- Email: [email protected]
Integrating acoustic emission into percolation theory to predict permeability enhancement
Accepted Manuscript Integrating acoustic emission into percolation theory to predict permeability enhancement A. Sakhaee-Pour, Abhishek Agrawal PII:
S0920-4105(17)30040-2
DOI:
10.1016/j.petrol.2017.10.003
Reference:
PETROL 4326
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 4 January 2017 Revised Date:
21 July 2017
Accepted Date: 2 October 2017
Please cite this article as: Sakhaee-Pour, A., Agrawal, A., Integrating acoustic emission into percolation theory to predict permeability enhancement, Journal of Petroleum Science and Engineering (2017), doi: 10.1016/j.petrol.2017.10.003. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Integrating Acoustic Emission into Percolation Theory to Predict
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Permeability Enhancement
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A. Sakhaee-Poura,1, Abhishek Agrawalb
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Department of Petroleum Engineering, University of Houston, Houston, Texas,
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Petroleum and Geological Engineering School, University of Oklahoma, OK, USA
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Abstract: Hydraulic fracturing allows us to enhance the transport properties of a
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tight formation, but it remains difficult to predict the enhancement as a function of
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recorded acoustic events. With this in mind, we initiate pore-scale modeling of
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acoustic emission (AE) events based on percolation theory. The main objective is
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to predict the permeability enhancement by accounting for the number of acoustic
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events. We first develop a physically representative model of the intact pore space
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of the matrix of Tennessee sandstone at the core scale based on petrophysical
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measurements, which are porosity, permeability, and capillary pressure. A block-
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scale sample of the formation is then hydraulically fractured, where piezoelectric
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sensors record the events generated during stimulation. We predict the
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permeability enhancement of the formation at the core scale by accounting for the
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number of acoustic events per unit volume. Independent petrophysical
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measurements corroborate the predicted results based on percolation theory. The
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proposed model has major implications for characterizing the transport properties
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of the stimulated reservoir volume.
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Keywords: Acoustic emission (AE); Percolation theory; Hydraulic fracturing
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Introduction
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An acoustic emission (AE) is a transient elastic wave generated by the rapid
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release of energy within a material (Lockner, 1993), which can be detected using
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seismometers. AE events are associated with brittle fractures due to pressure and
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temperature. Analyzing AE has applications in earthquake seismology (Lei and
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Ma, 2014), predicting rock bursts and mine failures, fracture mapping (Phillips et
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al., 1998), monitoring mechanical performance (Cong et al., 2003), monitoring the
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condition of tools and health monitoring (Yapar et al., 2015).
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AE takes different forms because of variations in the frequency and amplitude of
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waves. Both seismic and microseismic events—a physical concept in earthquake
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seismology—are derived from AE. The science of seismology’s study of
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earthquake activity and the geophysical study of microseismic activity in rock are
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similar. There is a generation of acoustic signals whenever irreversible damage
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occurs (Lockner, 1993). The acoustic signals provide information about the size,
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the location, and the deformation mechanisms.
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Under loading, the structure deteriorates progressively in rocks and concrete, first
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in an uncorrelated way reflecting intrinsic heterogeneities. The stress fields of the
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microcracks interact, and the microcracks become correlated, as the density of the
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microcracks increases. The microcracks may coalesce to form a connected-through
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fracture as the culmination of progressive damage. AE events, due to microcracks
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growth, precede the macroscopic failure of rock and concrete samples under
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constant stress or constant strain rate loading (Stein et al., 2003; Ge, 2003).
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The petroleum industry carries out hydraulic fracturing in tight sand and shale
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reservoirs to improve their transport properties. A better approximation of the
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location and size of the connected fractures is crucial for evaluating success of
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formation stimulation and for modeling reservoir performance. The fracture
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orientation is also important in terms of stimulating the reservoir efficiently with
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minimum interference.
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Fractures created during stimulation can form a complex pattern, and are not
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necessarily planar. Thus, researchers have introduced the stimulated rock volume 3
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(SRV) for estimating well performance (Mayerhofer et al., 2008) based on three-
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dimensional microseismic events. A recent study has proposed using microseismic
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density to compute SRV at the reservoir scale (Meek et al., 2015), where
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gridblocks with no events are unstimulated and have intact transport properties.
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The transport properties of gridblocks with acoustic events are increased using an
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ad-hoc model. Researchers have also used a Kalman filter to interpolate the
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transport properties at the reservoir scale (Tarrahi et al., 2015). The proposed
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models have had some success in predicting the production rate of a formation, but
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they have not been tested against core- or block-scale measurements. The validity
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of the proposed models is critical, considering that reservoirs are highly
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heterogeneous, and the effective transport properties are controlled by different
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physics at different scales.
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Researchers also analyzed the fracture propagation based on percolation theory.
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Sahimi (2003) suggested that the initial stages of brittle fractures and percolation
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processes in a lattice are more or less similar. He proposed that percolation is a
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static process in which failure has nothing to do with the stress and strain field in
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the lattice, whereas the growth of fractures is not random, and depends on the
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stress and strain in the solid. Under certain conditions, Sahimi (2003) contended,
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the accumulation of damage and growth of cracks occur at random—for example,
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in a natural rock, where heterogeneities are broadly distributed and percolation
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systems can describe fracture.
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Sahimi (2003) also stated that, in the initial stages, the bonds that break are
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random, and the stress enhancement at the tip of a given microcrack is not large
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enough to ensure that the next microcrack occurs at the tip of the first microcrack.
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As more microcracks nucleate, however, the effect of stress enhancement becomes
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stronger, and deviations from random percolation increases. We assume that our
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lab measurements qualify for this condition, and use percolation theory to predict
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the permeability enhancement.
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The present study analyzes the permeability enhancement of Tennessee sandstone
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via analyzing acoustic events. It develops a physically representative model for the
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pore space at the core scale, which embraces pore throats and pore bodies. It then
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uses percolation theory to predict the permeability change at the core scale. The
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predicted results are tested against lab measurements.
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Methodology
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Pore-scale modeling. Pore-scale modeling is concerned with developing a
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physically representative model of the pore space of a formation. The pore space is 5
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composed of pore bodies and pore throats. The pore throats are narrow regions of
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the pore space that govern the interactions between connected pore bodies. The
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topological parameters of the pore throats and their spatial distribution control the
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effective transport properties of the matrix of a formation.
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There are two common methods for deriving the connected network of the pore
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throats and pore bodies: non-theoretical and theoretical. The non-theoretical
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models are based on extracting the network from micro-CT images of a sample
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(Khishvand et al., 2016) without any prior assumptions about the pore topology.
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The theoretical models use a theoretical distribution of the connected network of
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the pore throats and bodies to study the transport properties at the core scale.
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Washburn (1921) proposed the first theoretical pore model by representing the
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pore space as an assemblage of cylindrical capillaries. Purcell (1949) extended that
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concept to predict the permeability from capillary pressure measurements.
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Subsequently, Fatt (1956) suggested that the pore space could be mimicked using a
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regular lattice. Another theoretical approach assumes that spheres can represent the
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grains of a sedimentary rock, and thus the empty spaces between them mimic the
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void space of the porous medium (Bryant et al., 1993). More recently, researchers
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have shown that the acyclic pore model has applications in capturing the transport
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properties of shale formations (Sakhaee-Pour and Bryant, 2015) and those of The
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Geysers. Another example of a theoretical pore model is the multi-type model,
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which can be used for tight gas sandstones.
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The trend of capillary pressure measurements with wetting-phase saturation
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depends on the spatial distribution of the pore-throat size in the network of the
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connected pores (Mousavi and Bryant, 2012; 2013). We often inject mercury,
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which is a nonwetting phase to the solid grains, into the rock sample to measure
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the capillary pressure. Fig. 1a shows two common trends of the capillary pressure
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with wetting phase saturation: non-plateau-like and plateau-like (Sakhaee-Pour and
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Bryant, 2015).
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The nonwetting phase can invade a pore only when its capillary pressure is larger
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than the entry pressure of the corresponding pore throat. Wider pore throats have
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lower resistance against the invasion. In the network of the connected pores, the
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nonwetting phase can invade a pore only if it has access to the corresponding pore-
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throat size whose entry pressure is not larger than the applied capillary pressure.
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Thus, the invasion of the pore space is delayed, which is relevant to the plateau-
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like trend, when the spatial distribution of the pore-throat size is random. Fig. 1b–e
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shows how the random spatial distribution of the pore-throat size leads to a
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plateau-like trend in capillary pressure measurements, where the red represents the
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nonwetting phase and the line thickness denotes the pore throat size.
