Elastic properties of carbonates : measurements and modelling

This thesis is a multi-scale study of carbonate rocks, from the nanoscale and digital rock investigations to the imaging studies of carbonate reservoir analogues. The essential links between these extremes are the carbonate physical properties and rock-physics models, which are investigated here through the modelling of ultrasonic wave propagation in carbonate samples, focusing on elastic stress sensitivities, saturating fluids and porosity models. Validation of Gassmann fluid substitution in carbonates is also investigated using correlations between core and well log measurements.On the nanoscale, we use the nanoindentation technique in an oolitic limestone to directly measure the calcite Young modulus and derive bulk and shear moduli. We have found a large variation in the calcite bulk modulus, from 56 to 144 GPa. The high values obtained in some oolite rings were interpreted as genetically associated with biologically generated calcite (biocalcite). There are many measurements that achieve these values in brachiopod shells, but none in oolitic limestone. We associate the smaller values with microporosity, which is undetectable by our microCT or even SEM images. On the microscale we use the X-ray microCT images. From these images we can compute oolite elastic parameters using finite difference methods (FDM). In this oolite sample, calcite was segmented in two distinct phases. Nanoindentation provides the elastic parameters for each phase. The results of the modelling are compared with ultrasonic measurements on dry samples.To compute the properties of rocks on fluid-saturated samples, one needs to use fluid substitution methods, such as Gassmann’s equations. However, the applicability of Gassmann’s equations and the fluid substitution technique to carbonate rocks is still a subject of debate. Here we compare the results of fluid substitution applied to dry core measurements against sonic log data. The 36 meters of continuously sampled carbonates data, comes from a cretaceous reservoir buried at a depth of 5000 metres in the Santos Basin, offshore Brazil. Compressional and shear velocities, density and porosity were measured in 50 samples covering the entire interval. We obtain good agreement between the elastic properties obtained from core and log measurements. This shows that Gassmann’s fluid substitution is applicable to these carbonates, at least at sonic log frequencies.Carbonate microstructure is investigated using the stress dependency of shear and compressional wave velocities according to the dual porosity model of Shapiro (2003). The model assumes that the pore space contains two types of pores: stiff and compliant pores. Understanding the parameters of this model for different rocks is important for constraining stress effects in these rocks. The results for a carbonate dataset from the Santos Basin show a good correlation between compliant porosity and dry bulk modulus, total porosity and density for 29 samples of carbonates from the Santos Basin. The correlations seem to be different for different facies distribution, with different trends for mudstone facies and grainstone and rudstone facies. We also performed the same analysis using 66 samples of sandstones of diverse origins (Han et al., 1986): a good correlation appears between compliant porosity and the dry bulk modulus for all samples.If we correlate only the 7 samples from Fontainebleau sandstone, a good correlation also appears between total and compliant porosity. This analysis shows that the correlation is facies dependent also for sandstones.While Gassmann’s equations may be valid for low frequencies, they are not applicable at higher frequencies, where squirt dispersion is significant. We propose a workflow to model wave dispersion and attenuation due to the squirt flow using the geometrical parameters of the pore space derived from the stress dependency of elastic moduli on dry samples. Our analysis shows the dispersion is controlled by the squirt flow between equant pores and intermediate pores (with aspect ratios between 10-3 - 2·10-1). Such intermediate porosity is expected to close at confining pressures of between 200-2000 MPa. We also infer the magnitude of the intermediate porosity and its characteristic aspect ratio. Substituting these parameters into the squirt model, we have computed elastic moduli and velocities of the water-saturated rock and compared these predictions against laboratory measurements of these velocities.The agreement is good for a number of clean sandstones, but much worse for a broad range of shaley sandstones. Our predictions show that dispersion and attenuation caused by the squirt flow between compliant and stiff pores may occur in the seismic frequency band. Confirmation of this prediction requires laboratory measurements of elastic properties at these frequencies.The carbonate system of Telegraph Station, Shark Bay (WA), is a unique environment where coquinas, stromatolites and microbial mats are linked: an excellent analogue to carbonate pre-salt offshore Brazil. We acquired 7.5 km of GPR data and high resolution seismic data in the coquina ridges. They are composed by calcite shells deposited by cyclones, which show excellent high resolution GPR images, being a low loss dielectric medium. Three classes of coquinas were mapped: tabular layers, convex-up crest and washover fan. From the correlation of 14C dating of 50 samples and the mapped events we can estimate an average rate of one event every 13 years. From our interpretation the Holocene regression is continuous but not homogeneous. Carbonate dissolution features, faults, trends and discontinuities were mapped. Analysis of these features helps us understand reservoir porosity and permeability distribution in carbonate deposits, and can be used to constrain reservoir properties in pre-salt carbonates in Brazilian basins

