Experimental Investigation into Hydraulic Fracture Network Propagation in Gas Shales Using CT Scanning Technology

Multistage fracturing of the horizontal well is recognized as the main stimulation technology for shale gas development. The hydraulic fracture geometry and stimulated reservoir volume (SRV) is interpreted by using the microseismic mapping technology. In this paper, we used a computerized tomography (CT) scanning technique to reveal the fracture geometry created in natural bedding-developed shale (cubic block of 30 cm × 30 cm × 30 cm) by laboratory fracturing. Experimental results show that partially opened bedding planes are helpful in increasing fracture complexity in shale. However, they tend to dominate fracture patterns for vertical stress difference Δσ _v  ≤ 6 MPa, which decreases the vertical fracture number, resulting in the minimum SRV. A uniformly distributed complex fracture network requires the induced hydraulic fractures that can connect the pre-existing fractures as well as pulverize the continuum rock mass. In typical shale with a narrow (<0.05 mm) and closed natural fracture system, it is likely to create complex fracture for horizontal stress difference Δσ _h  ≤ 6 MPa and simple transverse fracture for Δσ _h  ≥ 9 MPa. However, high naturally fractured shale with a wide open natural fracture system (>0.1 mm) does not agree with the rule that low Δσ _h is favorable for uniformly creating a complex fracture network in zone. In such case, a moderate Δσ _h from 3 to 6 MPa is favorable for both the growth of new hydraulic fractures and the activation of a natural fracture system. Shale bedding, natural fracture, and geostress are objective formation conditions that we cannot change; we can only maximize the fracture complexity by controlling the engineering design for fluid viscosity, flow rate, and well completion type. Variable flow rate fracturing with low-viscosity slickwater fluid of 2.5 mPa s was proved to be an effective treatment to improve the connectivity of induced hydraulic fracture with pre-existing fractures. Moreover, the simultaneous fracturing can effectively reduce the stress difference and increase the fracture number, making it possible to generate a large-scale complex fracture network, even for high Δσ _h from 6 MPa to 12 MPa.     

Effect of roughness on water flow through a synthetic single rough fracture

A single fracture is usually idealized theoretically as smooth parallel plates, but the real fractures are rough-walled with points of contact. Though relative roughness is considered in quantifying the flow through a single rough fracture (SRF) previously, additional factors such as the distribution of rough elements and bending degree of streamlines should be considered in order to obtain more accurate results. Semiempirical friction factor (f) and discharge per unit width (q) equations are first deduced taking relative roughness, roughness elements distribution and streamline reattachment length into consideration. A horizontal SRF model was then set up and a series of experiments and simulations were performed. Main conclusions are drawn: Recirculation of streamlines arises in the rough element and the intensity of the recirculation increases with the angle from which the streamlines enter into the rough elements and Reynolds number (Re); streamlines are discontinuously distributed when asperity height is large and nonlinear flow occurs; the nonlinearity of the flow increases with the increasing the asperity height and Re; the critical value of related roughness used to judge whether the influence of roughness on water flow through a SRF can be ignored or not should be much lower than 0.033; the revised f and q equations under laminar flow through a SRF are proved to be better when calculating the f and q values.     

Debris flow density determined by grain composition

Density is one of the most important parameters of debris flows. Because observing an active debris flow is very difficult, finding a method to estimate debris flow density is urgently needed for disaster mitigation engineering. This paper proposes an effective empirical equation in terms of grain size distribution (GSD) parameters based on observations in Jiangjia Gully, Yunnan Province, China. We found that the GSD follows P(D) = KD ^-μ exp(? D/Dc), with μ and Dc representing the fine and coarse grains, respectively. In particular, μ is associated with some characteristic porosity of soil in the natural state and increases with increased porosity. Dc characterizes the grain size range of the flow and increases with the grain concentration. Studies show that flow density is related to both parameters in power law. Here, we propose an empirical equation for estimating flow density: ρ = 1.26μ ^-0.132 + 0.049Dc^0.443, which provides not only an estimation of the density for a flow, but also describes the variation in density with the GSD of material composition; this provides important information related to the design of debris flow engineering structures.     