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(b) (c) (d) (e) Figure 1. (a) The plateau-like and non-plateau-like trends of capillary pressure with wetting phase saturation. (b–e) The mercury intrusion experiments with the plateau-like trend, which corresponds to the random distribution of the pore-throat size on the network of connected pores. The mercury is shown in red and the line thickness is representative of the pore-throat size. 143
A physically representative model of Tennessee sandstone. We analyzed
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Tennessee sandstone, which is homogeneous and light brown in color. Routine
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core analysis showed that the porosity and the permeability of an intact Tennessee
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core plug were equal to 5.5% and 4 µd. Mineralogy was performed using the 8
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Fourier Transform Infrared Spectroscopy (FTIR) technique, and quartz was found
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to be the main mineral (average 59 wt. %) lesser minor amounts of clays. An
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average grain size of 190 µm was obtained from a thin-section image of Tennessee
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sandstone taken under polarized light.
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Mercury injection allowed us to determine the pore-throat size distributions. Fig. 2
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shows the lab measurements conducted on a core plug. Our conclusion is that the
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pore-throat size distribution in the network of the connected pores is random
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because the trend of the capillary pressure with wetting-phase saturation is plateau-
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like. The trend of the capillary pressure with non-wetting phase saturation (= 1 –
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wetting-phase saturation) is also plateau-like, but we illustrate the former one as it
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is more common.
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(b) Figure 2. (a) Capillary pressure measurements of a Tennessee sandstone shows a plateau-like trend, which is consistent with a random pore-throat size distribution in the network of connected pores. (b) Pore-throat size distribution of the sample is determined based on the Young-Laplace relation. 160
The pore-throat size distribution is determined using the capillary pressure
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measurements (Fig. 2b). The capillary pressure is increased incrementally, and the
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injected fluid volume at each increment is measured. The incremental volume
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indicates the pore volume associated with a specific pore-throat size, which is
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determined from the applied capillary pressure. The volume fraction of each pore-
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throat size is equal to the ratio of the injected mercury volume to the pore volume,
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and the pore-throat size is a function of the capillary pressure, based on the Young-
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Laplace relation, as follows:
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2σcos θ
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where Pc is capillary pressure, σ is the interfacial tension,θ is the contact angle, and
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r is the pore throat radius. The interfacial tension of mercury is 487 × 10
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and its contact angle is 140o.
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The network modeling approach is used here to simulate the intact pore space of
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the Tennessee sandstone. In network modeling, the pore bodies (sites) are
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interconnected via pore throats. The pore body is shown with black circle and the
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pore throat with dashed line. The flow rate between adjacent sites is determined as
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follows: ∆!
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∆!
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where
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pore throat (the dashed line in Fig. 3a), ∆! is the pressure difference between the
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sites (the two neighboring sites in Fig. 3a), r is the pore-throat radius (Eq. 1), L is
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the pore-throat length, and μ is the fluid viscosity.
is the hydraulic conductance of a connecting
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is the flow rate,
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We created a two-dimensional regular lattice model, with 500 ×1200 throats, to
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mimic the intact pore space. The spatial distribution of the pore-throat size, shown
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in Fig. 2b, is randomly distributed in the network model. To determine the
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permeability, we apply a pressure gradient across the large-scale (network) model 11
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and assume that the mass is conserved at each site. The flow rate, which is
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computed under steady-state conditions, at the entrance of the large-scale model
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allows us to determine the permeability based on Darcy’s law.
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The pore-throat length (length of dashed line in conceptual Fig. 3a) is 190 µm,
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which makes the network size equal to 95 mm × 228 mm. The thickness of the
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model is tuned such that its porosity becomes equal to 5.5%, which is measured in
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the lab. These parameters lead to a network model, whose volume is equal to 1cm3.
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The permeability of the tuned network model becomes equal to 4 md, which is
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consistent with the measured permeability. The network model is physically
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representative of the intact pore space because it can predict the measured
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permeability when its porosity and the pore-throat size distribution are
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representative of the formation.
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The developed pore model is two-dimensional while the sample is three-
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dimensional. The model is suitable only because it can capture the petrophysical
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measurements conducted on core plugs; it has sufficient complexity to mimic the
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pore-scale processes. Two reasons can be given to justify the difference between
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the dimensions. First, the network model is simply a tool to account for the
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effective connectivity of the sites and their interactions. The spatial distribution of
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the sites can be changed to form a three-dimensional structure. Second, the two-
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dimensional model may be accurate for a representative slice of the actual pore
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space. A three-dimensional model can be generated from a representative slice.
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Thus, it is sufficient to study only the representative slice of the sample, rather than
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the actual three-dimensional sample.
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Integrating acoustic emission into percolation theory to predict permeability
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enhancement. This study employs percolation theory to predict the permeability
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enhancement of the formation at the core scale. It first reviews percolation theory
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based on the random distribution assumption. It then clarifies how percolation
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theory can relate acoustic events to the high-permeability paths created in
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formation stimulation.
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Percolation takes place when one medium spreads randomly through another
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(Berkowitz and Ewing, 1998). Examples include the diffusion of a solute through a
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solvent, disease spreading in a society, and fluid spreading in a porous medium
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(Broadbent and Hammersley, 1957). Randomness is the key feature of percolation
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theory and arises due to different mechanisms that are relevant to the penetrating
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and penetrated media (Sahini and Sahimi, 1994).
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Site and bond percolations are the two main categories of percolation phenomena.
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The former is more relevant to the present study and discussed here. Fig. 3a shows
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a network model where the black circles and the dashed lines indicate the absence
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of the fluid. The red squares and the solid lines indicate the presence of the fluid.
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The percolation takes place when the fluid forms a connected-through path in the
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model. The connected-through path is shown in red in Fig. 3b.
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The number of the sites occupied by the fluid relative to the total number of sites is
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equal to the probability (p), which is equal to unity when the fluid fills all the sites
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and to zero when there is no fluid in the model. The probability of the model is
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equal to the percolation threshold when percolation takes place (Dean and Bird,
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1967). The number of the occupied sites exceeds a certain number when the
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probability becomes equal to the percolation threshold. Fig. 3c shows a network
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model where the fluid occupies different sites randomly, and the percolated path is
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shown in red in Fig. 3b where the fluid forms a path from the left to the right of the
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model.
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Figure 3. (a) Site percolation where the pore body (site) is filled randomly by fluid. The black color corresponds to the absence of the fluid. (b) Shows a condition where percolation takes place and there is a connected-through path form the left to the right of the model. (c) Conceptual model for pore-scale modeling of an acoustic event. The acoustic events are assumed to be indicators of micro-fractures that interact with the adjacent pore bodies of the intact pore space. 244
We use a physically representative pore model to implement the effects of the
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microfractures on the transport properties. The pore space is treated as a network
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of pore bodies (sites) that interact with each other through pore throats (Fig. 3c).
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Each event in the representative volume is indicative of a large pore body, shown
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as a red triangle in Fig. 3c. The large pore body, whose volume is equal to the void
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space that resides in the microfracture, is connected to adjacent pores via pore
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throats, shown with dashed red lines. The transport properties of the pore throats
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connected to the large pore are dependent on the characteristic size of the
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microfracture.
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The large pore body is distributed randomly as a site, which classifies the problem
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as a site percolation. Percolation theory predicts large-scale behavior by accounting
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for randomly interconnecting small-scale phenomena. Our assumption is that the
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small-scale fractures form a connected-through path when the number of acoustic
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events per unit volume exceeds a certain value, which is relevant to the percolation
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threshold.
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The large pores (red triangles in Fig. 3c) are connected to all the pores of the intact
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pore space (black circles in Fig. 3c) in the stimulated region. Fig. 3 is a conceptual
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illustration, and the permeability calculation based on the proposed method is
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discussed subsequently (Eq. 2). The volume fraction of the stimulated regions
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depends on the number of acoustic events per unit volume of the representative
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volume that corresponds to the percolation threshold. For instance, Fig. 3c shows a
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condition where the number of acoustic events per unit volume of the
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representative volume is equal to 2, and the large pores form a connected-through
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path when this ratio becomes equal to 6.
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The total volume of the physically representative model is divided into the number
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of events recorded per unit volume for the fractured plug. The volume fraction of
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the stimulated region for partially fractured samples is equal to the ratio of its 16
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number of events per unit volume to the number of events per unit volume for the
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fractured plug. We consider a one-dimensional flow model where the stimulated
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and intact regions act in series, which allows us to determine the core-plug
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permeability as follows:
* + *−+ + ') '.
(3)
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where Keff is the effective permeability of a partially fractured plug, Km is the
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matrix permeability of an intact sample, Kf is the permeability of a fully fractured
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plug, N is the total volume of the model, and n is the stimulated region volume.
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Hydraulic fracturing of a Tennessee sandstone block. We cut and polished a
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cylindrical Tennessee sandstone and stimulated the block-scale sample under
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triaxial loading conditions. The sample diameter was 4 in and its length was
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approximately 5-1/2 in. A hole of ¼ inch in diameter was drilled in the center of
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the core and extended up to half the sample length. The hole was completed with a
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¼ inch OD tube that was cemented (Damani, 2013).
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Triaxial stress (vertical stress = 3000 psi, maximum horizontal stress = 2000 psi,
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minimum horizontal stress = 500 psi) was applied to replicate the in-situ stress
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conditions. The loading system was designed to allow triaxial loading of the rock 17
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sample with simultaneous injection of fracturing fluid and recording of acoustic
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emissions. The three stresses were applied using confining fluid pressure,
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hydraulic flat jacks, and an axial piston (Fig. 4).