Bounds for seismic dispersion and attenuation in poroelastic rocks

Recently, Hashin-Shtrikman bounds for bulk and shear moduli of elastic composites have been extended to the moduli of composite viscoelastic media. Since viscoelastic moduli are complex, the viscoelastic bounds form a closed curve on a complex plane. We apply these general viscoelastic bounds to a particular case of a porous solid saturated with a Newtonian fluid. Our analysis shows that for poroelastic media, the viscoelastic bounds for the bulk modulus are represented by a semi-circle and a segment of the real axis, connecting formal HS bounds (computed for an inviscid fluid). Furthermore, these bounds are independent of frequency and realizable. We also show that these viscoelastic bounds account for viscous shear relaxation and squirt-flow dispersion, but do not account for Biot's global flow dispersion

Testing Gassmann fluid substitution in carbonates: sonic log versus ultrasonic core measurements

The technique of fluid substitution is widely used to model elastic properties of rocks saturated with different fluids The applicability of this technique to in-situ seismic and sonic measurements is a matter of frequent debate. Most of the analysis is based on laboratory measurements, with little or no constraints from field environments. In addition, until recently, most of the data were from sand reservoirs. Applicability of Gassmann fluid substitution to carbonates is even more uncertain. To analyze this problem, we compare elastic moduli obtained using fluid substitution against the moduli obtained from sonic and density logs The dry moduli for fluid substitution are obtained from ultrasonic measurements on 50 core samples from a cretaceous reservoir buried at 5000 meters depth in Santos Basin, offshore Brazil. The good agreement between the saturated moduli obtained from cores and logs is obtained. This shows that the Gassmann equations can be applied not only in siliciclastic reservoirs, but also deep and complex carbonates reservoirs

A new model for squirt-flow attenuation and dispersion in fluid-saturated rocks

We develop a new simple model of squirt-flow model attenuation and dispersion, in which most parameters can be independently measured or estimated from measurements. The pore space of the rock is assumed to consist of stiff porosity and compliant (or soft) pores present at grain contacts. The effect of isotropically distributed soft pores is modeled by considering pressure relaxation in a disk-shaped gap between adjacent grains. This derivation gives the complex and frequency-dependent effective bulk and shear moduli of a rock, in which the soft pores are liquid-saturated and stiff pores are dry. The resulting squirt model is consistent with Gassmann s and Mavko-Jizba equations at low and high frequencies, respectively

Estimation of Carbonate Elastic Properties Using Nanoindentation and Digital Images

Petrophysical properties of carbonate reservoirs are less predictable than the properties of silisiclastic reservoirs. The main reason for that is chemical interaction of carbonate rocks with percolating fluids, ion exchange and recrystallization in geological time. Quantification of the elastic variability of carbonate grains on the microscale is the first step to constrain models and to obtain more realistic predictions of practically important rock properties of carbonate reservoirs. In this study we present elastic moduli of an oolite sample from the Pleistocene Dampier Formation of Southern Carnarvon Basin, Western Australia obtained by the nanoindentation technique.Young moduli of this highly heterogeneous sample are measured at 49 points regularly distributed in a 70x70micrometer rectangular grid on the surface. The frequency diagram shows bimodal distribution of the Young moduli that correspond to dense calcite phase and rare (dissolved) calcite phase. These two solid phases are apparent in the high resolution scanning electron microscope images. We used the obtained moduli of the dense and rare phases for numerical modelling of elastic properties of the carbonate sample from micro-CT images. The results of the numerical modelling using finite element code are compared with the elastic moduli obtained from acoustic velocities measured by ultrasonic technique

Diretrizes Brasileiras de Medidas da Pressão Arterial Dentro e Fora do Consultório – 2023

