Viscid-inviscid interaction associated with incompressible flow past wedges at high Reynolds number

An analytical method is suggested for the study of the viscid inviscid interaction associated with incompressible flow past wedges with arbitrary angles. It is shown that the determination of the nearly constant pressure (base pressure) prevailing within the near wake is really the heart of the problem, and the pressure can only be established from these interactive considerations. The basic free streamline flow field is established through two discrete parameters which adequately describe the inviscid flow around the body and the wake. The viscous flow processes such as the boundary layer buildup, turbulent jet mixing, and recompression are individually analyzed and attached to the inviscid flow in the sense of the boundary layer concept. The interaction between the viscous and inviscid streams is properly displayed by the fact that the aforementioned discrete parameters needed for the inviscid flow are determined by the viscous flow condition at the point of reattachment. It is found that the reattachment point behaves as a saddle point singularity for the system of equations describing the recompressive viscous flow processes, and this behavior is exploited for the establishment of the overall flow field. Detailed results such as the base pressure, pressure distributions on the wedge, and the geometry of the wake are determined as functions of the wedge angle

Seismic imaging of hydraulically-stimulated fractures: A numerical study of the effect of the source mechanism

We present a numerical study of seismic imaging of hydraulically stimulated fractures using a single source from an adjacent fracturing-process. The source is either a point force generated from the perforation of the casing of the well or a double-couple as is typically observed from the induced microseismicity. We assume that the fracture is sufficiently stimulated to be imaged by reflected seismic energy. We show for a specific monitoring geometry of hydrofracturing that not only different waves (P and S) but also different source mechanisms from the same region form an image of different parts of the target fracture and thus add complementary information. The strategy presented here might be used as an additional monitoring tool of the hydrofracturing process

Review of hydraulic fracture mapping using advanced accelerometer-based receiver systems

Hydraulic fracturing is an important tool for natural gas and oil exploitation, but its optimization has been impeded by an inability to observe how the fracture propagates and what its overall dimensions are. The few experiments in which fractures have been exposed through coring or mineback have shown that hydraulic fractures are complicated multi-stranded structures that may behave much differently than currently predicted by models. It is clear that model validation, fracture optimization, problem identification and solution, and field development have all been encumbered by the absence of any ground truth information on fracture behavior in field applications. The solution to this problem is to develop techniques to image the hydraulic fracture in situ from either the surface, the treatment well, or offset wells. Several diagnostic techniques have been available to assess individual elements of the fracture geometry, but most of these techniques have limitations on their usefulness. For example, tracers and temperature logs can only measure fracture height at the wellbore, well testing and production history matching provide a productive length which may or may not be different from the true fracture length, and tiltmeters can provide accurate information on azimuth and type of fracture (horizontal or vertical), but length and height can only be extracted from a non-unique inversion of the data. However, there is a method, the microseismic technique, which possesses the potential for imaging the entire hydraulic fracture and, more importantly, its growth history. This paper discusses application of advanced technology to the microseismic method in order to provide detailed accurate images of fractures and their growth processes

The role of rock joint frictional strength in the containment of fracture propagation

The fracturing phenomenon within the reservoir environment is a complex process that is controlled by several factors and may occur either naturally or by artificial drivers. Even when deliberately induced, the fracturing behaviour is greatly influenced by the subsurface architecture and existing features. The presence of discontinuities such as joints, artificial and naturally occurring faults and interfaces between rock layers and microfractures plays an important role in the fracturing process and has been known to significantly alter the course of fracture growth. In this paper, an important property (joint friction) that governs the shear behaviour of discontinuities is considered. The applied numerical procedure entails the implementation of the discrete element method to enable a more dynamic monitoring of the fracturing process, where the joint frictional property is considered in isolation. Whereas fracture propagation is constrained by joints of low frictional resistance, in non-frictional joints, the unrestricted sliding of the joint plane increases the tendency for reinitiation and proliferation of fractures at other locations. The ability of a frictional joint to suppress fracture growth decreases as the frictional resistance increases; however, this phenomenon exacerbates the influence of other factors including in situ stresses and overburden conditions. The effect of the joint frictional property is not limited to the strength of rock formations; it also impacts on fracturing processes, which could be particularly evident in jointed rock masses or formations with prominent faults and/or discontinuities

Microseismic monitoring of the B-sand hydraulic fracture experiment at the DOE/GRI multi-site project

Six hydraulic-fracture injections into a fluvial sandstone at a depth of 4500 ft were monitored with multi-level triaxial seismic receivers in two wells, resulting in maps of the growth and final geometry of each fracture based upon microseismic activity. These diagnostic images show that the hydraulic fractures are highly contained for smaller-volume KCl-water injections, but height growth is significant for the larger-volume, higher-rate, higher-viscosity treatments. Fracture lengths for most injections are similar. Final results are also compared with fracture models

Evaluation of a downhole tiltmeter array for monitoring hydraulic fractures

A series of hydraulic-fracture experiments using a downhole tiltmeter array, called an inclinometer array, was conducted at the Department of Energy (DOE)/Gas Research Institute (GRI) Multi-Site facility in Colorado. The inclinometer array was used to measure the deformation of the reservoir rock in response to hydraulic fracture opening and confirm microseismically measured results. In addition, the inclinometer array was found to be a useful tool for accurately measuring closure stress, measuring residual widths of both propped and unpropped fractures, estimating proppant distribution, and evaluating values of in situ moduli

Application of microseismic technology to hydraulic fracture diagnostics: GRI/DOE Field Fracturing Multi-Sites Project

The objective of the Field Fracturing Multi-Sites Project (M-Site) is to conduct field experiments and analyze data that will result in definitive determinations of hydraulic fracture dimensions using remote well and treatment well diagnostic techniques. In addition, experiments will be conducted to provide data that will resolve significant unknowns with regard to hydraulic fracture modeling, fracture fluid rheology and fracture treatment design. These experiments will be supported by a well-characterized subsurface environment as well as surface facilities and equipment conducive to acquiring high-quality data. It is anticipated that the project`s research advancements will provide a foundation for a fracture diagnostic service industry and hydraulic fracture optimization based on measured fracture response. The M-Site Project is jointly sponsored by the Gas Research Institute (GRI) and the US Department of Energy (DOE). The site developed for M-Site hydraulic fracture experimentation is the former DOE Multiwell Experiment (MWX) site located near Rifle, Colorado. The MWX project drilled three closely-spaced wells (MWX-1, MWX-2 and MWX-3) which were the basis for extensive reservoir analyses and tight gas sand characterizations in the blanket and lenticular sandstone bodies of the Mesaverde Group. The research results and background knowledge gained from the MWX project are directly applicable to research in the current M-Site Project

Microseismic Monitoring of the Mounds Drill Cuttings Injection Tests

This paper describes the microseismic mapping of repeated injections of drill cuttings into two separate formations at a test site near Mounds, OK. Injections were performed in sandstone and shale formations at depths of 830 and 595 m, respectively. Typical injection disposal was simulated using multiple small-volume injections over a three-day period, with long shut-in periods interspersed between the injections. Microseismic monitoring was achieved using a 5-level array of wireline-run, triaxial- accelerometer receivers in a monitor well 76 m from the disposed well. Results of the mapped microseismic locations showed that the disposal domti W= generally aligns with the major horizontal stress with some variations in azimuth and that wide variations in height and length growth occurred with continued injections. These experiments show that the cuttings injection process cm be adequately monitored from a downhole, wireline-run receiver array, thus providing process control and environmental assurance