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Oil was then injected into the hole at a rate of 10 cm3/min. The pressure starts to
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increase in the hole and the fluid diffuses into the pore space of the rock.
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Consequently, localized microcracking is initiated in the rock and with continued
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oil injection, the microcracks start to coalesce and form a large fracture. The block
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breaks down at 4336 psi, which was indicated by a sharp fall in the pump pressure.
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Figure 4. Hydraulic fracturing lab experimental setup. The figure on the left shows an expanded view of the triaxial loading system with axial loading, confining vessel and flat jacks to apply transverse stress. The figure on the right shows the sample covered with copper jacket mounted on the base plate of the triaxial loading system. (Damani et al., 2012; Damani, 2013).
The AE events can be divided into pre- and post-breakdown events. Pre-
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breakdown events may be caused by rock failure due to stress induced by wellbore
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pressurization and the injected fluid diffusing locally into matrix whereas post-
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breakdown events may be caused by flow through the fracture and failure of
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asperities along the fracture faces. In our experiment, most events were post-
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breakdown events (Fig. 5).
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Figure 5. Pump pressure and cumulative AE events with time 312
There were 16 piezoelectric sensors mounted on the block, with one on the top,
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one on the bottom, and the remaining 14 on the cylindrical surface of the sample,
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distributed uniformly over the azimuth and the height. AE events showed a delayed
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response, with the first events being captured at the breakdown and thereafter
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increasing rapidly. The average error in hypocenter locations for this test was +/-
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5.34 mm, and the amplitude of the events ranged from 0.1 to 0.9 volts. The total
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number of events was equal to 1564, and the density was higher close to the large
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fracture (Fig. 6). To locate the AE events, the individual arrival times of the
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compressional waves associated were recorded automatically. The first arrivals
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were used to determine the event location using a weighted least squares inversion
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algorithm (Damani, 2013). A frequency of 50 kHz to 1.5 MHz was used to filter
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the good events; the rest of the events with frequencies outside the range were
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treated as noise.
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Figure 6. Spatial locations of 1564 AE events recorded during hydraulic fracturing of a Tennessee sandstone block in a (a) three-dimensional coordinate system, (b) 21
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X-Y plane, and (c) X-Z plane. (d) The size of the blue bubbles corresponds to the amplitude of the acoustic events. The green circles represent the sensor locations. 326
Results
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The physically representative pore model is used here to predict the permeability
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enhancement at the core scale. The number of AE events per unit volume
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(#Events/volume) is determined for a core plug that has a large fracture, which can
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be observed with the naked eye. This ratio corresponds to the percolation ratio
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when the fracture forms a connected-through path. The permeability measurements
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of other core plugs, extracted from the stimulated block, provide independent
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evidence to test the model.
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We extracted five core plugs from the stimulated Tennessee sandstone block for
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petrophysical characterization (Fig. 7). One plug was extracted right on top of the
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large fracture (Left wing in Fig. 7a), whereas the other four plugs were extracted
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from either side of the large fracture (Right Wing in Fig. 7a). Table 1 lists the
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spatial locations of the core plugs with respect to the coordinate system shown in
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Fig. 7, their bulk volume, and the number of acoustic events. The core plug with
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the connected-through fracture is referred to as the Fractured plug in Table 1 and
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has the largest #Events/volume and highest permeability; the other plugs are
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named Plugs 1−4 in Table 1.
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Figure 7. (a-b) Block-scale sample of a hydraulically fractured Tennessee sandstone, where the holes show the locations of the extracted core plugs for permeability measurements. The fracture left and right wings are shown by blue red lines, respectively. (c) Scanning electron microscope (SEM) image of the fractured core plugs that shows a connected-through fractures in the sample.
Fig. 7 shows a scanning electron microscope (SEM) image of the formation where
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there is a connected-through fracture in the sample, which is created during
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hydraulic fracturing of the block. The high-resolution image shows the fracture
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with no confinement. The high resolution suggests that the aperture size of the
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connected fracture could be on the order of 1–10 µm.
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We measured the permeability of each core plug listed in as a function of effective
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stress (Table 2). The confining stress was changed where the pore pressure was
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200 psi. The pore pressure was fixed using the AP-608TM permeameter, and the
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effective stress was calculated as follows: Effective stress = Confining stress – Pore pressure
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The lab measurements are normalized with respect to the measured value measured
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for each sample when the effective stress is equal to 300 psi (Fig. 8). The results
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are normalized with respect to the confined conditions because they are more
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representative of in-situ conditions. The rate of the permeability decrease with the
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effective stress is relatively similar for different samples, especially at low
363
effective stress. The similarity suggests that the permeability decline is controlled
364
by the change in the effective aperture size of the fractures. The similarity could
365
also be a result of a homogeneous material distribution. The decrease rate of the
366
fractured plug deviates from the other plugs as the effective stress increases, which
367
could be due to the plastic deformation. The lab measurements revealed that the
368
plug permeability did not recover fully to the original value because of the plastic
369
deformation after the test when the confining stress was removed.
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Figure 8. The permeability decreases as the effective stress increases for different plugs.
The fractured plug permeability was also measured as a function of the confining
375
stress. The fractured plug permeability was 5.342 md when the confining stress
376
was equal to 1000 psi. The measured permeability is used as an estimate for the
377
permeability of the stimulated region (Fig. 3c). The measured permeability is also
378
used to normalize the results, denoted by k fractured plug in Fig. 8.
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The spatial locations of the recorded events and the bulk volume of each core plug
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determine the number of AE events per unit volume (#Events/volume). This ratio
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is equal to 6.95 cm-3 for the fractured plug, which corresponds to the percolation
383
threshold. We predicted the permeability of the core plug when this ratio is smaller
384
than the percolation threshold based on percolation theory, using the physically
385
representative pore model. Fig. 9 reveals that the core-scale measurements
386
corroborate the predicted results. The permeability of the formation remains close
387
to the intact value at the core scale when the #Events/volume is smaller than the
388
threshold value. Our model also suggests that the stimulated permeability increases
389
by a factor of 2 relative to the intact permeability ( = 4md). Thus, the intact
390
permeability remains close to the matrix permeability, as opposed to the fractured
391
plug permeability.
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Figure 9. Core-scale measurements corroborate the physically representative pore model, which predicts the permeability enhancement based on percolation theory. The stimulated permeability remains very close to that of the matrix, as opposed to that of the fractured plug, when the number of acoustic events per unit volume (#Events/volume) is smaller than the percolation threshold. 392
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We used all the data available from the core plugs recovered from the block
394
sample to test our model. Most AE events occur on the fracture, which is the
395
reason for the absence of lab measurements with #Event/volume between 3 and 6.
396
The core plugs with small #Events/volume were taken as close as possible to the
397
main fracture. Nonetheless, the simulation results and lab measurements indicate
398
that the permeability close to the main fracture remains close to the intact
399
permeability and the enhanced permeability does not increase linearly with
400
#Events/volume.
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Now, we turn to the sensitivity of the results to the amplitude of the events
403
recorded (Fig. 10). The amplitude cutoff (%) is defined as removing events that
404
have amplitude values in the bottom x% of the total events. The number of events
405
per unit volume (#Events/volume) decreases the most for the fractured plug. The
406
significant decrease for the fractured plug indicates that there is a wide amplitude
407
range. Nevertheless, it is apparent that the cutoff value does not change the trend of
408
results because it only shifts them monotonically.
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Plug 1 Plug 2
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#Events/Volume (1/cm3)
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0%
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40% 60% Amplitude cutoff (%)
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Figure 10. #Events/volume decreases monotonically with increasing amplitude cutoff.
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Dahi and Lorenzo (2011) indicated that low-frequency events were the tensile
412
events causing Mode I failure. Low-frequency events are beyond the scope of the
413
present work, because our device does not record events below 50 kHz. We
414
considered four kinds of failure mechanisms: shear, tensile, compressive, and
415
complex. Our hypothesis is that each event is an indicative of a microfracture, and
416
the microfractures form a macrofracture when #Events/volume reaches a critical
417
value.
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Discussion
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In petroleum engineering, the ultimate goal of most research, including the present
421
study, is to be applied in field. The presented model and lab measurements predict
422
the permeability enhancement of a stimulated region, without a connected-through
423
fracture, based on its acoustic emission. The stimulated region is also referred to as
424
the process zone (Znag et al. 2000). Our study suggests that the enhanced
425
permeability remains close to the intact permeability, and that it is unrealistic to
426
use a linear approximation for the stimulated region permeability. Knowing that, in
427
the absence of a connected-through fracture, the permeability increase is not very
428
significant is crucial for building a realistic reservoir model.
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Another issue is the size of the stimulated region. The size of the stimulated region,
431
whose permeability is close to the intact permeability, relative to the overall
432
domain is equal to the size of the core plug to the block. We can predict the
433
stimulated region size if the results can be scaled to the field conditions. The
434
stimulated region size close to each fracture can be predicted by accounting for the
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fracture length.