Hypertension is one of the primary modifiable risk factors for morbidity and mortality worldwide, being a major risk factor for coronary artery disease, stroke, and kidney failure. Furthermore, it is highly prevalent, affecting more than one-third of the global population. Blood pressure measurement is a MANDATORY procedure in any medical care setting and is carried out by various healthcare professionals. However, it is still commonly performed without the necessary technical care. Since the diagnosis relies on blood pressure measurement, it is clear how important it is to handle the techniques, methods, and equipment used in its execution with care. It should be emphasized that once the diagnosis is made, all short-term, medium-term, and long-term investigations and treatments are based on the results of blood pressure measurement. Therefore, improper techniques and/or equipment can lead to incorrect diagnoses, either underestimating or overestimating values, resulting in inappropriate actions and significant health and economic losses for individuals and nations. Once the correct diagnosis is made, as knowledge of the importance of proper treatment advances, with the adoption of more detailed normal values and careful treatment objectives towards achieving stricter blood pressure goals, the importance of precision in blood pressure measurement is also reinforced. Blood pressure measurement (described below) is usually performed using the traditional method, the so-called casual or office measurement. Over time, alternatives have been added to it, through the use of semi-automatic or automatic devices by the patients themselves, in waiting rooms or outside the office, in their own homes, or in public spaces. A step further was taken with the use of semi-automatic devices equipped with memory that allow sequential measurements outside the office (ABPM; or HBPM) and other automatic devices that allow programmed measurements over longer periods (HBPM). Some aspects of blood pressure measurement can interfere with obtaining reliable results and, consequently, cause harm in decision-making. These include the importance of using average values, the variation in blood pressure during the day, and short-term variability. These aspects have encouraged the performance of a greater number of measurements in various situations, and different guidelines have advocated the use of equipment that promotes these actions. Devices that perform HBPM or ABPM, which, in addition to allowing greater precision, when used together, detect white coat hypertension (WCH), masked hypertension (MH), sleep blood pressure alterations, and resistant hypertension (RHT) (defined in Chapter 2 of this guideline), are gaining more and more importance. Taking these details into account, we must emphasize that information related to diagnosis, classification, and goal setting is still based on office blood pressure measurement, and for this reason, all attention must be given to the proper execution of this procedure.La hipertensión arterial (HTA) es uno de los principales factores de riesgo modificables para la morbilidad y mortalidad en todo el mundo, siendo uno de los mayores factores de riesgo para la enfermedad de las arterias coronarias, el accidente cerebrovascular (ACV) y la insuficiencia renal. Además, es altamente prevalente y afecta a más de un tercio de la población mundial. La medición de la presión arterial (PA) es un procedimiento OBLIGATORIO en cualquier atención médica o realizado por diferentes profesionales de la salud. Sin embargo, todavía se realiza comúnmente sin los cuidados técnicos necesarios. Dado que el diagnóstico se basa en la medición de la PA, es claro el cuidado que debe haber con las técnicas, los métodos y los equipos utilizados en su realización. Debemos enfatizar que una vez realizado el diagnóstico, todas las investigaciones y tratamientos a corto, mediano y largo plazo se basan en los resultados de la medición de la PA. Por lo tanto, las técnicas y/o equipos inadecuados pueden llevar a diagnósticos incorrectos, subestimando o sobreestimando valores y resultando en conductas inadecuadas y pérdidas significativas para la salud y la economía de las personas y las naciones. Una vez realizado el diagnóstico correcto, a medida que avanza el conocimiento sobre la importancia del tratamiento adecuado, con la adopción de valores de normalidad más detallados y objetivos de tratamiento más cuidadosos hacia metas de PA más estrictas, también se refuerza la importancia de la precisión en la medición de la PA. La medición de la PA (descrita a continuación) generalmente se realiza mediante el método tradicional, la llamada medición