to the presene of oriented fratures, stress and kerogen amongst other reservoir properties. hese properties all impat hydrauli stimulation efforts and play an important role in the ability to produe low permeability reservoirs. Logging wellbores, vertial or horizontal, does not give a omplete understanding of anisotropi nature of the reservoir as it only measures formation slowness in one diretion. owever, the geometries assoiated with modern seismi aquisition are able to more ompletely determine anisotropi parameters from refletion and traveltime data reorded over numerous propagation diretions. o analyze and interpret the seismially derived anisotropi attributes, the LMR rossplot is extended to onsider anisotropi omponents of the stiffness tensor. he anisotropi version of LMR attributes is assoiated to rok properties beyond lithology as it is now related to fabri and oriented rak geometry. ertial transverse isotropy is investigated using published rok physis models. A method is presented that illustrates how to interpret the expanded attributes and how seismi attributes an help in understanding the elasti properties of reservoir rok with respet to potential ompletion efforts ramifiations. Introdution he Lambda-Mu-Rho (LMR) attritbutes were introdued by Goodway et al (997) as a way to distinguish varying lithology and fluid ontent from seismi attributes. It introdued a different perspetive on elasti rok properties distint from the onventional ompressional (P) veloity or impedane and shear (S) veloity or impedane (or the ratio) attribute rossplots. o illustrate the point, onsider the elasti stiffness tensor represented as a matrix using the oigt notation, C. () 55 he upper diagonal omponents represent the P-wave propagation while the lower diagonal omponents are the shear omponents. he omponent is represented in terms of Lame parameters is () whih is the P-wave modulus. he lower half of the diagonal is expressed as GeoConvention 05: New orizons

2 he off diagonal omponent in isotropi media is simply. () (4) where is the modulus relating normal stress to a perpendiular strain. he differene between a p s rossplot and an LMR rossplot is simply different omponents of the elasti stiffness tensor: on diagonal versus off diagonal stiffness omponents. he variation in and in the lithologies of interest will determine whih spae is more suitable for interpretation. It is noted that omputing in the speial ase of isotropi media is given by. (5) For anisotropi media, omputing is not as straightforward. Given the geometries present within logging programs, only ertain parts of the elasti stiffness tensor an be measured. For example, a vertial wellbore measuring ompressional and shear traveltimes populates the, and 55 omponents of the stiffness tensor shown in figure. Figure. Shemati showing vertial borehole and measurable omponents of stiffness tensor. he green and yellow arrows in figure show partile motion for a vertial propagation orresponding to P and S waves respetively. Similarly, in a horizontal well drilled in the x diretion, the, 55 and are measured. For vertial transverse isotropy, the 5 independent elasti stiffness omponents are shown below as well as an equivalent form in terms of Lame parameters (adapted from Goodway, 00) I (6) In a vertial borehole, the measured traveltimes fail to provide any information for,, and (any of the horizontal and transverse omponents. o fill in the information gap, seismi data and a rok physis model is used to help onstrain and ultimately interpret attributes derived from seismi data. Method he effetive field model (EFM) is used to haraterize I roks that are either intrinsially anisotropi, ontains some anisotropi omponents or has oriented inlusions (pores and/or raks). Rok phsyis models are onstruted that show the interrelationship between the omponents of the elasti stiffness GeoConvention 05: New orizons

3 tensor and anisotropi geometry using the method presented by Sevostianov et al (005) with seismi appliation examples shown by Sayers (0),. he LMR rossplot spae is expanded to visualize the anisotropi tensor. It onsiders not only the and omponents but also the other off diagonal and shear omponents, and. Conventional LMR is but a subset of the potential rossplot spae. Extending the rossplot spae demonstrates how the elasti parameters vary with respet to anisotropi geometry (I versus I for example) and expeted seismi response. An appropriate rossplot spae now inludes rossplotting the two independent shear omponents ( and in I media) against the two independent off diagonal terms ( and in I media). Figure a shows the log data in an isotropi LMR rossplot while figure b shows the same log data transformed using = 0.5 and = = 0. with anisotropi rok physis trends. Well data in both figures is olor oded by quartz volume. he geometry of the anisotropi rok, fit to log data with seismi estimates of and, helps interpret the elasti properties. a) b) Figure. Left) Isotropi LMR rossplot Right),, and rossplot with anisotropi rok rok physis trends with varying pore aspet ratio (). Red α =, Blue α = 5, Blak α = 0. As Goodway (00) has noted, represents the off diagonal omponent of the elasti tensor, obtainainable from surfae seismi data. From this perspetive, the extended LMR rossplot provides insight to seisimially derived estimates of anisotropy, in partiular. As shown by Sayers (995), to first order is a funtion of, through with (7) (8) Sine = p and = s, an be omputed with a seismi estimate of. Note that when + < negative our. In suh ases, the rossplot should display a skew towards the origin while a positive will move away. Comparing measured variations in anisotropy with EFM anisotropi models allows for interpretation of reservoir fabri. Appliations GeoConvention 05: New orizons