Microfacies analysis and cyclostratigraphy of the upper cretaceous- lower paleogene succession of Bir Dakhl section,north eastern desert,Egypt

The Bir Dakhl section which is located in the southern Galala plateau, north eastern desert was sampled for microfacies analysis of the upper Cretaceous–lower Paleogene succession. Microfacies analysis led to the recognition of eight mixed clastic-carbonate facies types (black shale lithofacies MF-1, pure shale lithofacies MF-2, sandy shale lithofacies MF-3, marly shale lithofacies MF-4, mudstone microfacies MF-5, foraminiferal wackestone microfacies MF-6, bioclastic wackestone microfacies MF-7, and bioclastic packstone microfacies MF-8) of the studied interval. These microfacies can be grouped into three depositional environments: inner, middle and outer ramp. The interpreted depositional environments have been suggested to range from neritic to middle bathyal (~ 700 m). Based on cyclostratigraphy, five deepening upward cycles and three shallowing upward cycles have been differentiated in Bir Dakhl section.     

Physical simulation research on evolution laws of clay aquifuge stability during slice mining

The aquifuge stability is the key to study the impacts of coal mining on the aquifer. Based on the geological conditions of a mine in Yili of Xinjiang, China, this paper has studied the stability evolution laws of clay aquifuge during extremely thick coal seam mining by similar material simulation experiment in the laboratory. For the water-swelling and expansion property of clay aquifuge, the reasonable proportion of the similar material is firstly determined by taking the uniaxial compressive strength and the permeability coefficient as core indexes. Then, the overlying strata movement coupled solid–liquid physical model is established. In addition, the aquifuge deformation, the water level changes of the aquifer, and the height of fracture zone in overburden are analyzed during the slice mining. The research results indicate that the clay aquifuge will gradually occur instability failure during the mining of the working face, and the aquifuge stability has the threshold effects. When the ratio of the vertical displacement of the aquifuge to the thickness is D_v/T?≤?58.0%, the ratio of the horizontal displacement to the thickness is D_h/T?≤?17.0%, and the height of fractured zone in overburden is below the aquifuge, the mining-induced fractures may be closed and the aquifuge stability could be maintained. If D_v/T?≥?75.0%, D_h/T?≥?23.9%, and the height of fractured zone in overburden is within the aquifuge, the fractures will develop and connect the aquifuge and the stability failure of the aquifuge will occur, which has a direct correlation with the mining height.     

An adjoint-based optimization method for gas production in shale reservoirs

In this work, we consider a new model for flow in a multiporosity shale gas reservoir constructed within the framework of an upscaling procedure where hydraulic fractures are treated as (\(n-1\)) interfaces (\(n=2,3\)). Within this framework, the hydrodynamics is governed by a new pressure equation in the shale matrix which is treated as a homogenized porous medium composed of organic matter (kerogen aggregates with nanopores) and inorganic impermeable solid (clay, calcite, quartz) separated from each other by a network of interparticle pores of micrometer size. The solution of the pressure equation is strongly influenced by the constitutive response of the retardation parameter and effective hydraulic conductivity where the former incorporates gas adsorption/desorption in the nanopores of the kerogen. By focusing our analyses on this nonlinear diffusion equation in the domain occupied by the shale matrix, an optimization strategy seated on the adjoint sensitivity method is developed to minimize a cost functional related to gas production and net present value in a single hydraulic fracture. The gradient of the objective functional computed with the adjoint formulation is explored to update the controlled pressure drop aiming to optimize production in a given window of time. The combination of the direct approach and gradient-based optimization using the adjoint formulation leads to the construction of optimal production scenarios under controlled pressure decline in the well. Numerical simulations illustrate the potential of the methodology proposed herein in optimizing gas production.     

