Estimate the Effective Elastic Properties of Digitized Porous Rocks by Inverting the Cracks Unresolved

Current imaging technique such as micro X-ray CT can provide us detailed 3D micro-structures of porous rocks that can be used in numerical simulation so as to predict elastic properties of rocks saturated with different fluids. However, limited by the resolution the imaging process can provide, we usually lose the small features of rocks such as cracks and micro-pores, consequences of which can cause over-predicted effective elastic properties of porous rocks. In this paper, we present an inversion scheme to estimate the lost cracks during imaging process with Monte-Carlo algorithm. This method combines numerical simulation with theoretical models – the differential effective media model and Kuster-Toksöz model. Compared to the traditional inversion algorithms solely based on theoretical models, the algorithm presented in this paper utilizes the micro-structures of porous rocks resolved and takes the advantages of computational results from the digitized rocks, which in fact provides us much information of rocks and limits our inversion space for cracks. At end, we demonstrate the capability of this method on predicting the elastic properties of Berea sandstones measured in laboratory.Schlumberger Doll ResearchMassachusetts Institute of Technology. Earth Resources Laborator

Pore-scale modelling of elastic properties in hydrate-bearing sediments using 4-D synchrotron radiation imaging

Acknowledgments The financial support for this study was from PetroChina. We also thank S. K. Sahoo for sharing the high resolution 4D synchrotron radiation imaging data of hydrate formation.Peer reviewedPublisher PD

The Impact Of Stress Dependent Permeability Alteration On Gas Based EOR In The Bakken Formation

Effective stress exerted on porous rocks can change and alter reservoir permeability accordingly during reservoir development. The permeability evolution under different reservoir statues will impact oil production and EOR design in the Bakken shale porous media. An accurate permeability model can improve capturing the fluid transport mechanism and create a reliable long-term dynamic fluid forecast via reservoir simulation. This research is focused on studying permeability alteration behavior under different pressure circumstances. The reservoir gradually loses its original pore pressure during production, increasing reservoir net effective stress. Therefore, a reduction in reservoir properties such as permeability or porosity can occur in response to net stress change within the pores due to the withdrawal of the fluids from the reservoir. In contrast, a fluid injection can reduce formation pressure drop and maintain pressure during the development process in tight rock reservoirs. However, physical parameters (e.g., permeability) cannot be fully recovered, and back to its initial value, this nature of rock is characterized as stress sensitivity or hysteresis. Stress-dependent properties are hard to model accurately in reservoir simulation because of the uncertainty associated with the stress-dependent coefficients and correlations. The conventional reservoir simulators use the compressibility concept to consider the change of pore volume, where the rock properties are usually assumed to be insensitive to the evolution of the stress state. However, reservoir compaction and stress changes can significantly impact reservoir management and production performance. In this study, a review of different rock characterizations of the Three forks and Bakken core samples to determine stress dependency of permeability and its hysteresis during pressurizing/ depressurizing rock samples is conducted. Core samples from the Middle Bakken formation in North Dakota for further permeability alteration experiments are utilized. This data will be used to evaluate the permeability behavior with respect to critical pressure known as pressure shock. Also, the data analytic approach to model permeability on a larger scale based on several inputs such as depth, different net confining stress, and porosity is performed. Numerical reservoir simulation using Bakken and Three Forks formation is utilized to integrate permeability pressure correlation in simulation modeling and compare several injection scenarios with non-sensitive permeability models. The results indicate that ignoring the effect of slope discontinuity at a critical effective stress using the same equation for a whole range of data is inaccurate. Indeed, developing permeability-stress correlations cause inapplicable mathematical models and, consequently, erroneous permeability damage prediction. Following this concept, modifying the correlation for two Bakken cores shows that considering the critical points on each hysteresis path could improve the final form of the stress-dependent permeability relationship. Also, machine learning modeling using available lab core data can be used as an alternative method to capture Bakken and Three Forks permeability changes under different net confining stress while incorporating the critical pressure effect. Furthermore, to evaluate the several gas injection scenarios, the timely reservoir pressure change is divided into three distinct regions where critical effective pressure impact and miscibility of gas injection vary based on current reservoir statutes. The results demonstrate that gas injection in these formations is a strong function of fracture/matrix permeability damage. Compared to the model without considering stress-dependent permeability, the cumulative production could reduce because the permeability decreases along with reservoir pressure decline. As a result, considering permeability modeling in numerical simulation can help to understand the role of different injection scenarios and enhance the knowledge for controlling and managing reservoir production by proper operation decisions in unconventional reservoirs