4 An integrated model an be onstruted to aount for anisotropy present in unonventional reservoirs using well data, estimated values of and, and rok physis models. Below are some appliations utilizing anisotropi parameters. Stress Profiling Stress profiling has been disussed by ernik and Milova (0) and Sayers (0) showing the impat and inreased stress as a funtion of ( ). he stress perturbations equations for I media are given by Sayers (0) where p p (9) p p. For uniaxial strain ( = = 0) the / ratio determines stress perturbation. he omponent an be measured seismially through derived either from fourth other moveout analysis or amplitude variation with offset. Anisotropi Rok Strength Aside from estimating stress perturbations, another possible appliation is determining strength anisotropy (Jaeger et al, 007). Given the presene of elasti anisotropy it is likely that strength anisotropy is also present. he ondition for shear failure is desribed mathematially as sin UCS tan (0) os where UCS is the unonfined ompressive strength and is the angle of internal frition. With the strong orrelation between Young s modulus (E) and UCS, elasti anisotropy would indiate strength anisotropy. For I media there are two measurable E, horizontal (E h ) and vertial (E v ) defined as E h () E v () Figure below shows how variations in only, hange and vertial and horizontal Young s modulus. Figure. ertial (blue) and horizontal (red) Youngs modulus and (blak) as a funtion of GeoConvention 05: New orizons 4

5 Assoiating the variations in with the rok physis models with respet to expeted mineralogy and porosity variations an help in assessing the signifiane of the anisotropi parameters, whether it be assoiated with intrinisi matrix anisotropy or preferentially aligned raks. he differene between intrinsi and oriented inlusions will impat ompletions perfomane. he in-situ stress state, its orientation with respet to the symmetry axis of the anisotropi rok and rok strength anisotropy will result in different types of failure. aking into onsideration the variable rok strength and stress state an help in prediting ompletion effiay and aelerate optimization of future programs. Conlusions he LMR attritbutes are a subset of the elasti stiffness tensor whih an be extended to onsider different anisotropi parameters. Beause LMR fouses on the off diagonal omponent fo the tensor, it inherently represents the important parameter in determining stress perturbations. It also an show potential variation in rok strength by variation in the shear modulus. Using published rok physis models an help in giving phsyial signifiane to the observed anisotropy leading to better reservoir haraterization of unonventional plays. As always, it is important to alibrate models and seismi estimates to well and ore data when available. Referenes Goodway, B., 00, AO and Lame' onstants for rok parameterization and fluid detetion: Reorder, 6, no. 6, Goodway, W., Chen,., and Downton, J., 997, Improved AO fluid detetion and lithology disrimination using Lamé petrophysial parameters; "Lambda-Rho", "Mu-Rho", & "Lambda/Mu fluid stak", from P and S inversions: 67 Annual Internat. Mtg., So. Expl. Geophys., Expanded Abstrats, Sayers, 0, he effet of kerogen on the elasti anisotropy of organi-rih shales: Geophysis, 78, Sayers, 005, Seismi anisotropy of shales: Geophysial Prospeting, 5, Sevostianov, I., N. Yilmaz,. Kushh, and. Levin, 005, Effetive elasti properties of matrix omposites with transversely- isotropi phases: International Journal of Solids and Strutures, 4, Sayers, 995. Simplified anisotropy parameters for transversely isotropi sedimentary roks, Geophysis, 60,9-95 ernik L., and Milova, J., 0, Rok physis of organi shales: he Leading Edge, Marh, 8-. ashemi, M., Ghazvinian, A., & aghihian, A. (009, January). Exat Satisfation of Uniaxial ensile And Compressive Strengths of Rok In a New Failure Criterion Considering Brittle-Dutile ransition As an Initial Boundary Condition. In Proeedings of the 009 International Symposium on Rok Mehanis:" Rok Charaterisation, Modelling and Engineering Design Methods. Jaeger, J.C., Cook, N.G.W., Zimmerman, R.W.: Fundamentals of Rok Mehanis. Blakwell Publishing, Malden (007) GeoConvention 05: New orizons 5