The gas density and “volume” Schmidt law for spiral galaxies

The equilibrium thickness of the isothermal layers of interstellar gas and volume gas densities ρ _gas in the plane of the disk as a function of galactocentric distance R are computed for seven spiral galaxies (including the Milky Way) using an axisymmetrical model. In this model, the thickness of the stellar disk varies with R and remains approximately equal to the minimum thickness of a stable equilibrium disk. We found the disk thickness to increase toward the periphery in at least five of the seven galaxies. The density of the stellar disk decreases with R faster than ρ _gas , so that gas dominates at the disk peripheries in terms of density. A comparison of the azimuthally averaged star formation rate SFR and the gas density shows the absence of a universal Schmidt law SFR ～ρ _gas ⁿ for galaxies. However, the SFRs in various galaxies are better correlated with the volume than the gas surface density. The parameter n in the Schmidt law formally calculated using the least-squares method lies in the interval 0.8–2.4, being, on average, close to 1.5. The values of n calculated separately for the molecular gas display substantial scatter, but are, on average, close to unity. The value of n appears to increase with decreasing ρ _gas , so that the fraction of gas that actively participates in star formation decreases with n.     

Finite-difference modelling of anisotropic wave scattering in discrete fracture model

The presence of fractures in reservoir rocks causes scattering of seismic wave energy. In this paper, we utilize the finite-difference modelling technique to study these scattering effects to gain more insights into the effects and assess the validity of using anisotropic wave scattering energy as a diagnostic tool to characterize fractured hydrocarbon reservoirs. We use a simplified fractured reservoir model with four horizontal layers with a fractured-layer as the third layer. The fractures are represented by grid cells containing equivalent anisotropic medium by the use of the linear slip equivalent model. Our results show that the scattered energy, quantified through estimates of the seismic quality factor (Q) is anisotropic, exhibiting a characteristic elliptical (\(\cos 2\theta \)) variations relative to the survey azimuth angle \(\theta \). The fracture normal is inferred from the minor axis of the Q ellipse. This direction correlates with the direction of maximum wave scattering. Minimum wave scattering occurs in the fracture strike direction inferred from the major axis of the Q ellipse. These results provide more complete insights into anisotropic wave scattering characteristics in fractured media and thus, validate the practical utility of using anisotropic attenuation attribute as an additional diagnostic tool for delineation of fracture properties from seismic data.     

Model reduction and discretization using hybrid finite volumes for flow in porous media containing faults

In this paper, we study two different model reduction strategies for solving problems involving single phase flow in a porous medium containing faults or fractures whose location and properties are known. These faults are represented as interfaces of dimension N ? 1 immersed in an N dimensional domain. Both approaches can handle various configurations of position and permeability of the faults, and one can handle different fracture permeabilities on the two inner sides of the fracture. For the numerical discretization, we use the hybrid finite volume scheme as it is known to be well suited to simulating subsurface flow. Some results, which may be of use in the implementation of the proposed methods in industrial codes, are demonstrated.     

A Criterion for Brittle Failure of Rocks Using the Theory of Critical Distances

This paper presents a new analytical criterion for brittle failure of rocks and heavily over-consolidated soils. Griffith’s model of a randomly oriented defect under a biaxial stress state is used to keep the criterion simple. The Griffith’s criterion is improved because the maximum tensile strength is not evaluated at the boundary of the defect but at a certain distance from the boundary, known as half of the critical distance. This fracture criterion is known as the point method, and is part of the theory of critical distances, which is utilised in fracture mechanics. The proposed failure criterion has two parameters: the inherent tensile strength, σ ₀, and the ratio of the half-length of the initial crack/flaw to the critical distance, a/L. These parameters are difficult to measure but they may be correlated with the uniaxial compressive and tensile strengths, σ _c and σ _t. The proposed criterion is able to reproduce the common range of strength ratios for rocks and heavily overconsolidated soils (σ _c/σ _t = 3–50) and the influence of several microstructural rock properties, such as texture and porosity. Good agreement with laboratory tests reported in the literature is found for tensile and low-confining stresses.     