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The presented results are relevant to fluid injection into a dry sample. The size of
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the stimulated region and the spatial distribution of the events may change if the
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sample is initially saturated and when conducted for a different formation. Our 29
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model is based on the assumption that the spatial distribution of the pore-throat
441
size is random, which is realistic for Tennessee sandstone. The developed model
442
needs modifications when this assumption is not realistic.
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Conclusions
445
We developed a physically representative pore model of an intact Tennessee
446
sandstone at the core scale by analyzing its permeability, porosity, and capillary
447
pressure measurements. Our main objective was to predict the permeability
448
enhancement by accounting for acoustic emission (AE) events. Our assumption
449
was that each event is representative of a microcrack or is indicative of an asperity
450
which compressed during fracture closure. This assumption implies that a
451
connected-through fracture is formed when the number of AE events per unit
452
volume becomes larger than the threshold value.
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We predicted the permeability enhancement of a formation based on percolation
455
theory. Our study shows that the stimulated permeability of a formation at the core
456
scale is much smaller than the fractured plug permeability if the number of events
457
per volume is smaller than the threshold value. The permeability enhancement of
458
the core plug, relative to intact conditions, is close to 2 when the fracture does not
459
form a connected-through path. The proposed model, which relates the number of
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acoustic emission events to the enhanced permeability based on percolation theory,
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has major applications in determining the transport properties of the stimulated
462
reservoir volume.
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Acknowledgements
465
The authors are grateful to Carl Sondergeld and Akash Damani for sharing some of
466
the lab measurements (Damani et al., 2012; Damani 2013) analyzed in this study.
467
The authors are also grateful for the constructive comments of four anonymous
468
reviewers.
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Declarations
471
The authors declare that they have no competing interests. ASP developed and
472
tested the main concept of the present study. He integrated the acoustic emission
473
events into percolation theory to predict the permeability enhancement. ASP wrote
474
and revised the manuscript. AA coded the two-dimensional network of the sample
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and prepared the plots.
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References
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Berkowitz, B., and Ewing, R. P., 1998, Percolation theory and network modeling applications in
479
soil physics, Surveys in Geophysics, 19(1), 23–72.
480 31
ACCEPTED MANUSCRIPT
481
Broadbent, S. R., and Hammersley, J. M., 1957, Percolation processes, In Mathematical
482
Proceedings of the Cambridge Philosophical Society, 53, 629–641.
483
Bryant, S. L., Mellor, D. W., and Cade, C. A., 1993, Physically representative network models of
485
transport in porous media, AIChE Journal, 39(3), 387–396.
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484
486 487
Chong, K. P., Carino, N. J., and Washer, G., 2003, Health monitoring of civil
488
infrastructures, Smart Materials and structures, 12(3), 483.
SC
489
Dahi Taleghani, A., & Lorenzo, J. M. (2011, January 1). An Alternative Interpretation of
491
Microseismic Events during Hydraulic Fracturing. Society of Petroleum Engineers.
492
doi:10.2118/140468-MS.
M AN U
490
493 494
Damani, A., Sharma, A., Sondergeld, C., and Rai. C.S., 2012, Acoustic emission and SEM
495
analyses of hydraulic fractures under triaxial stress conditions, Presented at SEG Annual
496
Meeting, Las Vegas, Nevada, USA, November 4–9. SEG-1585.
TE D
497 498
Damani, A., 2013. Acoustic mapping and fractography of laboratory induced hydraulic
499
fractures (Doctoral dissertation, University of Oklahoma).
500
Dean, P., and Bird, N. F, 1967, Monte Carlo estimates of critical percolation probabilities,
502
In Mathematical Proceedings of the Cambridge Philosophical Society, 63(2), 477–479.
AC C
503
EP
501
504
Fatt, I., 1956, The network model of porous media. I. Capillary pressure characteristics, AIME
505
Pet Trans. 207,144–59.
506 507
Ge, M., 2003, Analysis of source location algorithms: Part I. Overview and non-iterative
508
methods, Journal of Acoustic Emission, 21(1), 21–28.
509
32
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510
Khishvand, M., Alizadeh, A. H., and Piri, M., 2016, In-situ characterization of wettability and
511
pore-scale displacements during two-and three-phase flow in natural porous media, Advances in
512
Water Resources, 97, 279–298.
513
Lei, X., and Ma, S., 2014, Laboratory acoustic emission study for earthquake generation
515
process, Earthquake Science, 27(6), 627–646.
RI PT
514
516
Lockner, D., 1993, The role of acoustic emission in the study of rock fracture, International
518
Journal of Rock Mechanics and Mining Sciences and Geomechanics 30(7), 883–899.
SC
517
519
Mayerhofer, M. J., Lolon, E., Warpinski, N. R., Cipolla, C. L., Walser, D. W., and Rightmire, C.
521
M., 2010, What is stimulated reservoir volume?, SPE Production and Operations, 25(01), 89–98.
M AN U
520
522
Meek, R. A., Suliman, B., Bello, H., and Hull, R., 2015, Well space modeling, SRV prediction
524
using microseismic, seismic rock properties and structural attributes in the Eagle Ford shale of
525
south Texas, Presented at SPE Unconventional Resources Technology Conference, San Antonio,
526
Texas, USA, July 20–22, URTEC-2173501-MS.
527
TE D
523
Mousavi, M. A., and Bryant, S. L., 2012, Connectivity of pore space as a control on two-phase
529
flow properties of tight-gas sandstones, Transport in porous media, 94(2), 1–18.
530
EP
528
Mousavi, M. A., and Bryant, S. L., 2013, Geometric models of porosity reduction by ductile
532
grain compaction and cementation. AAPG bulletin, 97(12), 2129–48.
533
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531
534
Phillips, W. S., Fairbanks, T. D., Rutledge, J. T., and Anderson, D. W., 1998, Induced
535
microearthquake patterns and oil-producing fracture systems in the Austin
536
chalk, Tectonophysics 289(1), 153–169.
537 538
Purcell, W. R., 1949, Capillary pressures-their measurement using mercury and the calculation
539
of permeability therefrom, Journal of Petroleum Technology, 1(02), 39–48.
33
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540
Sahimi, M., 2003, Heterogeneous Materials: Nonlinear and breakdown properties and atomistic
541
modeling (Vol. 2). Springer Science & Business Media.
542
Sahini, M., and Sahimi M., 1994, Applications of percolation theory (CRC Press).
544 545
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Sakhaee-Pour, A., and Bryant, S. L., 2015, Pore structure of shale, Fuel, 143, 467–475.
546
Stein, S., Wysession, M., and Houston, H., 2003, Books-An Introduction to Seismology,
548
Earthquakes, and Earth Structure, Physics Today 56(10), 65–72.
SC
547
549
Tarrahi, M., Jafarpour, B., and Ghassemi, A., 2015, Integration of microseismic monitoring data
551
into coupled flow and geomechanical models with ensemble Kalman filter, Water Resources
552
Research, 51(7), 5177–5197.
553 554
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Washburn, E. W., 1921, The dynamics of capillary flow, Physical review 17(3), 273.
555
Yapar, O., Basu, P. K., Volgyesi, P., and Ledeczi, A., 2015, Structural health monitoring of
557
bridges with piezoelectric AE sensors, Engineering Failure Analysis, 56, 150–169.
558
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Zang, A., Wagner, F. C., Stanchits, S., Janssen, C., and Dresen, G., 2000, Fracture process zone
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in granite. Journal of Geophysical Research: Solid Earth, 105(B10), 23651–23661.
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Table 1. Spatial location, number of acoustic events, and the block volume of the
573
core plug extracted from the stimulated Tennessee sandstone block shown in Fig.
574
7. X(mm)
Y(mm)
Z(mm)
#Events
Bulk
#Events/volume
volume
(cm-3)
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Plug
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(cm3)
Plug 2
30
Plug 3
30
Plug 4
30
Fractured
-32
12.5
31
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30
0.13
12
15.21
0.79
-12.5
31
6
13.25
0.45
-12.5
58
21
13.25
1.54
0
78
134
19.27
6.95
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15.21
58
plug 575
2
12.5
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Plug 1
577 578
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579 580
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581 582
Diameter (mm) 25.4
Permeability (md) 0.008
Plug 2
27
25.4
0.007
Plug 3
31
Plug 4
27
Fractured plug
39
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Plug 1
Length (mm) 31
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Table 2. Plug length, diameter, and permeability at 300 psi effective stress.
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25.4
0.007
25.4
0.007
25.4
8.097
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Highlights • We conduct comprehensive lab measurements to hydraulically fracture a block-
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scale sample of Tennessee sandstone.
• We model pore-space alteration of Tennessee sandstone during hydraulic
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fracturing.
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• We predict permeability of the stimulated reservoir volume based on the percolation theory.
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• We test our model with independent lab measurements.
