Produção Científica



Artigo em Revista
09/03/2022

Time evolution of the first-order linear acoustic/elastic wave equation using Lie product formula and Taylor expansion
We propose a new numerical solution to the first-order linear acoustic/elastic wave equation. This numerical solution is based on the analytic solution of the linear acoustic/elastic wave equation and uses the Lie product formula, where the time evolution operator of the analytic solution is written as a product of exponential matrices where each exponential matrix term is then approximated by Taylor series expansion. Initially, we check the proposed approach numerically and then demonstrate that it is more accurate to apply a Taylor expansion for the exponential function identity rather than the exponential function itself. The numerical solution formulated employs a recursive procedure and also incorporates the split perfectly matched layer boundary condition. Thus, our scheme can be used to extrapolate wavefields in a stable manner with even larger time-steps than traditional finite-difference schemes. This new numerical solution is examined through the comparison of the solution of full acoustic wave equation using the Chebyshev expansion approach for the matrix exponential term. Moreover, to demonstrate the efficiency and applicability of our proposed solution, seismic modelling results of three geological models are presented and the processing time for each model is compared with the computing time taking by the Chebyshev expansion method. We also present the result of seismic modelling using the scheme based in Lie product formula and Taylor series expansion for the firstorder linear elastic wave equation in vertical transversely isotropic and tilted transversely isotropic media as well. Finally, a post-stack migration results are also shown
using the proposed method.

Artigo em Revista
09/03/2022

Potencial gerador e maturidade térmica dos folhelhos da Formação Barreirinha, borda sul da Bacia do Amazonas, Brasil
Este trabalho tem como objetivo avaliar o potencial gerador e o efeito da intrusiva ígnea básica na maturidade térmica das amostras com base no estudo de geoquímica orgânica e palinologia. Foram estudadas 15 amostras de rocha coletadas em um afloramento da Formação Barreirinha, borda sul da Bacia do Amazonas. Nesse afloramento foi observada uma soleira de basalto que pode ter influenciado os dados geoquímicos das amostras localizadas no topo do perfil. Os teores de Carbono orgânico total (COT; 0,04–2,06%) e os resultados da pirólise Rock-Eval indicam a presença de querogênio predominantemente dos tipos II e III, potencial gerador de hidrocarbonetos (S2; 0,04–3,00 mg HC/g rocha) variando de pobre a médio, baixa concentração de hidrocarbonetos livres (S1; 0,01–0,25 mg HC/g rocha) e uma variação na maturidade termal (Tmáx: 359–605°C).
A razão aquático-terrestre (RAT; 0,08–1,16) indica a predominância de deposição de matéria orgânica algálica, e as razões dos biomarcadores saturados [Hopanos/esteranos; gamacerano/(gamacerano + C30 hopano); TTP/(TTP + DIA); e esteranos C27-C28-C29] indicam um paleoambiente marinho com contribuição variável de componentes terrestres, devido as oscilações do nível do mar ocorridas durante o Devoniano Superior. A razão entre os isoprenóides Pristano e Fitano (P/F: 1,6–7,1) apontam ambiente sub-óxico. Os resultados da cromatografia gasosa e das razões de biomarcadores saturados dos extratos orgânicos [Ts/(Ts + Tm); C29 αββ/(αββ + ααα); C29 S/(C29 S + C29R)] indicam a variação na maturidade térmica ao longo do afloramento, e sugerem a geração e migração de óleo e gás, e/ou a degradação termal de alguns biomarcadores saturados.

Artigo em Revista
09/03/2022

Some problems related to nonlinear 3Dmagnetoelasticity
We consider some direct and inverse problems associated with the vibration of an elastic conductive body governed by the Lamé and Maxwell equations coupled through the nonlinear magnetoelastic effect. First, we prove the existence and uniqueness result for a mixed initial-boundary value problem. Uniqueness is proved under additional assumptions on the smoothness of the solution. Second, we prove the solvability of an inverse problem, which consists of identifying the unknown scalar function α(t) in the elastic force α(t)β(x, t) acting on the body when some additional measurement is available.

