http://mech.spbstu.ru/images/b/bd/Potyondy_Cundall_2004_A_bonded-particle_model_for_rock.pdf

A bonded-particle model for rock

The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

/pdf/validity-of-cubic-law-for-fluid-flow-in-a-deformable-rock-2ynq4id3hq.pdf

VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

https://www.math.ubc.ca/~peirce/Computer%20simulation%20of%20HF_Adachi_Siebrits_Peirce_Desroaches_IJRM_MS_V44_p739_2007.pdf

Computer simulation of hydraulic fractures

A clumped particle model for rock

What Is Stimulated Reservoir Volume

Imaging of microseismic data is the process by which we use information about the source locations, timing, and mechanisms of the induced seismic events to make inferences about the structure of a petroleum reservoir or the changes that accompany injections into or production from the reservoir. A few key projects were instrumental in the development of downhole microseismic imaging. Most recent microseismic projects involve imaging hydraulic-fracture stimulations, which has grown into a widespread fracture diagnostic technology. This growth in the application of the technology is attributed to the success of imaging the fracture complexity of the Barnett Shale in the Fort Worth basin, Texas, and the commercial value of the information obtained to improvecompletions and ultimately production in the field. The use of commercial imaging in the Barnett is traced back to earlier investigations to prove the technology with the Cotton Valley imaging project and earlier experiments at the M-Site in the Piceance ...

Petroleum reservoir characterization using downhole microseismic monitoring

Microseismic Imaging of Hydraulic Fracture Complexity in the Barnett Shale

Dynamic micromechanical models are used to analyze crack nucleation and propagation in brittle rock. Models of rock are created by bonding together thousands of individual particles at points of contact. The feasibility of using these bonded particle models to reproduce rock mechanical behavior is explored by comparing model behavior to results from actual laboratory tests on different rock types. The behavior of two granite models are examined in detail to study cracking and failure patterns that occur during compressional loading. Because discontinuum models are being used, the rock models are free to crack and break apart under stress, such that the micromechanics of cracking can be examined. Stress waves are allowed to propagate outward from each crack, and it is shown that these dynamic waves significantly affect the rock behavior. As the peak stress in the modeled rock is approached and many of the bonds are close to breaking, a passing wave from a nearby crack is sufficient to break more bonds. This causes clusters of cracks to be created, and then eventual macroscopic shear failure occurs as these clusters connect to bisect the sample. The failure patterns observed in the granite models are similar to those observed in actual laboratory tests.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000JB900085

Micromechanical modeling of cracking and failure in brittle rocks

Naturally fractured rock mass is highly inhomogeneous and contains geological discontinuities at various length scales. Hydraulic fracture stimulation in such a medium could result in complex fracture systems instead of simple planar fractures. In this study, we carried out fully coupled multiscale numerical analysis to investigate some key coupled processes of fluid-driven fracture propagation in naturally fractured rock mass. The numerical analysis follows the concept of the synthetic rock mass (SRM) method initially developed in the discrete element method (DEM). We introduce a total of five case study examples, including fracture initiation and near wellbore tortuosity, hydraulic fracture interaction with natural fractures, multi-stage hydraulic fracturing with discrete fracture network (DFN), in-fill well fracturing and frac hits after depletion-induced stress change, and induced seismicity associated with fault reactivation. Through those case studies, we demonstrate that with an advanced numerical modeling tool, the complex fracturing associated with hydraulic fracturing in naturally fractured rock mass can be qualitatively analyzed and the extent of various uncertainties can be assessed.

Investigating Hydraulic Fracturing Complexity in Naturally Fractured Rock Masses Using Fully Coupled Multiscale Numerical Modeling

With the current industry trend toward instrumented oil fields and smart well completions, the permanent deployment of geophones or other acoustic sensors to complement standard engineering gauges is being promoted as a way to map reservoir dynamics. The biggest push is from the time-lapse seismic practitioners, although the deployment of permanent seismic instrumentation is also potentially an ideal route to monitor passive seismicity.

Shawn Maxwell

Papers

Petroleum reservoir characterization using downhole microseismic monitoring

Microseismic Imaging of Hydraulic Fracture Complexity in the Barnett Shale

Micromechanical modeling of cracking and failure in brittle rocks

Investigating Hydraulic Fracturing Complexity in Naturally Fractured Rock Masses Using Fully Coupled Multiscale Numerical Modeling

The role of passive microseismic monitoring in the instrumented oil field