S0920-4105(17)30040-2
DOI:
10.1016/j.petrol.2017.10.003
Reference:
PETROL 4326
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 4 January 2017 Revised Date:
21 July 2017
Accepted Date: 2 October 2017
Please cite this article as: Sakhaee-Pour, A., Agrawal, A., Integrating acoustic emission into percolation theory to predict permeability enhancement, Journal of Petroleum Science and Engineering (2017), doi: 10.1016/j.petrol.2017.10.003. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Integrating Acoustic Emission into Percolation Theory to Predict
2
Permeability Enhancement
3
A. Sakhaee-Poura,1, Abhishek Agrawalb
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a
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Department of Petroleum Engineering, University of Houston, Houston, Texas,
USA b
Petroleum and Geological Engineering School, University of Oklahoma, OK, USA
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Abstract: Hydraulic fracturing allows us to enhance the transport properties of a
9
tight formation, but it remains difficult to predict the enhancement as a function of
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recorded acoustic events. With this in mind, we initiate pore-scale modeling of
11
acoustic emission (AE) events based on percolation theory. The main objective is
12
to predict the permeability enhancement by accounting for the number of acoustic
13
events. We first develop a physically representative model of the intact pore space
14
of the matrix of Tennessee sandstone at the core scale based on petrophysical
15
measurements, which are porosity, permeability, and capillary pressure. A block-
16
scale sample of the formation is then hydraulically fractured, where piezoelectric
17
sensors record the events generated during stimulation. We predict the
18
permeability enhancement of the formation at the core scale by accounting for the
19
number of acoustic events per unit volume. Independent petrophysical
20
measurements corroborate the predicted results based on percolation theory. The
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Email: [email protected] 1
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proposed model has major implications for characterizing the transport properties
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of the stimulated reservoir volume.
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Keywords: Acoustic emission (AE); Percolation theory; Hydraulic fracturing
25
Introduction
27
An acoustic emission (AE) is a transient elastic wave generated by the rapid
28
release of energy within a material (Lockner, 1993), which can be detected using
29
seismometers. AE events are associated with brittle fractures due to pressure and
30
temperature. Analyzing AE has applications in earthquake seismology (Lei and
31
Ma, 2014), predicting rock bursts and mine failures, fracture mapping (Phillips et
32
al., 1998), monitoring mechanical performance (Cong et al., 2003), monitoring the
33
condition of tools and health monitoring (Yapar et al., 2015).
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AE takes different forms because of variations in the frequency and amplitude of
36
waves. Both seismic and microseismic events—a physical concept in earthquake
37
seismology—are derived from AE. The science of seismology’s study of
38
earthquake activity and the geophysical study of microseismic activity in rock are
39
similar. There is a generation of acoustic signals whenever irreversible damage
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40
occurs (Lockner, 1993). The acoustic signals provide information about the size,
41
the location, and the deformation mechanisms.
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Under loading, the structure deteriorates progressively in rocks and concrete, first
44
in an uncorrelated way reflecting intrinsic heterogeneities. The stress fields of the
45
microcracks interact, and the microcracks become correlated, as the density of the
46
microcracks increases. The microcracks may coalesce to form a connected-through
47
fracture as the culmination of progressive damage. AE events, due to microcracks
48
growth, precede the macroscopic failure of rock and concrete samples under
49
constant stress or constant strain rate loading (Stein et al., 2003; Ge, 2003).
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The petroleum industry carries out hydraulic fracturing in tight sand and shale
52
reservoirs to improve their transport properties. A better approximation of the
53
location and size of the connected fractures is crucial for evaluating success of
54
formation stimulation and for modeling reservoir performance. The fracture
55
orientation is also important in terms of stimulating the reservoir efficiently with
56
minimum interference.
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Fractures created during stimulation can form a complex pattern, and are not
59
necessarily planar. Thus, researchers have introduced the stimulated rock volume 3
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(SRV) for estimating well performance (Mayerhofer et al., 2008) based on three-
61
dimensional microseismic events. A recent study has proposed using microseismic
62
density to compute SRV at the reservoir scale (Meek et al., 2015), where
63
gridblocks with no events are unstimulated and have intact transport properties.
64
The transport properties of gridblocks with acoustic events are increased using an
65
ad-hoc model. Researchers have also used a Kalman filter to interpolate the
66
transport properties at the reservoir scale (Tarrahi et al., 2015). The proposed
67
models have had some success in predicting the production rate of a formation, but
68
they have not been tested against core- or block-scale measurements. The validity
69
of the proposed models is critical, considering that reservoirs are highly
70
heterogeneous, and the effective transport properties are controlled by different
71
physics at different scales.
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Researchers also analyzed the fracture propagation based on percolation theory.
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Sahimi (2003) suggested that the initial stages of brittle fractures and percolation
75
processes in a lattice are more or less similar. He proposed that percolation is a
76
static process in which failure has nothing to do with the stress and strain field in
77
the lattice, whereas the growth of fractures is not random, and depends on the
78
stress and strain in the solid. Under certain conditions, Sahimi (2003) contended,
79
the accumulation of damage and growth of cracks occur at random—for example,
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in a natural rock, where heterogeneities are broadly distributed and percolation
81
systems can describe fracture.
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Sahimi (2003) also stated that, in the initial stages, the bonds that break are
84
random, and the stress enhancement at the tip of a given microcrack is not large
85
enough to ensure that the next microcrack occurs at the tip of the first microcrack.
86
As more microcracks nucleate, however, the effect of stress enhancement becomes
87
stronger, and deviations from random percolation increases. We assume that our
88
lab measurements qualify for this condition, and use percolation theory to predict
89
the permeability enhancement.
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The present study analyzes the permeability enhancement of Tennessee sandstone
92
via analyzing acoustic events. It develops a physically representative model for the
93
pore space at the core scale, which embraces pore throats and pore bodies. It then
94
uses percolation theory to predict the permeability change at the core scale. The
95
predicted results are tested against lab measurements.
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Methodology
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Pore-scale modeling. Pore-scale modeling is concerned with developing a
99
physically representative model of the pore space of a formation. The pore space is 5
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composed of pore bodies and pore throats. The pore throats are narrow regions of
101
the pore space that govern the interactions between connected pore bodies. The
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topological parameters of the pore throats and their spatial distribution control the
103
effective transport properties of the matrix of a formation.
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There are two common methods for deriving the connected network of the pore
106
throats and pore bodies: non-theoretical and theoretical. The non-theoretical
107
models are based on extracting the network from micro-CT images of a sample
108
(Khishvand et al., 2016) without any prior assumptions about the pore topology.
109
The theoretical models use a theoretical distribution of the connected network of
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the pore throats and bodies to study the transport properties at the core scale.
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Washburn (1921) proposed the first theoretical pore model by representing the
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pore space as an assemblage of cylindrical capillaries. Purcell (1949) extended that
114
concept to predict the permeability from capillary pressure measurements.
115
Subsequently, Fatt (1956) suggested that the pore space could be mimicked using a
116
regular lattice. Another theoretical approach assumes that spheres can represent the
117
grains of a sedimentary rock, and thus the empty spaces between them mimic the
118
void space of the porous medium (Bryant et al., 1993). More recently, researchers
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have shown that the acyclic pore model has applications in capturing the transport
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properties of shale formations (Sakhaee-Pour and Bryant, 2015) and those of The
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Geysers. Another example of a theoretical pore model is the multi-type model,
122
which can be used for tight gas sandstones.
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The trend of capillary pressure measurements with wetting-phase saturation
125
depends on the spatial distribution of the pore-throat size in the network of the
126
connected pores (Mousavi and Bryant, 2012; 2013). We often inject mercury,
127
which is a nonwetting phase to the solid grains, into the rock sample to measure
128
the capillary pressure. Fig. 1a shows two common trends of the capillary pressure
129
with wetting phase saturation: non-plateau-like and plateau-like (Sakhaee-Pour and
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Bryant, 2015).
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The nonwetting phase can invade a pore only when its capillary pressure is larger
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than the entry pressure of the corresponding pore throat. Wider pore throats have
134
lower resistance against the invasion. In the network of the connected pores, the
135
nonwetting phase can invade a pore only if it has access to the corresponding pore-
136
throat size whose entry pressure is not larger than the applied capillary pressure.
137
Thus, the invasion of the pore space is delayed, which is relevant to the plateau-
138
like trend, when the spatial distribution of the pore-throat size is random. Fig. 1b–e
139
shows how the random spatial distribution of the pore-throat size leads to a
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plateau-like trend in capillary pressure measurements, where the red represents the
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nonwetting phase and the line thickness denotes the pore throat size.
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(b) (c) (d) (e) Figure 1. (a) The plateau-like and non-plateau-like trends of capillary pressure with wetting phase saturation. (b–e) The mercury intrusion experiments with the plateau-like trend, which corresponds to the random distribution of the pore-throat size on the network of connected pores. The mercury is shown in red and the line thickness is representative of the pore-throat size. 143
A physically representative model of Tennessee sandstone. We analyzed
144
Tennessee sandstone, which is homogeneous and light brown in color. Routine
145
core analysis showed that the porosity and the permeability of an intact Tennessee
146
core plug were equal to 5.5% and 4 µd. Mineralogy was performed using the 8
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Fourier Transform Infrared Spectroscopy (FTIR) technique, and quartz was found
148
to be the main mineral (average 59 wt. %) lesser minor amounts of clays. An
149
average grain size of 190 µm was obtained from a thin-section image of Tennessee
150
sandstone taken under polarized light.
