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- Volume 69, Issue 3, 2021
Geophysical Prospecting - Volume 69, Issue 3, 2021
Volume 69, Issue 3, 2021
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Water‐flooding and consolidation of reservoir chalk – effect on porosity and Biot's coefficient
Authors Tobias B. Gram, Frederik P. Ditlevsen, Klaus Mosegaard and Ida L. FabriciusABSTRACTImproved oil recovery from chalk reservoirs by water‐flooding may cause mechanical weakening and change in elasticity. Confined compressive strength testing of chalk from a North Sea reservoir was done in water‐saturated and oil‐saturated conditions. During testing, elastic wave velocities were sampled by ultrasonic transducers, so that subsequently Biot's coefficient could be modelled. The porosity declined via an ‘elastic phase’, a ‘transitional phase’, an ‘elastoplastic phase’ and a ‘strain hardening phase’, but Biot's coefficient indicates that these terms may be partly misleading. In the ‘elastic phase’, porosity and Biot's coefficient decrease, indicating elastoplastic deformation. In the ‘transitional phase’, Biot's coefficient increases as a reflection of breaking contact cement (pore collapse), whereas Biot's coefficient remains stable in the ‘elastoplastic phase’, indicating elastic deformation on the virgin curve. Plastic deformation takes place during phases of creep, where both porosity and Biot's coefficient decrease. Similarly, in the ‘strain hardening phase’, both porosity and Biot's coefficient decrease as a reflection of elastoplastic deformation. For chalk with 45%–47% porosity, the ‘transitional phase’ begins at 8 MPa axial stress when water‐saturated and at 12 MPa when oil‐saturated. For chalk with 41%–43% porosity, the corresponding stresses are 16 and 20 MPa. For chalk with 32%–36% porosity, the corresponding stresses are 23 and 31 MPa. Chalk samples with irreducible water saturation and movable oil were water‐flooded. They yield at stresses close to corresponding oil‐saturated samples, but after flooding show compaction trends not significantly different from the water‐saturated samples. Water‐flooding promotes pore collapse as reflected in an increasing Biot's coefficient. The consequent softening effect on acoustic impedance is small as compared with the effect of increasing fluid density. With respect to 4D seismic, water‐flooding causes distinctly higher acoustic impedance and Poisson's ratio irrespective of compaction.
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Macroscopic non‐Biot's material properties of sandstone with pore‐coupled wave‐induced fluid flows
Authors Shuna Chen, Xiaotao Wen, Igor B. Morozov, Wubing Deng and Zhege LiuABSTRACTWave‐induced pore‐fluid flows are recognized as an important cause of seismic‐wave attenuation at frequencies below 1 kHz within heterogeneous rocks. By using Lagrangian continuum mechanics, wave‐induced pore‐fluid flow mechanisms can be classified strictly on the basis of macroscopic non‐Biot's material properties. In this classification, type I and II wave‐induced pore‐fluid flows are identified by local internal deformations being elastically coupled with either the whole Biot's rock or only with its pore fluid, respectively. Type III wave‐induced pore‐fluid flow is defined as a mixture of types I and II. For all types of wave‐induced pore‐fluid flows, the model predicts all rock properties observed in rock‐deformation experiments, such as the frequency‐dependent poroelastic moduli. The observed attenuation peaks and effective moduli can be used to invert for new, non‐Biot's material properties of porous rock. In data examples, we focus on the pore‐fluid coupled (type II) wave‐induced pore‐fluid flow mechanism and compare it to a previous analysis of type I. Non‐Biot's elastic and viscous rock properties are inverted for by fitting the effective drained bulk moduli measured in two previously published experiments: (1) with real sandstone including two saturating fluids and multiple confining pressures, and (2) a numerical experiment with heterogeneous sandstone containing mesoscopic‐ and microscopic‐scale wave‐induced pore‐fluid flows. Compared with a previous study of type I wave‐induced pore‐fluid flow, the data‐fitting method is improved by focusing on attenuation peaks and additional points in the observed spectra. For both of these experiments, both type I and II interpretations yield accurate fitting of the observed attenuation and dispersion spectra. Combinations of type I and II models (type III) yield a broad variety of acceptable mechanical models. This ambiguity of inversion shows that the different types of wave‐induced pore‐fluid flows cannot be differentiated in conventional attenuation/dispersion experiments. However, these WIFF types are physically meaningful and lead to rigorous equations of rock deformation that can be used in many applications.
