Solid viscosity of fluid-saturated porous rock with squirt flows at seismic frequencies

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. D395-D404 ◽  
Author(s):  
Wubing Deng ◽  
Igor B. Morozov
Keyword(s):  
Wave Attenuation ◽  
Pore Space ◽  
Numerical Algorithms ◽  
Heterogeneous Porous Media ◽  
Macroscopic Model ◽  
Porous Rock ◽  
Two Phase ◽  
Waveform Modeling ◽  
Flow Models ◽  
Porous Frame

We have developed a macroscopic model for a two-phase medium (solid porous rock frame plus saturating pore fluid) with squirt flows based on Lagrangian continuum mechanics. The model focuses on improved physics of rock deformation, including explicit differential equations in time domain, causality, linearity, frequency-independent parameters with clear physical meanings, and an absence of mathematical internal or memory variables. The approach shows that all existing squirt-flow models can be viewed as microscopic models of viscosity for solid rock. As in existing models, the pore space is differentiated into compliant and relatively stiff pores. At lower frequencies, the effects of fluid flows within compliant pores are described by bulk and shear solid viscosities of the effective porous frame. Squirt-flow effects are “Biot consistent,” which means that there exists a viscous coupling between the rock frame and the fluid in stiff pores. Biot’s poroelastic effects associated with stiff porosity and global flows are also fully included in the model. Comparisons with several squirt-flow models show good agreement in predicting wave attenuation to approximately 1 kHz frequencies. The squirt-flow viscosity for sandstone is estimated in the range of [Formula: see text], which is close to field observations. Because of its origins in rigorous mechanics, the model can be used to describe any wavelike and transient deformations of heterogeneous porous media or finite bodies encountered in many field and laboratory experiments. The model also leads to new numerical algorithms for wavefield modeling, which are illustrated by 1D finite-difference waveform modeling.

A simple and general macroscopic model for local-deformation effects in fluid-saturated porous rock

2019 ◽  
Vol 220 (3) ◽  
pp. 1893-1903
Author(s):  
Wubing Deng ◽  
Igor B Morozov
Keyword(s):  
Material Properties ◽  
Seismic Waves ◽  
Wave Attenuation ◽  
Spatial Scales ◽  
Local Deformation ◽  
Macroscopic Model ◽  
Porous Rock ◽  
Specific Flow ◽  
Frequency Independent ◽  
Consistent Manner

SUMMARY Wave-induced fluid flows (WIFF) can be viewed as cases of broader local-deformation (LD) phenomena and represent the principal causes of seismic-wave attenuation in fluid-saturated porous rock. Most existing WIFF models refer to greatly simplified microstructures and specific flow patterns, such as planar divergent flows within thin cracks (squirt flows, SF) or flows within patchy-saturation zones. However, such microstructures represent only idealized mathematical models that may be impossible to consistently identify within a given rock. At the same time, most details of such microstructures are insignificant for seismic waves, which are only sensitive to averaged properties of the medium. To perform microstructure-independent modelling of LD effects, we develop a simple yet general approach based entirely on a macroscopic local-deformation variable. This variable is broadly analogous to Biot's fluid content and is illustrated for two specific microstructural models. The macroscopic model is Biot-consistent and uses only time- and frequency-independent material properties. Both local and global (Biot's) pore flows and all types of waves and deformations are explained in a rigorous and consistent manner. The model allows constraining a minimal set of material properties responsible for all observed elastic and anelastic effects in porous rock. Because of making no assumptions about the microstructures and their spatial scales, this approach should comprise at least some of the existing WIFF models. In particular, this model accurately reproduces all attenuation and velocity dispersion spectra predicted by a broadly used SF model. The model also contains effects not considered previously, such as bulk viscosity of pore fluid and viscous coupling between the rock frame and fluid-filled pores. The model offers straightforward extensions to multiple porosities and cases of viscous fluids in primary pores. Based on the resulting differential equations, physically consistent schemes for numerical modelling of seismic wavefields can be developed for porous rock with arbitrary LD effects.

Numerical Modelling and Sensitivity Analysis of Gas Kick Migration and Unloading of Riser

2019 ◽  
Author(s):  
Dalila Gomes ◽  
Knut S. Bjørkevoll ◽  
Kjell K. Fjelde ◽  
Johnny Frøyen
Keyword(s):  
Sensitivity Analysis ◽  
Transient Flow ◽  
Numerical Algorithms ◽  
Drilling Fluids ◽  
Two Phase ◽  
Worst Case ◽  
Numerical Diffusion ◽  
Flow Models ◽  
Gas Kick ◽  
Water Based