Modeling of the effects of wave-induced fluid motion on seismic velocity and attenuation in porous rocks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 2010.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 169-181).In this thesis, we use the X-ray CT images of Berea sandstones to carry out the numerical study of the effects of wave-induced fluid motion on seismic velocity and attenuation in porous rocks. In numerical modeling, it is possible to control the factors and inputs that are hard to accomplish in laboratory measurements and isolate those of interest that have significant impact on the seismic responses; this can help in understanding the fundamental physics of seismic waves propagating in saturated porous rocks. The ultimate goal of computational rock physics is to supplement the traditional laboratory measurements, that are time consuming and costly, with cheaper numerical experiments that allow the parameter space to be explored more thoroughly. For this purpose, in this thesis we develop a computational method for time domain simulation of wave propagation in poroelastic medium. The medium is composed of an elastic matrix saturated with a Newtonian fluid. The method operates on a digitized representation of the medium where a distinct material phase and properties are specified at each volume cell. The dynamic response to an acoustic excitation is modeled mathematically with a coupled system of equations: elastic wave equation in the solid matrix and linearized Navier-Stokes equation in the fluid. Implementation of the solution is simplified by introducing a common numerical form for both solid and fluid cells and using a rotated-staggered-grid finite-difference scheme which allows stable solutions without explicitly handling the fluid-solid boundary conditions. A stability analysis is incorporated and can be used to select gridding and time step size as a function of material properties. The numerical results are shown to agree with the analytical solution for an idealized porous medium of periodically alternating solid and fluid layers. When applying the linear solver to compute the effective elastic properties of 3D digitized porous rocks, we find discrepancies between the numerical results and the laboratory measurements. The reason for such a problem is the loss of small features, such as cracks and micro-pores, in the digitized matrix of rocks during the imaging process of aggregation. A hybrid approach, combining the numerical computation 3 and the effective media theories, is developed to deduce the lost cracks from a limited number of laboratory measurements. This approach can recover the lost cracks and is capable of predicting the effective elastic properties of the rock matrix. Compared to the traditional inversion schemes based only on the effective media theories, this hybrid scheme has the advantage of utilizing the complex micro-structures of 3D digitized porous rocks that are resolved in the imaging process, and it helps limit the inversion space for crack distribution. In the study of the dynamic and low-frequency responses of saturated porous rocks, we employ the stress-strain calculation in numerical modeling so as to compute the velocities and attenuations of rock samples, the sizes of which are much smaller than the seismic wavelength of interest. For these cases, transmission measurement cannot be used. Realizing the significant contribution of small cracks to the total attenuation, we extend the hybrid approach by incorporating the modified squirt-flow model where a fluid with frequency-dependent bulk modulus is introduced. Therefore, attenuation due to viscous fluid in stiff pores, that are resolved in the imaging process, can be computed numerically. Attenuation due to viscous fluid in compliant pores can be determined by the modified squirt-flow model since we know the crack distribution. In the inversion for crack distribution, besides using the velocities of P- and S-waves measured in laboratory for the dry and water-saturated cases, measured attenuation data of P-waves are also used so as to further constrain the inversion, and to improve the uniqueness of the inversion results. By using such an extended hybrid approach, we are able to predict both the velocities of saturated porous rocks and the attenuations. From numerical study with the linear solver, we can conclude that the linear solver is able to accurately couple elastic solid and viscous fluid and handle high material contrast and the complex micro-structures of 3D digitized porous rocks. The stress-strain calculation is capable of computing the velocities and attenuations of saturated porous rocks the sizes of which are much smaller than the wavelength of interest. The hybrid approach is a practical way to study the seismic properties of saturated porous rocks until high enough resolution digitized data and enough computational resources are available. From the computations, we observe that the small features, such as cracks lost in the imaging process, are critical for accurately predicting velocities and attenuations of saturated porous rocks. Generally, attenuation is more sensitive to the viscosity of the saturating fluid than velocity is, and attenuation due to viscous fluid in compliant pores is greater than that due to viscous fluid in stiff pores.by Yang Zhang.Ph.D

3D Imaging and simulation of elastic properties of porous materials

The latest advancements in 3D computed tomography and numerical simulations have led to the introduction of a new digital approach. The new digital approach has enhanced the capability to generate 3D images and investigate the microstructure of complex porous materials. These images allow the numerical simulation of a wide range of physical properties to be performed when combined with imaging and analysis algorithms for phase separation. Researchers are able to obtain precise geometric descriptions and directly calculate the structure's elastic properties by using 3D imaging technique. It is also found that these advancements have enabled researchers to simulate the elastic deformation of porous materials and calculate the acoustic response of arbitrary complex media using the finite element method (FEM)