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Biot effective stress parameter in poroelastic anisotropic media: Static and dynamic case
Authors Sharif M. Morshed, Evgeny M. Chesnokov and Alexandra A. VikhorevaABSTRACTStress, rock microstructure and frequency are the three key factors that influence the velocities of elastic waves and, hence, are sensitive to the Biot effective stress parameter (α) in porous rocks. The effective stress in an isotropic poroelastic medium relates to applied pressure and pore pressure, with the Biot parameter (α) as a scaling factor of the pore pressure. This paper provides an independent derivation of the tensor characteristics of α through elastic moduli, a microscopic effective medium derivation, and frequency‐dependent behaviour of α for an anisotropic medium. We provide an explicit expression, especially for isotropic rock under uniaxial stress, considering the nonlinear part of elastic constants. In the effective medium derivation, we assumed that the rock contained both isolated pores and connected pores saturated with liquid. To support our theoretical formulation, we calculated the Biot tensor of sandstone and shale by inverting the ultrasonic velocities of transversely isotropic rock under uniaxial stress where mineralogical composition and porosity are known. Even though porosity and rock microstructure play significant roles in α as stress varies, we also see as much as a 21% difference between horizontal and vertical components of α for rocks with transversely isotropic symmetry. We then estimated the frequency‐dependent Biot tensor for transversely isotropic models using numerical calculations. We noticed significant differences between vertical (α33) and horizontal (α11) components of α, especially at the surface seismic frequency band. However, uniaxial stress and horizontally aligned microstructure influence the elastic moduli and Biot tensor contrarily. In general, anisotropy due to uniaxial stress shows lower α33 and higher α11. The proposed method shows an excellent prediction of α33 and α11 for given data of uniaxial stress and vice versa.
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Effect of porosity gradient on the permeability tensor
Authors Mahyar Madadi and Tobias M. MüllerABSTRACTExperimental investigations often reveal that there is a correlation between porosity and permeability in rocks. The most commonly used model to predict the porosity–permeability relation is due to Kozeny–Carman or its many modifications. However, these models are problematic because they always involve an empirical constant and, in macroscopically heterogeneous porous media with non‐uniform porosity, more than one empirical constant would be required. Moreover, the tensor character of the permeability is not accounted for when the permeability is conceptualized as a plain function of the porosity. To overcome these limitations, we devise an approach by analysing the drag force in the volume averaging framework of poroelasticity. This allows us to deduce an expression for the inverse permeability tensor. It is the sum of the inverse of the permeability pertaining to a representative volume element and the second spatial derivative of porosity. Therefore, the gradient of porosity changes the permeability depending on the variations of macroscopic porosity variations. This result is thought to be relevant in applications where porosity maps are converted into permeability maps.
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Integrating rock physics laboratory data and modelling to improve uplift characterization methodology
Authors Sondre Torset, Rune M. Holt and Kenneth DuffautABSTRACTModelling changes in elastic wave velocities in sediments and rocks as they undergo burial and uplift can reveal aspects of their burial history. This has implications in the petroleum risking procedures, as aspects such as hydrocarbon maturation and reservoir quality are key ingredients. Previous modelling for such a purpose assumes constant velocity and porosity during uplift after the cessation of cementation. Laboratory data of a synthetic sandstone formed under stress, and subjected to loading and unloading cycles are used to test this assumption. The experimental P‐wave velocities show a clear increase in stress dependence during the uplift simulation. Besides, the P‐wave anisotropy transforms from negative to positive. These observations are combined to make an updated modelling workflow to mimic the experimental results better. The modelling is conducted in different phases. Loading before cementation is modelled using a triaxial granular medium theory. For the laboratory data, a novel anisotropic formulation of the patchy cement model captures the observed trends. A modified crack model incorporates the stress sensitivity seen during the unloading that simulates uplift. The results of the integrated rock physics workflow mimic the laboratory data very well. A conceptual field example using the rock physics workflow illustrates how the exclusion of the stress dependence during uplift can lead to an underestimation of the exhumation magnitude.