casual o de consultorio. Con el tiempo, se han agregado alternativas a través del uso de dispositivos semiautomáticos o automáticos por parte del propio paciente, en salas de espera o fuera del consultorio, en su propia residencia o en espacios públicos. Se dio un paso más con el uso de dispositivos semiautomáticos equipados con memoria que permiten mediciones secuenciales fuera del consultorio (AMPA; o MRPA) y otros automáticos que permiten mediciones programadas durante períodos más largos (MAPA). Algunos aspectos en la medición de la PA pueden interferir en la obtención de resultados confiables y, en consecuencia, causar daños en las decisiones a tomar. Estos incluyen la importancia de usar valores promedio, la variación de la PA durante el día y la variabilidad a corto plazo. Estos aspectos han alentado la realización de un mayor número de mediciones en diversas situaciones, y diferentes pautas han abogado por el uso de equipos que promuevan estas acciones. Los dispositivos que realizan MRPA o MAPA, que además de permitir una mayor precisión, cuando se usan juntos, detectan la hipertensión de bata blanca (HBB), la hipertensión enmascarada (HM), las alteraciones de la PA durante el sueño y la hipertensión resistente (HR) (definida en el Capítulo 2 de esta guía), están ganando cada vez más importancia. Teniendo en cuenta estos detalles, debemos enfatizar que la información relacionada con el diagnóstico, la clasificación y el establecimiento de objetivos todavía se basa en la medición de la presión arterial en el consultorio, y por esta razón, se debe prestar toda la atención a la ejecución adecuada de este procedimiento.A hipertensão arterial (HA) é um dos principais fatores de risco modificáveis para morbidade e mortalidade em todo o mundo, sendo um dos maiores fatores de risco para doença arterial coronária, acidente vascular cerebral (AVC) e insuficiência renal. Além disso, é altamente prevalente e atinge mais de um terço da população mundial. A medida da PA é procedimento OBRIGATÓRIO em qualquer atendimento médico ou realizado por diferentes profissionais de saúde. Contudo, ainda é comumente realizada sem os cuidados técnicos necessários. Como o diagnóstico se baseia na medida da PA, fica claro o cuidado que deve haver com as técnicas, os métodos e os equipamentos utilizados na sua realização. Deve-se reforçar que, feito o diagnóstico, toda a investigação e os tratamentos de curto, médio e longo prazos são feitos com base nos resultados da medida da PA. Assim, técnicas e/ou equipamentos inadequados podem levar a diagnósticos incorretos, tanto subestimando quanto superestimando valores e levando a condutas inadequadas e grandes prejuízos à saúde e à economia das pessoas e das nações. Uma vez feito o diagnóstico correto, na medida em que avança o conhecimento da importância do tratamento adequado, com a adoção de valores de normalidade mais detalhados e com objetivos de tratamento mais cuidadosos no sentido do alcance de metas de PA mais rigorosas, fica também reforçada a importância da precisão na medida da PA. A medida da PA (descrita a seguir) é habitualmente feita pelo método tradicional, a assim chamada medida casual ou de consultório. Ao longo do tempo, foram agregadas alternativas a ela, mediante o uso de equipamentos semiautomáticos ou automáticos pelo próprio paciente, nas salas de espera ou fora do consultório, em sua própria residência ou em espaços públicos. Um passo adiante foi dado com o uso de equipamentos semiautomáticos providos de memória que permitem medidas sequenciais fora do consultório (AMPA; ou MRPA) e outros automáticos que permitem medidas programadas por períodos mais prolongados (MAPA). Alguns aspectos na medida da PA podem interferir na obtenção de resultados fidedignos e, consequentemente, causar prejuízo nas condutas a serem tomadas. Entre eles, estão: a importância de serem utilizados valores médios, a variação da PA durante o dia e a variabilidade a curto prazo. Esses aspectos têm estimulado a realização de maior número de medidas em diversas situações, e as diferentes diretrizes têm preconizado o uso de equipamentos que favoreçam essas ações. Ganham cada vez mais espaço os equipamentos que realizam MRPA ou MAPA, que, além de permitirem maior precisão, se empregados em conjunto, detectam a HA do avental branco (HAB), HA mascarada (HM), alterações da PA no sono e HA resistente (HAR) (definidos no Capítulo 2 desta diretriz). Resguardados esses detalhes, devemos ressaltar que as informações relacionadas a diagnóstico, classificação e estabelecimento de metas ainda são baseadas na medida da PA de consultório e, por esse motivo, toda a atenção deve ser dada à realização desse procedimento