The Bajocian–Bathonian plant fossil from the Hojedk formation,Lenjan section,Kerman, Iran

The Jurassic successions represent a wide distribution in North of the Kerman province. These successions include Ab-Haji, Badamu, and Hojedk formations. The Hojedk Formation contains the plant fossils. The Lenjan section is one of the suitable areas for paleontological studies on the Hojedk Formation. The study section is mostly composed of green sandstone and shale with several interbedded coal veins with different thicknesses. The thickness of the Hojedk Formation is about 200 m in the Lenjan section. In this study, seven genera and 13 species of macro plant fossils were identified and described, including Nilssonia undulata, Nilssonia bozorga, Nilssonia berriesi, Nilssonia sp., Klukia cf. exilis, Klukia exilis, Cladophlebis antarctica, Coniopteris lobata, Coniopteris murrayana, Elatocladus confertus, Podozamites sp., Equisetites sp., and Coniopteris sp. The Bajocian–Bathonian can be attributed to the Lenjan section based on the recognized flora.     

Assessing the vegetation canopy influences on wind flow using wind tunnel experiments with artificial plants

Wind erosion causes serious problems and considerable threat in most regions of the world. Vegetation on the ground has an important role in controlling wind erosion by covering soil surface and absorbing wind momentum. A set of wind tunnel experiments was performed to quantitatively examine the effect of canopy structure on wind movement. Artificial plastic vegetations with different porosity and canopy shape were introduced as the model canopy. Normalized roughness length (Z ₀/H) and shear velocity ratio (R) were analyzed as a function of roughness density (λ). Experiments showed that Z ₀/H increases and R decreases as λ reaches a maximum value, λ _max, while the values of Z ₀/H and R showed little change with λ value beyond as λ _max.     

Investigation into the change of the porosity parameter during transition from laboratory to reservoir conditions

The purpose of the investigation is to reveal the dependences of P _p = f(C _p) on reservoir conditions and the lithological composition of rocks. The samples were studied using a set of lithological-petrographic investigations. To obtain the dependences on thermobaric conditions, 90 samples of different porosities (C _p) of 15, 20, and 25% were collected. As a result, the general pattern of the change in the rock resistivity during the transition from atmospheric conditions of measuring to reservoir conditions was established. Dependences of porosity parameter P _p on porosity coefficient C _p were obtained for three values of formation water salinity and three reservoir conditions. The measurement errors of the porosity parameter P _p were calculated using dependences obtained under atmospheric conditions.     

Plug shaped burrows <Emphasis Type="Italic">Conichnus - Conostichus</Emphasis> from the Late Cretaceous of Bagh Group,Gujarat, western India

Plug-shaped ichnofossils Conichnus conicus, Conostichus broadheadi and C. stouti are found in the intercalated micritic sandstone and sandy allochemic limestone shale sequence of Bagh Group, Narmada district, Gujarat. These ichnospecies occur at two stratigraphic levels and shows distinct morphological features interpreted as resting/dwelling structures of sea anemone. The occurrence of these ichnospecies along with oyster fossils genera like Bosostrea and Indostrea indicate shallow marine environment.     

Analytical expressions for three-phase generalized relative permeabilities in water- and oil-wet capillary tubes

We analyze three-phase flow of immiscible fluids taking place within an elementary capillary tube with circular cross-section under water- and oil-wet conditions. We account explicitly for momentum transfer between the moving phases, which leads to the phenomenon of viscous coupling, by imposing continuity of velocity and shear stress at fluid-fluid interfaces. The macroscopic flow model which describes the system at the Darcy scale includes three-phase effective relative permeabilities, K _{i j,r} , accounting for the flux of the ith phase due to the presence of the jth phase. These effective parameters strongly depend on phase saturations, fluid viscosities, and wettability of the solid matrix. In the considered flow setting, K _{i j,r} reduce to a set of nine scalar quantities, K _{i j,r} . Our results show that K _{i j,r} of the wetting phase is a function only of the fluid phase own saturation. Otherwise, K _{i j,r} of the non-wetting phase depends on the saturation of all fluids in the system and on oil and water viscosities. Viscous coupling effects (encapsulated in K _{i j,r} with i ≠ j) can be significantly relevant in both water- and oil-wet systems. Wettability conditions influence oil flow at a rate that increases linearly with viscosity ratio between oil and water phases.     