Artigo em Revista
09/03/2022

AN ANALYTICAL SOLUTION OF THE SATURATED AND INCOMPRESSIBLE POROELASTIC MODEL FOR TRANSIENT WAVE PROPAGATION
A transient wave propagation model is provided as a consequence of a new theory of porous media and wave propagation in saturated poroelastic media. This theory, in the linear case, becomes to be equivalent to the theory proposed by de Boer, R., Ehlers, W. & Liu, Z. in 1993. It leads to a model for the 1-D porous saturated column problem, which after the appropriate establishment of boundary and initial conditions, can be solved analytically
with the aid of the Laplace transform concerning time. Numerical experiments are performed to illustrate the behavior of constituents displacement fields. The theory results in having an inertial effect on the motion of solid constituents as commonly expected. However, in contrast to Biot’s theory, is not introduced by the present theory the relative acceleration as an interactive force between solid and fluid constituents to account for the apparent inertial
effect.

Artigo em Revista
09/03/2022

Computation of Acoustic Velocity of Natural Gases With an Alternative Heat Capacity Ratio Equation and Application to Seismic Modeling
We investigate three formulations for computing acoustic velocity of natural gas and derive an equation for the heat capacity ratio, which plays a central role in these formulations. The first formulation is a compilation of fundamental equations available in the engineering literature, referred to as the DASH formulation. The second formulation is a development from the first, in which we use the derived equation for the heat capacity ratio (modified DASH). The third formulation is a mainstream method implemented in Geoscience (BW formulation). All three formulations stem from virial Equations of State that take preponderance in the exploration stage, when the detailed fluid composition is unknown and compositional methods are frequently inapplicable. We test the formulations on an extensive experimental data set of acoustic velocity of natural gases and compare the resulting accuracies. Both DASH and modified DASH formulations provide significantly higher accuracy when compared to the BW formulation. Additionally, the modified DASH, as we derive in this work, has the highest accuracy at pressures above 7000 psi, a condition typically encountered in the Brazilian pre-salt reservoirs. In a final step, we investigate how these
different formulations and corresponding accuracies in velocity computation may affect seismic modeling, using a single interface model between a dense gas reservoir and a
sealing rock. A direct comparison of amplitude versus offset modeling using our modified DASH formulation and the BW formulation shows up to 50% difference in amplitude calculation in a sensitivity exercise, especially at the longer offsets and higher pressures.

Artigo em Revista
09/03/2022

NUMERICAL SIMULATION OF SEISMIC WAVES IN POROUS MEDIA
This work presents a mathematical algorithm for modeling the propagation of poroelastic waves. We have shown how the classical Biot equations can be put into Ursin’s
form in a plane-layered 3D porous medium. Using this form, we have derived explicit formulas that can be used as the basis of an efficient computational algorithm. To validate the algorithm, numerical simulations were performed using both the poroelastic and equivalent elastic models. The results obtained confirmed the proposed algorithm’s reliability, identifying the main wave events in both low-frequency and high-frequency regimes in the reservoir
and laboratory scales, respectively. We have also illustrated the influence of some physical
parameters on the attenuation and dispersion of the slow wave.

Artigo em Revista
07/03/2022

An application of the Marchenko internal multiple elimination scheme formulated as a least-squares problem
Images produced by migration of seismic data related to complex geology are often contaminated by artifacts due to the presence of internal multiple reflections. These reflections are created when the seismic wave is reflected more than once in a source-receiver path and can be interpreted as the main coherent noise in seismic data. Several schemes have been developed to predict and subtract internal multiple reflections from measured data, such as the Marchenko multiple elimination (MME) scheme that eliminates the referred events without requiring a subsurface model or an adaptive subtraction approach. The MME scheme is data-driven, can remove or attenuate most of these internal multiples, and was originally based on the Neumann series solution of Marchenko’s projected equations. However, the Neumann series approximate solution is conditioned to a convergence criterion. We reformulate the MME as a least-squares problem (LSMME) in such a way that it can provide an alternative that avoids a convergence condition as required in the Neumann series approach. To demonstrate the LSMME scheme performance, we apply it to 2D numerical examples and compare the results with those obtained by the conventional MME scheme. In addition, we evaluate the successful application of our method through the generation of in-depth seismic images, by applying reverse time migration (RTM) to the original data set and to those obtained through MME and LSMME schemes. From the RTM results, we found that the application of both schemes on seismic data allows the construction of seismic images free of artifacts related to internal multiple events.