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Mercury injection allowed us to determine the pore-throat size distributions. Fig. 2
153
shows the lab measurements conducted on a core plug. Our conclusion is that the
154
pore-throat size distribution in the network of the connected pores is random
155
because the trend of the capillary pressure with wetting-phase saturation is plateau-
156
like. The trend of the capillary pressure with non-wetting phase saturation (= 1 –
157
wetting-phase saturation) is also plateau-like, but we illustrate the former one as it
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is more common.
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(b) Figure 2. (a) Capillary pressure measurements of a Tennessee sandstone shows a plateau-like trend, which is consistent with a random pore-throat size distribution in the network of connected pores. (b) Pore-throat size distribution of the sample is determined based on the Young-Laplace relation. 160
The pore-throat size distribution is determined using the capillary pressure
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measurements (Fig. 2b). The capillary pressure is increased incrementally, and the
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injected fluid volume at each increment is measured. The incremental volume
164
indicates the pore volume associated with a specific pore-throat size, which is
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determined from the applied capillary pressure. The volume fraction of each pore-
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throat size is equal to the ratio of the injected mercury volume to the pore volume,
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and the pore-throat size is a function of the capillary pressure, based on the Young-
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Laplace relation, as follows:
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2σcos θ
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where Pc is capillary pressure, σ is the interfacial tension,θ is the contact angle, and
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r is the pore throat radius. The interfacial tension of mercury is 487 × 10
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and its contact angle is 140o.
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The network modeling approach is used here to simulate the intact pore space of
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the Tennessee sandstone. In network modeling, the pore bodies (sites) are
175
interconnected via pore throats. The pore body is shown with black circle and the
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pore throat with dashed line. The flow rate between adjacent sites is determined as
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follows: ∆!
π
4
8μ&
∆!
(2)
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where
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pore throat (the dashed line in Fig. 3a), ∆! is the pressure difference between the
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sites (the two neighboring sites in Fig. 3a), r is the pore-throat radius (Eq. 1), L is
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the pore-throat length, and μ is the fluid viscosity.
is the hydraulic conductance of a connecting
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is the flow rate,
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We created a two-dimensional regular lattice model, with 500 ×1200 throats, to
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mimic the intact pore space. The spatial distribution of the pore-throat size, shown
186
in Fig. 2b, is randomly distributed in the network model. To determine the
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permeability, we apply a pressure gradient across the large-scale (network) model 11
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and assume that the mass is conserved at each site. The flow rate, which is
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computed under steady-state conditions, at the entrance of the large-scale model
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allows us to determine the permeability based on Darcy’s law.
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The pore-throat length (length of dashed line in conceptual Fig. 3a) is 190 µm,
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which makes the network size equal to 95 mm × 228 mm. The thickness of the
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model is tuned such that its porosity becomes equal to 5.5%, which is measured in
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the lab. These parameters lead to a network model, whose volume is equal to 1cm3.
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The permeability of the tuned network model becomes equal to 4 md, which is
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consistent with the measured permeability. The network model is physically
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representative of the intact pore space because it can predict the measured
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permeability when its porosity and the pore-throat size distribution are
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representative of the formation.
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The developed pore model is two-dimensional while the sample is three-
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dimensional. The model is suitable only because it can capture the petrophysical
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measurements conducted on core plugs; it has sufficient complexity to mimic the
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pore-scale processes. Two reasons can be given to justify the difference between
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the dimensions. First, the network model is simply a tool to account for the
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effective connectivity of the sites and their interactions. The spatial distribution of
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the sites can be changed to form a three-dimensional structure. Second, the two-
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dimensional model may be accurate for a representative slice of the actual pore
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space. A three-dimensional model can be generated from a representative slice.
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Thus, it is sufficient to study only the representative slice of the sample, rather than
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the actual three-dimensional sample.
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Integrating acoustic emission into percolation theory to predict permeability
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enhancement. This study employs percolation theory to predict the permeability
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enhancement of the formation at the core scale. It first reviews percolation theory
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based on the random distribution assumption. It then clarifies how percolation
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theory can relate acoustic events to the high-permeability paths created in
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formation stimulation.
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Percolation takes place when one medium spreads randomly through another
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(Berkowitz and Ewing, 1998). Examples include the diffusion of a solute through a
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solvent, disease spreading in a society, and fluid spreading in a porous medium
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(Broadbent and Hammersley, 1957). Randomness is the key feature of percolation
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theory and arises due to different mechanisms that are relevant to the penetrating
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and penetrated media (Sahini and Sahimi, 1994).
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Site and bond percolations are the two main categories of percolation phenomena.
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The former is more relevant to the present study and discussed here. Fig. 3a shows
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a network model where the black circles and the dashed lines indicate the absence
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of the fluid. The red squares and the solid lines indicate the presence of the fluid.
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The percolation takes place when the fluid forms a connected-through path in the
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model. The connected-through path is shown in red in Fig. 3b.
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The number of the sites occupied by the fluid relative to the total number of sites is
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equal to the probability (p), which is equal to unity when the fluid fills all the sites
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and to zero when there is no fluid in the model. The probability of the model is
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equal to the percolation threshold when percolation takes place (Dean and Bird,
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1967). The number of the occupied sites exceeds a certain number when the
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probability becomes equal to the percolation threshold. Fig. 3c shows a network
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model where the fluid occupies different sites randomly, and the percolated path is
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shown in red in Fig. 3b where the fluid forms a path from the left to the right of the
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model.
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Figure 3. (a) Site percolation where the pore body (site) is filled randomly by fluid. The black color corresponds to the absence of the fluid. (b) Shows a condition where percolation takes place and there is a connected-through path form the left to the right of the model. (c) Conceptual model for pore-scale modeling of an acoustic event. The acoustic events are assumed to be indicators of micro-fractures that interact with the adjacent pore bodies of the intact pore space. 244
We use a physically representative pore model to implement the effects of the
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microfractures on the transport properties. The pore space is treated as a network
247
of pore bodies (sites) that interact with each other through pore throats (Fig. 3c).
248
Each event in the representative volume is indicative of a large pore body, shown
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as a red triangle in Fig. 3c. The large pore body, whose volume is equal to the void
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space that resides in the microfracture, is connected to adjacent pores via pore
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throats, shown with dashed red lines. The transport properties of the pore throats
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connected to the large pore are dependent on the characteristic size of the
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microfracture.
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The large pore body is distributed randomly as a site, which classifies the problem
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as a site percolation. Percolation theory predicts large-scale behavior by accounting
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for randomly interconnecting small-scale phenomena. Our assumption is that the
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small-scale fractures form a connected-through path when the number of acoustic
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events per unit volume exceeds a certain value, which is relevant to the percolation
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threshold.
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The large pores (red triangles in Fig. 3c) are connected to all the pores of the intact
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pore space (black circles in Fig. 3c) in the stimulated region. Fig. 3 is a conceptual
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illustration, and the permeability calculation based on the proposed method is
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discussed subsequently (Eq. 2). The volume fraction of the stimulated regions
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depends on the number of acoustic events per unit volume of the representative
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volume that corresponds to the percolation threshold. For instance, Fig. 3c shows a
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condition where the number of acoustic events per unit volume of the
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representative volume is equal to 2, and the large pores form a connected-through
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path when this ratio becomes equal to 6.
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The total volume of the physically representative model is divided into the number
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of events recorded per unit volume for the fractured plug. The volume fraction of
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the stimulated region for partially fractured samples is equal to the ratio of its 16
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number of events per unit volume to the number of events per unit volume for the
276
fractured plug. We consider a one-dimensional flow model where the stimulated
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and intact regions act in series, which allows us to determine the core-plug
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permeability as follows:
* + *−+ + ') '.
(3)
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'())
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where Keff is the effective permeability of a partially fractured plug, Km is the
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matrix permeability of an intact sample, Kf is the permeability of a fully fractured
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plug, N is the total volume of the model, and n is the stimulated region volume.
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Hydraulic fracturing of a Tennessee sandstone block. We cut and polished a
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cylindrical Tennessee sandstone and stimulated the block-scale sample under
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triaxial loading conditions. The sample diameter was 4 in and its length was
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approximately 5-1/2 in. A hole of ¼ inch in diameter was drilled in the center of
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the core and extended up to half the sample length. The hole was completed with a
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¼ inch OD tube that was cemented (Damani, 2013).
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Triaxial stress (vertical stress = 3000 psi, maximum horizontal stress = 2000 psi,
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minimum horizontal stress = 500 psi) was applied to replicate the in-situ stress
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conditions. The loading system was designed to allow triaxial loading of the rock 17
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sample with simultaneous injection of fracturing fluid and recording of acoustic
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emissions. The three stresses were applied using confining fluid pressure,
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hydraulic flat jacks, and an axial piston (Fig. 4).