Reaction-induced grain boundary cracking and anisotropic fluid flow during prograde devolatilization reactions within subduction zones

Devolatilization reactions during prograde metamorphism are a key control on the fluid distribution within subduction zones. Garnets in Mn-rich quartz schist within the Sanbagawa metamorphic belt of Japan are characterized by skeletal structures containing abundant quartz inclusions. Each quartz inclusion was angular-shaped, and showed random crystallographic orientations, suggesting that these quartz inclusions were trapped via grain boundary cracking during garnet growth. Such skeletal garnet within the quartz schist formed related to decarbonation reactions with a positive total volume change (?V _t > 0), whereas the euhedral garnet within the pelitic schists formed as a result of dehydration reaction with negative ?V _t values. Coupled hydrological–chemical–mechanical processes during metamorphic devolatilization reactions were investigated by a distinct element method (DEM) numerical simulation on a foliated rock that contained reactive minerals and non-reactive matrix minerals. Negative ?V _t reactions cause a decrease in fluid pressure and do not produce fractures within the matrix. In contrast, a fluid pressure increase by positive ?V _t reactions results in hydrofracturing of the matrix. This fracturing preferentially occurs along grain boundaries and causes episodic fluid pulses associated with the development of the fracture network. The precipitation of garnet within grain boundary fractures could explain the formation of the skeletal garnet. Our DEM model also suggests a strong influence of reaction-induced fracturing on anisotropic fluid flow, meaning that dominant fluid flow directions could easily change in response to changes in stress configuration and the magnitude of differential stress during prograde metamorphism within a subduction zone.     

Analysis of Methods for Computing the Trajectories of Dust Particles in a Gas–Dust Circumstellar Disk

A systematic analysis ofmethods for computing the trajectories of solid-phase particles applied in modern astrophysics codes designed for modeling gas–dust circumstellar disks has been carried out for the first time. Themotion of grains whose velocities are determinedmainly by the gas drag, that is, for which the stopping time or relaxation time for the velocity of the dust to the velocity of the gas t_stop is less than or comparable to the rotation period, are considered. The methods are analyzed from the point of view of their suitability for computing the motions of small bodies, including dust grains less than 1 μm in size, which are strongly coupled to the gas. Two test problems are with analytical solutions. Fast first order accurate methods that make it possible to avoid additional restrictions on the time step size τ due to gas drag in computations of the motion of grains of any size are presented. For the conditions of a circumstellar disk, the error in the velocity computations obtained when using some stable methods becomes unacceptably large when the time step size is τ > t_stop. For the radial migration of bodies that exhibit drifts along nearly Keplerian orbits, an asymptotic approximation, sometimes called the short friction time approximation or drift flux model, gives a relative error for the radial-velocity computations equals to St², where St is the Stokes number, the ratio of the stopping time of the body to some fraction of the rotation period (dynamical time scale) in the disk.     

Assessment of textural variational pattern and electrical conduction of economic and accessible Quaternary hydrolithofacies via geoelectric and laboratory methods in SE Nigeria: A case study of select locations in Akwa Ibom State