Artigo em Revista
07/03/2022

3D reverse time migration using a wavefield domain dynamic approach
3D Reverse-time migration (RTM) is a powerful technique for imaging complex geologic structures. This approach requires a significant computational effort, demanding a high amount of memory for storing the source's wavefields, consequently leading to a high cost to perform the imaging condition. Thus, this work aims to reduce these problems by introducing a dynamic approach (DA) that considers the sparsity of the wavefield in the first periods of propagation. The RTM combined with the DA (RTM-DA) approximates the computational domain to the propagation domain, which is the region delimited by the wavefront. In practical terms, the computational domain expands together with the wavefront, reflecting in a very significant economy of memory and reduction of processing time when compared to the conventional RTM, which we denominate as a static approach (RTM-SA). To reduce the sparsity of the wavefields in the first periods of propagation, we have built an empirical 3D filter that maps each timestep of the wavefield and gives the coordinates to approximate the computational domain to the propagation domain. We compare both approaches using the 3D SEG/EAGE Salt model and demonstrate that the RTM-DA is more efficient than the RTM-SA in terms of memory consumption and computational time, preserving the quality of the seismic image.

Artigo em Revista
07/03/2022

Influence of Bubble-point Pressure on the Gas Formation in an Oil Reservoir Under Water Injection
To evaluate the oil recovering in a reservoir producing at the bubble-point pressure, we performed numerical simulations using a sandbox model and a black oil approach for the reservoir, and the tool-kit CFD software OpenFOAM. A new solver treats the three-phase dynamics of the oil water-gas in the reservoir. The calculation includes four cases with different pressures of the injection and production wells to explore the free gas formation. Our results show that even keeping constant the pressure unbalance between the injection and production wells, we observe different dynamics. There is no gas formation and a typical production profile results if the bottom-hole pressure is just above the bubble-point in the injection and production wells. In case only the production well bottom-hole pressure is just below the bubble-point, we see no gas formation near the injection well and oscillatory gas formation around the production well. We see a triphasic flow along with the whole domain if both bottom hole pressures are just below the bubble-point. However, if the bottom-hole pressure in both wells goes further below, the gas flow rate no more oscillates and the gas formation becomes continuous. We have also treated a special case to analyze the influence of gravity on the triphasic flow. Here we observed the gravity segregation to be not significant.

Artigo em Revista
17/02/2021

Interferometric redatuming by deconvolution and correlation-based focusing
Seismic interferometry is a method used to calculate wavefields for sources and receivers that are located where only sources or only receivers are available. There are correlation- or deconvolution-based interferometric methods that can be used to reposition the seismic array from the earth’s surface to an arbitrary datum at depth. Based on the one-way reciprocity theorems of convolution and correlation type, we have determined that interferometric redatuming can be achieved in a deconvolution-only procedure in three steps. The first two steps consist of separately retrieving, for sources at the earth’s surface, the downward- and upward-propagating Green’s functions at receivers at the datum, which are then used in the third step to reposition the sources to the datum. For the involved deconvolutions, transmitted and backscattered wavefields need to be modeled with a velocity model between the acquisition and datum levels. Our numerical experiments demonstrate that the method can help to reduce nonphysical events and other artifacts that commonly arise in purely correlation-based procedures. If a high-quality overburden-velocity model is available, it correctly accounts for inhomogeneities in the overburden medium. Because the method’s sensitivity to the velocity model is mainly introduced by backscattering at overburden heterogeneities, a smooth model is sufficient when overburden scattering is weak.
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