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Seismic dispersion and attenuation in Mancos shale – laboratory measurements
Authors V. Mikhaltsevitch, M. Lebedev, M. Pervukhina and B. GurevichABSTRACTWe present the results of a low‐frequency study of Mancos shale, where we first elaborate a stress–strain methodology of laboratory low‐frequency experiments to estimate the elastic moduli of shales, and then apply this methodology to investigate the influence of partial water saturation on the elastic and anelastic parameters, velocities and P‐wave anisotropy of Mancos shale. We also analyse the applicability of the anisotropic Gassmann theory for predictions of the stiffness tensor components of the water‐saturated shale with non‐expandable clay content presented in our case by illite (33%) and chamosite (9.1%) minerals. The effect of water saturation was studied using two samples drilled in vertical and parallel directions to the formation bedding. The experiments were carried out at a confining pressure of 10 MPa in the frequency range from 0.1 to 100 Hz. Prior to measurements, the samples were saturated in desiccators at six different values of relative humidity ranging from 9% to 97.5%. The results of our study demonstrate a reduction of Young's modulus and P‐wave anisotropy with saturation accompanied by a decrease in shear stiffnesses. The latter indicates the inapplicability of the anisotropic Gassmann theory to Mancos shale. Our measurements of attenuation carried out on the vertical and horizontal samples saturated at a relative humidity of 97.5% revealed prominent attenuation peaks associated with partial saturation. We showed that the measurement results of the attenuation and Young's modulus dispersion are consistent with the causality principle presented by the Kramers–Kronig relations.
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Correcting density/sonic logs for total organic carbon to reduce uncertainty in pore pressure prediction
Authors Sam Green and Lev VernikABSTRACTPore pressure prediction in shales undergoing compaction, including both mechanical and chemical processes, is customarily related to the mechanism referred to disequilibrium compaction. However, even when this mechanism is established and the normal compaction trend in sonic velocity, as a proxy for shale porosity, is well constrained, the pore pressure prediction may be in error because of the lithological variation in shale composition. The presence of solid organic matter in excess amounts in shale formations that have never been exposed to the pressure–temperature conditions in the oil window is an example of these lithological effects, causing marked overprediction of pore pressure even in thermally immature mudrocks. This necessitates implementation of bulk density and sonic velocity log corrections in organic‐rich shales prior to performing standard pore pressure prediction workflows. In this paper, it is shown how these corrections can be made and the outcomes of the pore pressure prediction can be dramatically improved by using combination of rock physics models relating bulk density to total organic carbon and P‐wave velocity to bulk density in organic‐rich and conventional shales, respectively. To illustrate the workflow, a case study from a well drilled through the Kimmeridge Clay Formation in the North Sea, a well‐recognized source rock with total organic carbon content in the 2%–12% range and significant variation in clay content from 25% to 60%, both of which strongly affect the most commonly utilized log responses recorded in this formation. Using this old but data‐rich well, the importance of accounting for both total organic carbon and clay content variations in pore pressure prediction is demonstrated. It is also recognized that this workflow does not immediately apply to unconventional shale plays, where the pore pressure generation mechanisms are more complex and cannot be solely ascribed to compaction disequilibrium.
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Dispersion of flexural waves in a borehole with a tensile fracture in an anisotropic stress environment
Authors Kosuke Kayama, Hitoshi Mikada and Junichi TakekawaABSTRACTThe effect of tensile fracture in a vertical borehole under anisotropic horizontal stress conditions is numerically investigated in terms of the dispersion of flexural wave generated in dipole sonic logging. Our three‐dimensional model comprises a borehole filled with water and a tensile fracture intersecting the borehole in the borehole axial direction. Two shear waves are excited individually to produce particle displacements polarized in two orthogonal radial directions using two dipole sources aligned in the two polarized directions. A vertical array of equispaced dipole sensors is placed at the centre of the borehole along the borehole axis. We assumed that the surrounding formation possesses transversally isotropic anisotropy with the isotropy plane parallel to the borehole axis due to horizontal stress anisotropy. We examined the dispersion of flexural waves travelling along a borehole in our numerical models that include either fast or slow formation with various depths of tensile fractures. Our numerical results show that the deeper the penetration depth of a tensile fracture, the higher the slowness of shear waves polarized perpendicular to the tensile fracture for both slow and fast formation models. Our results indicate that the flexural dispersion behaviour could be used to investigate the depth of penetration of a tensile fracture that can be produced by either drilling or hydraulic fracturing.
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Data‐driven rock physics analysis of North Sea tertiary reservoir sands
Authors Per Avseth, Ivan Lehocki, Øyvind Kjøsnes and Odd SandstadABSTRACTWe have demonstrated an approach for data‐driven rock physics analysis, where we first do facies classification using elastic well log data from several wells, followed by facies‐constrained regression analysis to establish local rock physics relations for the prediction of VP and VS from geological input parameters. We have applied this approach to a multi‐well log data set (53 wells, 40 of which had reliable/useful data) from the greater Alvheim area. We show how we can derive very robust local empirical rock physics relations for the prediction of P‐wave and S‐wave velocities as well as densities, for given combinations of porosity and clay volume. These locally derived empirical relations are recommended instead of universal rock physics models, even when the latter are locally calibrated. Using elastic facies with geological characteristics (cemented versus unconsolidated; normally compacted versus injectites; homogeneous versus heterogeneous) helps to improve the predictability of the regression models. The local rock physics relations that we obtain can furthermore be used to create training data for AVO classification.