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Oil was then injected into the hole at a rate of 10 cm3/min. The pressure starts to
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increase in the hole and the fluid diffuses into the pore space of the rock.
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Consequently, localized microcracking is initiated in the rock and with continued
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oil injection, the microcracks start to coalesce and form a large fracture. The block
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breaks down at 4336 psi, which was indicated by a sharp fall in the pump pressure.
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Figure 4. Hydraulic fracturing lab experimental setup. The figure on the left shows an expanded view of the triaxial loading system with axial loading, confining vessel and flat jacks to apply transverse stress. The figure on the right shows the sample covered with copper jacket mounted on the base plate of the triaxial loading system. (Damani et al., 2012; Damani, 2013).
The AE events can be divided into pre- and post-breakdown events. Pre-
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breakdown events may be caused by rock failure due to stress induced by wellbore
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pressurization and the injected fluid diffusing locally into matrix whereas post-
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breakdown events may be caused by flow through the fracture and failure of
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asperities along the fracture faces. In our experiment, most events were post-
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breakdown events (Fig. 5).
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Figure 5. Pump pressure and cumulative AE events with time 312
There were 16 piezoelectric sensors mounted on the block, with one on the top,
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one on the bottom, and the remaining 14 on the cylindrical surface of the sample,
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distributed uniformly over the azimuth and the height. AE events showed a delayed
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response, with the first events being captured at the breakdown and thereafter
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increasing rapidly. The average error in hypocenter locations for this test was +/-
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5.34 mm, and the amplitude of the events ranged from 0.1 to 0.9 volts. The total
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number of events was equal to 1564, and the density was higher close to the large
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fracture (Fig. 6). To locate the AE events, the individual arrival times of the
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compressional waves associated were recorded automatically. The first arrivals
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were used to determine the event location using a weighted least squares inversion
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algorithm (Damani, 2013). A frequency of 50 kHz to 1.5 MHz was used to filter
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the good events; the rest of the events with frequencies outside the range were
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treated as noise.
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Figure 6. Spatial locations of 1564 AE events recorded during hydraulic fracturing of a Tennessee sandstone block in a (a) three-dimensional coordinate system, (b) 21
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X-Y plane, and (c) X-Z plane. (d) The size of the blue bubbles corresponds to the amplitude of the acoustic events. The green circles represent the sensor locations. 326
Results
328
The physically representative pore model is used here to predict the permeability
329
enhancement at the core scale. The number of AE events per unit volume
330
(#Events/volume) is determined for a core plug that has a large fracture, which can
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be observed with the naked eye. This ratio corresponds to the percolation ratio
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when the fracture forms a connected-through path. The permeability measurements
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of other core plugs, extracted from the stimulated block, provide independent
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evidence to test the model.
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We extracted five core plugs from the stimulated Tennessee sandstone block for
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petrophysical characterization (Fig. 7). One plug was extracted right on top of the
338
large fracture (Left wing in Fig. 7a), whereas the other four plugs were extracted
339
from either side of the large fracture (Right Wing in Fig. 7a). Table 1 lists the
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spatial locations of the core plugs with respect to the coordinate system shown in
341
Fig. 7, their bulk volume, and the number of acoustic events. The core plug with
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the connected-through fracture is referred to as the Fractured plug in Table 1 and
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has the largest #Events/volume and highest permeability; the other plugs are
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named Plugs 1−4 in Table 1.
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(a)
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Figure 7. (a-b) Block-scale sample of a hydraulically fractured Tennessee sandstone, where the holes show the locations of the extracted core plugs for permeability measurements. The fracture left and right wings are shown by blue red lines, respectively. (c) Scanning electron microscope (SEM) image of the fractured core plugs that shows a connected-through fractures in the sample.
Fig. 7 shows a scanning electron microscope (SEM) image of the formation where
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there is a connected-through fracture in the sample, which is created during
349
hydraulic fracturing of the block. The high-resolution image shows the fracture
350
with no confinement. The high resolution suggests that the aperture size of the
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connected fracture could be on the order of 1–10 µm.
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We measured the permeability of each core plug listed in as a function of effective
354
stress (Table 2). The confining stress was changed where the pore pressure was
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200 psi. The pore pressure was fixed using the AP-608TM permeameter, and the
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effective stress was calculated as follows: Effective stress = Confining stress – Pore pressure
(3)
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The lab measurements are normalized with respect to the measured value measured
359
for each sample when the effective stress is equal to 300 psi (Fig. 8). The results
360
are normalized with respect to the confined conditions because they are more
361
representative of in-situ conditions. The rate of the permeability decrease with the
362
effective stress is relatively similar for different samples, especially at low
363
effective stress. The similarity suggests that the permeability decline is controlled
364
by the change in the effective aperture size of the fractures. The similarity could
365
also be a result of a homogeneous material distribution. The decrease rate of the
366
fractured plug deviates from the other plugs as the effective stress increases, which
367
could be due to the plastic deformation. The lab measurements revealed that the
368
plug permeability did not recover fully to the original value because of the plastic
369
deformation after the test when the confining stress was removed.
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Figure 8. The permeability decreases as the effective stress increases for different plugs.
The fractured plug permeability was also measured as a function of the confining
375
stress. The fractured plug permeability was 5.342 md when the confining stress
376
was equal to 1000 psi. The measured permeability is used as an estimate for the
377
permeability of the stimulated region (Fig. 3c). The measured permeability is also
378
used to normalize the results, denoted by k fractured plug in Fig. 8.
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The spatial locations of the recorded events and the bulk volume of each core plug
381
determine the number of AE events per unit volume (#Events/volume). This ratio
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is equal to 6.95 cm-3 for the fractured plug, which corresponds to the percolation
383
threshold. We predicted the permeability of the core plug when this ratio is smaller
384
than the percolation threshold based on percolation theory, using the physically
385
representative pore model. Fig. 9 reveals that the core-scale measurements
386
corroborate the predicted results. The permeability of the formation remains close
387
to the intact value at the core scale when the #Events/volume is smaller than the
388
threshold value. Our model also suggests that the stimulated permeability increases
389
by a factor of 2 relative to the intact permeability ( = 4md). Thus, the intact
390
permeability remains close to the matrix permeability, as opposed to the fractured
391
plug permeability.
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Figure 9. Core-scale measurements corroborate the physically representative pore model, which predicts the permeability enhancement based on percolation theory. The stimulated permeability remains very close to that of the matrix, as opposed to that of the fractured plug, when the number of acoustic events per unit volume (#Events/volume) is smaller than the percolation threshold. 392
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We used all the data available from the core plugs recovered from the block
394
sample to test our model. Most AE events occur on the fracture, which is the
395
reason for the absence of lab measurements with #Event/volume between 3 and 6.
396
The core plugs with small #Events/volume were taken as close as possible to the
397
main fracture. Nonetheless, the simulation results and lab measurements indicate
398
that the permeability close to the main fracture remains close to the intact
399
permeability and the enhanced permeability does not increase linearly with
400
#Events/volume.
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Now, we turn to the sensitivity of the results to the amplitude of the events
403
recorded (Fig. 10). The amplitude cutoff (%) is defined as removing events that
404
have amplitude values in the bottom x% of the total events. The number of events
405
per unit volume (#Events/volume) decreases the most for the fractured plug. The
406
significant decrease for the fractured plug indicates that there is a wide amplitude
407
range. Nevertheless, it is apparent that the cutoff value does not change the trend of
408
results because it only shifts them monotonically.
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Plug 1 Plug 2
6 Plug 3
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Fractured Plug
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#Events/Volume (1/cm3)
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1
0%
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40% 60% Amplitude cutoff (%)
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Figure 10. #Events/volume decreases monotonically with increasing amplitude cutoff.
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Dahi and Lorenzo (2011) indicated that low-frequency events were the tensile
412
events causing Mode I failure. Low-frequency events are beyond the scope of the
413
present work, because our device does not record events below 50 kHz. We
414
considered four kinds of failure mechanisms: shear, tensile, compressive, and
415
complex. Our hypothesis is that each event is an indicative of a microfracture, and
416
the microfractures form a macrofracture when #Events/volume reaches a critical
417
value.
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Discussion
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In petroleum engineering, the ultimate goal of most research, including the present
421
study, is to be applied in field. The presented model and lab measurements predict
422
the permeability enhancement of a stimulated region, without a connected-through
423
fracture, based on its acoustic emission. The stimulated region is also referred to as
424
the process zone (Znag et al. 2000). Our study suggests that the enhanced
425
permeability remains close to the intact permeability, and that it is unrealistic to
426
use a linear approximation for the stimulated region permeability. Knowing that, in
427
the absence of a connected-through fracture, the permeability increase is not very
428
significant is crucial for building a realistic reservoir model.
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Another issue is the size of the stimulated region. The size of the stimulated region,
431
whose permeability is close to the intact permeability, relative to the overall
432
domain is equal to the size of the core plug to the block. We can predict the
433
stimulated region size if the results can be scaled to the field conditions. The
434
stimulated region size close to each fracture can be predicted by accounting for the
435
fracture length.