Role of compliant porosity in stress dependency of ultrasonic velocities in carbonates and sandstones

A study of complex dual-nature porosity of reservoir rocks is necessary for quantitative understanding of seismic wave propagation in reservoirs. We analyze here the ratios of stiff and compliant porosities in 6 samples of carbonates and 6 samples of sandstones, and effect of compliant porosity on ultrasonic shear and compressional wave velocities measured at effective stresses from 0 to 60 MPa. The compliant porosity is estimated from stress dependency of dry rock compressibility using isotropic Shapiro theory (2003). In the case of sandstones, we have direct measurements of porosity variations with pressure whichvalidate the estimated compliant porosities. Finally, we use Gassmann equations to estimate the stress dependence of shear and compressional wave velocitiesin saturated rocks. Two examples discussed here show that a better estimation is obtained using the high frequency unrelaxed frame shear and bulk modulus(Mavko&Jizzba,1991) to “saturate” the samples

Ultrasonic velocities in carbonates: laboratory data versus a new squirt-flow dispersion model

One of the main targets of oil exploration companies nowadays are carbonate reservoirs because of the huge amounts of oil discovered in carbonates recently. Prediction of petrophysical properties of carbonates is a challenge due to the diversity of these reservoir rocks. In order to investigate main petrophysical trends such as velocity-porosity or velocity-permeability in carbonate rocks, the ultrasonic measurements are undertaken in many laboratories worldwide. However, use of Gassmann’s relations to incorporate fluid saturation effects and predict velocities of saturated rock at seismic frequencies is problematic. As was shown in a number of works which reported both increase and decrease of elastic moduli with saturation, Gassmann’s relations do not work well on carbonates samples. The softening of elastic moduli is assumed to be caused by chemical transformation of carbonates and/or frame dissolution with saturation. The stiffening of carbonate rock with saturation is shown to be caused by the local flow (squirt) between pores of different shapes and orientations and expected to be captured with Mavko and Jizba high frequency relations.In this study we analyze the experimental ultrasonic measurements in dry and saturated carbonates where pore geometry is assumed to be mostly responsible for the departure from the Gassmann’s relation. However, the measured moduli do not match the predictions of Mavko and Jizba (1991) relations either. This indicates that the measurement frequency is not high enough to inhibit pressure communication between compliant and stiff pores. Here we use a new squirt model recently developed by Gurevich et al. (2009b) in order to derive the moduli of saturated carbonates from “dry” moduli and to predict aspect ratios of compliant pores and attenuation of P- and S-waves

A simple model for squirt-flow dispersion and attenuation in fluid-saturated granular rocks.

A major cause of seismic attenuation in fluid-saturated rocks is the flow of the pore fluid induced by the passing wave. At sonic and ultrasonic frequencies, attenuation appears to be dominated by the local (pore-scale) flow between pores of different shapes and orientations. A simple squirt flow model is developed in which all of the parameters can be independently measured or estimated from measurements. The pore space of the rock is assumed to consist of stiff porosity and compliant (or soft) pores present at grain contacts.The effect of isotropically distributed compliant pores is modeled by considering pressure relaxation in a disk-shaped gap between adjacent grains. This derivation gives the complex and frequency-dependent effective bulk and shear moduli of a rock, in which the compliant pores are liquid saturated and stiff pores are dry. The resulting squirt model is consistent with Gassmann's and Mavko–Jizba equations at low and high frequencies, respectively. The magnitude of attenuation and dispersion given by the model is directly related to the variation of dry bulk modulus with pressure and is relatively independent of fluid properties

Evolution of a coquina barrier in Shark Bay, Australia by GPR imaging: Architecture of a Holocene reservoir analog

The Holocene hypersaline carbonate system in Shark Bay, Australia is represented by microbial deposits (stromatolites and thrombolites) and a supratidal coquina beach ridge system which overlies the Pleistocene Bibra Formation and is prograding seaward, since 4500 years ago, over supratidal–intertidal microbial deposits as a consequence of Late Holocene sea level fall, and the high volume of bivalve shells available. The extent, internal architecture and ridge constructional types of coquina deposits in this World Heritage area have not been previously investigated in detail by cores tied with geophysical images. Here we document external and internal architecture of the Holocene coquina system in southeast Hamelin Pool showing three depositional units which comprise the ridge system construction: (1) tabular layers complex, (2) convex-up ridges and (3) washover deposits. Bivalve skeletons represent almost the total amount of bioclasts with symmetrical semi-circular formats and valve sizes 5–9 mm. Based on Ground Penetrating Radar (GPR) images the number of prograding layers present in each transect line varies from 252 to 433, which when compared with the measured 14C ages, shows lateral growth of the system at average rates from 10 years per layer on proximal older sequences to 30 years per layer in the younger and thicker packages which display more gentle inclination and sub-horizontal arrangement. Divergent orientation of tabular layers relates to changes in energy of currents and waves and involves time gaps and erosion. After earliest crest construction the system experienced a decrease in sea level (3600–3000 14C years BP) that left behind a sequence of parallel tabular layers with dip angles (> 10° to < 20°) which accreted seaward as the first major prograding event.The accretionary tabular layers progressively lost height till near 3000 years BP, representing continuous relative SL and storm energy fall, when the first major swale was constructed. Between 2000 and 3000 years BP a series of events constructed 4 large convex-up crests separated by swales overlying tabular layers. Marked changes in layer arrangement occurred since 1000 years ago when subsequent to erosional events the coastal system rearranged and is characterized by layers with low dip angle (< 10°). The Shark Bay ridge system represents the results of waves, surges and swash during storm activity and subsequent reworking history of eroded material in a context of continuous sea level fall. Alternating beach ridges and swales represent events of storm intensity variation during falling late Holocene SL. This progradational model of coquina ridge construction at Shark Bay is a useful analog for ancient coquina reservoirs deposited in lacustrine systems, since the hydrodynamic setting and semi-closed environment affected by storms is similar to some ancient examples such as the coquina reservoirs in the Campos Basin, Brazil