Abstract In deepwater wells there is a risk of gas entering the riser. This can be caused by gas being trapped by the BOP after a well kill operation, or it can be that the BOP was not closed quickly enough upon kick detection. With oil-based mud (OBM), gas is dissolved, and larger kicks may go undetected and circulated up in the riser by accident. If a gas kick comes into the riser, a rapid unloading event can occur. This can in worst case lead to a blowout scenario. In addition, the riser may be subject to a collapse load due to reduced liquid level inside. The unloading behavior will be different when comparing kicks in oil-based and water-based mud (WBM). For water-based muds, field experience and experiments have shown that gas can be trapped by the mud. This effect is the same that causes mud to capture cutting particles, and it is related to the non-Newtonian and time-dependent rheology behavior of the mud. The suspended gas can only be removed from the riser by circulation. The kick must therefore be of a certain volume to be able to unload the well. Modelling of the mentioned complex phenomena, with the violent transient phase seen when a large volume of gas expands as it moves towards the liquid surface in the riser, is still a challenge for numerical algorithms to do accurately and reliably. Robust handling of numerical diffusion in two-phase flow is one of the key topics, as are slippage and extension of gas in the liquid. The paper describes how an explicit numerical scheme (AUSMV) is used as a numerical solver with the application of the slope-limiter technique to handle numerical diffusion. This has not yet been done for unloading of gas in riser. A simulation case will be constructed considering gas migration and expansion in a long riser. A sensitivity analysis will be performed where both the kick volumes and the threshold for gas suspension will be varied to study when kicks will start to unload the well vs. situations where they will become fully suspended. The phenomena mentioned will be studied for water-base drilling fluids. The paper will review previous work on the subject and highlight how transient flow models can be useful for gaining more insight into how the gas behaves in risers and what can be done to mitigate the consequences.

scholarly journals Application of the mixed multiscale finite element method to parallel simulations of two-phase flows in porous media

2018 ◽  
Vol 73 ◽  
pp. 38 ◽  
Author(s):  
Maria Adela Puscas ◽  
Guillaume Enchéry ◽  
Sylvain Desroziers
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Heterogeneous Porous Media ◽  
Two Phase ◽  
Promising Alternative ◽  
Flow Models ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Element Method

The Mixed Multiscale Finite Element method (MMsFE) is a promising alternative to traditional upscaling techniques in order to accelerate the simulation of flows in large heterogeneous porous media. Indeed, in this method, the calculation of the basis functions which encompass the fine-scale variations of the permeability field, can be performed in parallel and the size of the global linear system is reduced. However, we show in this work that a two-level MPI strategy should be used to adapt the calculation resources at these two steps of the algorithm and thus obtain a better scalability of the method. This strategy has been implemented for the resolution of the pressure equation which arises in two-phase flow models. Results of simulations performed on complex reservoir models show the benefits of this approach.

scholarly journals Application of Regularized Hydrodynamic Equations for Direct Numerical Simulation of Micro-Scale Flows in Core Samples

2018 ◽  
Vol 210 ◽  
pp. 04026
Author(s):  
Boris Chetverushkin ◽  
Vladislav Balashov ◽  
Andrey Kuleshov ◽  
Evgeny Savenkov
Keyword(s):  
Numerical Simulation ◽  
Pore Space ◽  
Three Dimensional ◽  
Numerical Algorithms ◽  
Rock Physics ◽  
Core Sample ◽  
Two Phase ◽  
Central Difference ◽  
Core Samples ◽  
Voxel Representation

The paper is devoted to numerical simulation of three-dimensional isothermal two-phase two-component viscous fluid flows with surface effects in the pore space of core samples. The voxel representation of the flow domain is used suitable for digital rock physics applications. The flow is described by viscous compressible Navier-Stokes-Cahn-Hilliard equations. In order to use simple and computationally efficient explicit numerical algorithms with central difference approximations of spatial terms, a quasi-hydrodynamic regularization of equations is used. Simulation results of fluid displacement in pore space of realistic core sample (sandstone) are presented. The results demonstrate the applicability and good prospects of quasi-hydrodynamic regularization technique to solve the problem.

scholarly journals Port-Hamiltonian formulation of two-phase flow models

2021 ◽  
Vol 149 ◽  
pp. 104881
Author(s):  
H. Bansal ◽  
P. Schulze ◽  
M.H. Abbasi ◽  
H. Zwart ◽  
L. Iapichino ◽  
...  
Keyword(s):  
Two Phase Flow ◽  
Hamiltonian Formulation ◽  
Phase Flow ◽  
Two Phase ◽  
Flow Models

Numerical Simulation of Microscopic Formation of Carbon Dioxide Hydrate in Two-Phase Flow

2021 ◽  
Author(s):  
Alan Junji Yamaguchi ◽  
Kaito Kobayashi ◽  
Toru Sato ◽  
Takaomi Tobase
Keyword(s):  
Carbon Dioxide ◽  
Carbon Capture ◽  
Two Phase Flow ◽  
Pore Space ◽  
Carbon Capture And Storage ◽  
Hydrate Formation ◽  
Field Method ◽  
Phase Field Method ◽  
Phase Flow ◽  
Two Phase

Abstract The global warming is an important environmental concern and the carbon capture and storage (CCS) emerges as a very promising technology. Captured carbon dioxide (CO2) can be stored onshore or offshore in the aquifers. There is, however, a risk that stored CO2 will leak due to natural disasters. One possible solution to this is the natural formation of CO2 hydrates. Gas hydrate has an ice-like structure in which small gas molecules are trapped within cages of water molecules. Hydrate formation occurs under high pressure and low temperature conditions. Its stability under these conditions acts like a cap rock to prevent CO2 leaks. The main objective of this study is to understand how hydrate formation affects the permeability of leaked CO2 flows. The phase field method was used to simulate microscopic hydrate growth within the pore space of sand grains, while the lattice Boltzmann method was used to simulate two-phase flow. The results showed that the hydrate morphology within the pore space changes with the flow, and the permeability is significantly reduced as compared with the case without the flow.

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