Textural variational pattern of economic and accessible Quaternary aquifer repositories and its conductivity in the south-eastern Nigeria have been assessed through the integration of vertical electrical sounding and laboratory measurements. The results have shown the lithological attributes, pore-water and amount of residual clay minerals in the assumed clean sand; mechanism of charge fixation at the fluid - surface interface; intricate geometry of pores and pore channels; formation’s ability to transmit pore-water and cation exchange capacity.The connections of electrical and hydraulic properties and their distributions have been established. The average interface conductivity contributed by residual clay minerals in assumed clean sands of the aquifer repositories in the study area have been estimated as 30µS/m. Intrinsic average porosity and formation factor have been respectively deduced as 12% and 14.75. Comparing the simulated aquifer formation factor obtained from the observed porosity data with the observed aquifer formation factor, indicates the that study area has 0.5 ≤ a ≤ 0.8 pore geometry factor and 1.5 ≤ m ≤ 2.0 cementation factor as the best fitting values. The interrelations between aquifer parameters have been established through different plots and the aquifer have been empirically proved to be associated with residual clay minerals as the interface conductivity C_q is not equal to zero. The wide ranges of parameters estimated are an indication of variations in grain size. The estimated intrinsic average porosity, formation factor and the average BQ_v are viable in characterizing the aquifer flow dynamics and contaminant modelling in the associated aquifer sands For low pore geometry factors a (0.2) and low cementation factor m (0.5) the formation factor remains fairly constant. However, marked variability is noticed at higher a (1.0) and m (2.5). Despite the observed variability in formation factors at the indicated porosities, the spatial or geometrical spread of the formation factor remains unchanged in the aquifer units. The Tables for geoelectric and petrophysical parameters and the associated mathematical models generated in this study can be used for groundwater contaminant modelling and simulation of pore space parameters with reasonable accuracy.     

Simultaneous inversion application for characterizing Hamra Quartzite tight sand reservoir: a case study from Hassi Messaoud (Algeria)

Channel sand acts as a stratigraphic trap for hydrocarbon accumulation in many parts of the world. Delineation of this type of reservoir is crucial as channel sand may be scarce, and inaccurate location of the drilling wells could lose a huge currency. The Hassi Messaoud (HMD) field was subjected to multiphase tectonic events, where deep-seated structures were rejuvenated leading to intensive fault complexity. The main effective tectonic events upon the studied area are the Hercynian compression and deep erosion till the Ordovician Hamra Quartzite (HQZ) oil reservoir, followed by active Triassic rifting and filling the deeply eroded areas or the graben areas by eruptive volcanic rocks at Triassic time. Hercynian erosion and volcanic rocks distribution introduce a big uncertainty to the reservoir structural model. Amplitude versus offset (AVO) method is used as a helpful tool to differentiate channel sand from surrounding formations. Several attributes (P-impedance, S-impedance, longitudinal velocity Vp, shear velocity Vs and density ρ) are estimated from pre-stack seismic inversion. They have different sensitivity to the reservoir properties. Derived attributes such as Lamé parameters, incompressibility × density (λρ) and rigidity × density (μρ) can provide key lithology and fluid indicators (Goodway et al. 1997, Goodway CSEG Rec 26(6):39-60 2001). Petrophysically relating AVO attributes both to λρ and μρ and to each other in Lambda–Mu–Rho (LMR) cross-plot space can be a good tool for AVO interpretation (Rutherford and Williams Geophysics 54:680–688 1989 and Castagna and Swan Lead Edge 16(4):337–342 1997). After proper data conditioning, simultaneous inversion of pre-stack angle gathers is performed to get acoustic wave impedance (P-impedance), elastic wave impedances (S-impedance) and density ρ, then to calculate λρ and μρ volumes. In the studied area, λρ and μρ are used as a very important key to separate reservoir sands. The λρ and μρ curves are generated at each well location. Cross plots showed a fair separation of sand in the formation, i.e. higher μρ and lower λρ can detect sand. The output λρ and μρ volumes after simultaneous inversion follow the distribution of the sand which is consistent with the wells penetrating the target reservoir. This finding on the extension of the sand reservoir in terms of λρ and μρ. 3D cross-plot zonations are used for lithology discrimination. In this study, well logs were used to constrain lithology and to control the zonation filters by reducing the limits ambiguity. Other types of advanced attributes are calculated and tested. The obtained (μρ–λρ) volume acts as a good indicator for the sand distribution. It was finally used as sand presence index in the area. Also μρ has shown a good linear relationship with porosity. To note that the porosity volume is created based on the linear relationship with μρ. A product of derived porosity and the sand presence index (μρ–λρ) provides a good tool for reservoir characterization and lead to reservoir management, future planning of the field, and setting location for new wells.