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Seismic tuning of dispersive thin layers
Authors Giorgos Papageorgiou and Mark ChapmanABSTRACTThe wedge model is commonly used to study the limits of seismic resolution where conventionally the thickness of sub‐resolution seismic layers can be determined from thin layer tuning curves. Tuning curves relate the layer temporal thickness to the wavelet frequency, but, to our knowledge, no systematic study has been done to date of the effects of velocity dispersion and attenuation on tuning. In this work, we study the tuning properties of a thin layer dispersing according to the standard linear solid model. We show that the first tuning curve is sensitive to the attenuation, relative polarity and magnitude of the two reflection coefficients at the top and base of the layer. We provide an analytic formula for the upper bound in the mismatch between the elastic and dispersive tuning curves. We conclude that highly attenuative thin layers can appear thicker or thinner than they actually are depending on polarity and relative magnitude of reflection coefficients at the layer interfaces. Our results are particularly relevant in the quantification of CO2 where knowledge of the temporal thickness of CO2 layers is reliant on their tuning curves.
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From cradle to grave: how burial history controls the rock‐physics properties of quartzose sandstones
Authors Ivan Lehocki and Per AvsethABSTRACTRock‐physics properties of sands and sandstones are strongly affected by geological processes of the past, including deposition, compaction and exhumation. By honouring these geological processes, the rock‐physics modelling will be more predictive in areas with limited well control. This study performs rock‐physics modelling constrained by a given geological history, starting from deposition to mechanical and chemical compaction. Different geological factors, including sorting, grain size and clay coating, will affect the quartz cementation and rock stiffening of quartzose reservoir sandstones. By combining compaction models with rock‐physics contact theory, we can model the rock‐physics properties of sands/sandstones as a function of geologic time. We have demonstrated the approach on well log data from three selected wells on the Norwegian Continental Shelf, where the burial histories of the target reservoir sandstones are significantly different. We conclude that rock‐physics modelling constrained by burial history can be used to predict elastic properties quite accurately in these wells. The integrated approach presented in this study allows for more realistic rock‐physics depth trends in areas with complex burial history that can be used in AVO studies or to estimate net erosion associated with tectonic uplift.
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A workflow for multimineralogic carbonate rock physics modelling in a Bayesian framework: Brazilian pre‐salt reservoir case study
Authors Jonatan Dias, Jorge L. Lopez, Raquel Velloso and Fabio PerosiABSTRACTWe develop a workflow to estimate elastic attributes ( and ) of Pre‐Salt carbonate reservoirs using the Xu and Payne rock physics model in a depth‐variant multimineralogic fashion and apply it to one calibration and four extrapolation wells in a field in the Brazilian Santos Basin. Some of the parameters were stochastically simulated in a Bayesian framework to handle the model non‐uniqueness. Nuclear magnetic resonance porosity and mineralogic logs and x‐ray powder diffraction data from the studied wells and literature reference values were used for elastic solid media and dual‐porosity network modelling, bringing geological reasoning to the proposed workflow. Using rock physics templates, we improved our understanding of the reservoir petroelastic trends and devised alternative model parameterizations. Since the model was parameterized in a multimineralogic fashion with depth‐variant mineralogic information (e.g. volumes of carbonate, quartz and clay) as input, we improved elastic attribute estimations within the reservoir, increasing the model predictive power, compared to the common practice of allowing only porosity to vary with depth and representing the matrix properties by a depth‐invariant homogeneous or mixed mineral. We also investigated the workflow robustness and non‐uniqueness by studying its dependence on the choice of calibration well.
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Volumes & issues
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Volume 72 (2023 - 2024)
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Volume 71 (2022 - 2023)
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Volume 70 (2021 - 2022)
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Volume 69 (2021)
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Volume 68 (2020)
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Volume 67 (2019)
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Volume 66 (2018)
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Volume 65 (2017)
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Volume 64 (2015 - 2016)
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Volume 63 (2015)
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Volume 62 (2014)
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Volume 61 (2013)
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Volume 1 (1953)