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The presented results are relevant to fluid injection into a dry sample. The size of
438
the stimulated region and the spatial distribution of the events may change if the
439
sample is initially saturated and when conducted for a different formation. Our 29
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model is based on the assumption that the spatial distribution of the pore-throat
441
size is random, which is realistic for Tennessee sandstone. The developed model
442
needs modifications when this assumption is not realistic.
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Conclusions
445
We developed a physically representative pore model of an intact Tennessee
446
sandstone at the core scale by analyzing its permeability, porosity, and capillary
447
pressure measurements. Our main objective was to predict the permeability
448
enhancement by accounting for acoustic emission (AE) events. Our assumption
449
was that each event is representative of a microcrack or is indicative of an asperity
450
which compressed during fracture closure. This assumption implies that a
451
connected-through fracture is formed when the number of AE events per unit
452
volume becomes larger than the threshold value.
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We predicted the permeability enhancement of a formation based on percolation
455
theory. Our study shows that the stimulated permeability of a formation at the core
456
scale is much smaller than the fractured plug permeability if the number of events
457
per volume is smaller than the threshold value. The permeability enhancement of
458
the core plug, relative to intact conditions, is close to 2 when the fracture does not
459
form a connected-through path. The proposed model, which relates the number of
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acoustic emission events to the enhanced permeability based on percolation theory,
461
has major applications in determining the transport properties of the stimulated
462
reservoir volume.
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Acknowledgements
465
The authors are grateful to Carl Sondergeld and Akash Damani for sharing some of
466
the lab measurements (Damani et al., 2012; Damani 2013) analyzed in this study.
467
The authors are also grateful for the constructive comments of four anonymous
468
reviewers.
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Declarations
471
The authors declare that they have no competing interests. ASP developed and
472
tested the main concept of the present study. He integrated the acoustic emission
473
events into percolation theory to predict the permeability enhancement. ASP wrote
474
and revised the manuscript. AA coded the two-dimensional network of the sample
475
and prepared the plots.
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References
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Berkowitz, B., and Ewing, R. P., 1998, Percolation theory and network modeling applications in
479
soil physics, Surveys in Geophysics, 19(1), 23–72.
480 31
ACCEPTED MANUSCRIPT
481
Broadbent, S. R., and Hammersley, J. M., 1957, Percolation processes, In Mathematical
482
Proceedings of the Cambridge Philosophical Society, 53, 629–641.
483
Bryant, S. L., Mellor, D. W., and Cade, C. A., 1993, Physically representative network models of
485
transport in porous media, AIChE Journal, 39(3), 387–396.
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484
486 487
Chong, K. P., Carino, N. J., and Washer, G., 2003, Health monitoring of civil
488
infrastructures, Smart Materials and structures, 12(3), 483.
SC
489
Dahi Taleghani, A., & Lorenzo, J. M. (2011, January 1). An Alternative Interpretation of
491
Microseismic Events during Hydraulic Fracturing. Society of Petroleum Engineers.
492
doi:10.2118/140468-MS.
M AN U
490
493 494
Damani, A., Sharma, A., Sondergeld, C., and Rai. C.S., 2012, Acoustic emission and SEM
495
analyses of hydraulic fractures under triaxial stress conditions, Presented at SEG Annual
496
Meeting, Las Vegas, Nevada, USA, November 4–9. SEG-1585.
TE D
497 498
Damani, A., 2013. Acoustic mapping and fractography of laboratory induced hydraulic
499
fractures (Doctoral dissertation, University of Oklahoma).
500
Dean, P., and Bird, N. F, 1967, Monte Carlo estimates of critical percolation probabilities,
502
In Mathematical Proceedings of the Cambridge Philosophical Society, 63(2), 477–479.
AC C
503
EP
501
504
Fatt, I., 1956, The network model of porous media. I. Capillary pressure characteristics, AIME
505
Pet Trans. 207,144–59.
506 507
Ge, M., 2003, Analysis of source location algorithms: Part I. Overview and non-iterative
508
methods, Journal of Acoustic Emission, 21(1), 21–28.
509
32
ACCEPTED MANUSCRIPT
510
Khishvand, M., Alizadeh, A. H., and Piri, M., 2016, In-situ characterization of wettability and
511
pore-scale displacements during two-and three-phase flow in natural porous media, Advances in
512
Water Resources, 97, 279–298.
513
Lei, X., and Ma, S., 2014, Laboratory acoustic emission study for earthquake generation
515
process, Earthquake Science, 27(6), 627–646.
RI PT
514
516
Lockner, D., 1993, The role of acoustic emission in the study of rock fracture, International
518
Journal of Rock Mechanics and Mining Sciences and Geomechanics 30(7), 883–899.
SC
517
519
Mayerhofer, M. J., Lolon, E., Warpinski, N. R., Cipolla, C. L., Walser, D. W., and Rightmire, C.
521
M., 2010, What is stimulated reservoir volume?, SPE Production and Operations, 25(01), 89–98.
M AN U
520
522
Meek, R. A., Suliman, B., Bello, H., and Hull, R., 2015, Well space modeling, SRV prediction
524
using microseismic, seismic rock properties and structural attributes in the Eagle Ford shale of
525
south Texas, Presented at SPE Unconventional Resources Technology Conference, San Antonio,
526
Texas, USA, July 20–22, URTEC-2173501-MS.
527
TE D
523
Mousavi, M. A., and Bryant, S. L., 2012, Connectivity of pore space as a control on two-phase
529
flow properties of tight-gas sandstones, Transport in porous media, 94(2), 1–18.
530
EP
528
Mousavi, M. A., and Bryant, S. L., 2013, Geometric models of porosity reduction by ductile
532
grain compaction and cementation. AAPG bulletin, 97(12), 2129–48.
533
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531
534
Phillips, W. S., Fairbanks, T. D., Rutledge, J. T., and Anderson, D. W., 1998, Induced
535
microearthquake patterns and oil-producing fracture systems in the Austin
536
chalk, Tectonophysics 289(1), 153–169.
537 538
Purcell, W. R., 1949, Capillary pressures-their measurement using mercury and the calculation
539
of permeability therefrom, Journal of Petroleum Technology, 1(02), 39–48.
33
ACCEPTED MANUSCRIPT
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Sahimi, M., 2003, Heterogeneous Materials: Nonlinear and breakdown properties and atomistic
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modeling (Vol. 2). Springer Science & Business Media.
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Sahini, M., and Sahimi M., 1994, Applications of percolation theory (CRC Press).
544 545
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Sakhaee-Pour, A., and Bryant, S. L., 2015, Pore structure of shale, Fuel, 143, 467–475.
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Stein, S., Wysession, M., and Houston, H., 2003, Books-An Introduction to Seismology,
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Earthquakes, and Earth Structure, Physics Today 56(10), 65–72.
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Tarrahi, M., Jafarpour, B., and Ghassemi, A., 2015, Integration of microseismic monitoring data
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into coupled flow and geomechanical models with ensemble Kalman filter, Water Resources
552
Research, 51(7), 5177–5197.
553 554
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Washburn, E. W., 1921, The dynamics of capillary flow, Physical review 17(3), 273.
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Yapar, O., Basu, P. K., Volgyesi, P., and Ledeczi, A., 2015, Structural health monitoring of
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bridges with piezoelectric AE sensors, Engineering Failure Analysis, 56, 150–169.
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Zang, A., Wagner, F. C., Stanchits, S., Janssen, C., and Dresen, G., 2000, Fracture process zone
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in granite. Journal of Geophysical Research: Solid Earth, 105(B10), 23651–23661.
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Table 1. Spatial location, number of acoustic events, and the block volume of the
573
core plug extracted from the stimulated Tennessee sandstone block shown in Fig.
574
7. X(mm)
Y(mm)
Z(mm)
#Events
Bulk
#Events/volume
volume
(cm-3)
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Plug
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(cm3)
Plug 2
30
Plug 3
30
Plug 4
30
Fractured
-32
12.5
31
TE D
30
0.13
12
15.21
0.79
-12.5
31
6
13.25
0.45
-12.5
58
21
13.25
1.54
0
78
134
19.27
6.95
AC C
576
15.21
58
plug 575
2
12.5
EP
Plug 1
577 578
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579 580
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581 582
Diameter (mm) 25.4
Permeability (md) 0.008
Plug 2
27
25.4
0.007
Plug 3
31
Plug 4
27
Fractured plug
39
TE D
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Plug 1
Length (mm) 31
EP
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Table 2. Plug length, diameter, and permeability at 300 psi effective stress.
AC C
583
36
25.4
0.007
25.4
0.007
25.4
8.097
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Highlights • We conduct comprehensive lab measurements to hydraulically fracture a block-
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scale sample of Tennessee sandstone.
• We model pore-space alteration of Tennessee sandstone during hydraulic
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fracturing.
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• We predict permeability of the stimulated reservoir volume based on the percolation theory.
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• We test our model with independent lab measurements.