Seismic wave motion for a new model of hydraulic fracture with an induced low‐velocity zone

Abstract

Hydraulic fracture treatments induce microseismicity (i.e., discrete events plus noise) which can be recorded only by seismometers located in or near the treatment well bore. Seismograms recorded in the treatment well bore are composed of interacting phases which to date defy discrete identification and preclude standard inversion techniques to determine source characteristics, propagation path characteristics, or both. To understand the recorded data, synthetic seismograms have been generated using a finite difference approximation for a two-dimensional hydraulic fracture model which includes a treatment-induced, low-velocity zone (LVZ). The LVZ is produced by pore dilatancy in response to formation fluid pressurization caused by pressure diffusion from the treatment fluid and fracture opening. Borehole, seismometer coupling, fluid transport, and dynamic fracture effects are not considered. The models examined showed that a fixed-aperture fracture plus surrounding LVZ acted as a leaky waveguide confining the seismic energy and altering propagation characteristics which resulted in unconventional seismograms. The seismograms were composed of multiple transient phases caused by phase interactions and conversions at the waveguide boundaries and stationary phases corresponding to the eigenfrequency structure of the fracture-LVZ waveguide. BACKGROUNDHydraulic fracturing for enhancing the recovery of hydrocarbons has become a common reservoir engineering practice since it was first introduced at the Hugoton gas field in western Kansas in 1947 [Howard and Fast, 1970]. Over the intervening years, treatment procedures have evolved in an attempt to create fractures having specific or determinable characteristics (i.e., orientation, length, height, and aperture). For example, treatment parameters (e.g., injection rate, injection pressure, proppant concentration, and fracture fluid biochemistry and rheology) are varied in ways thought to maximize fracture fluid efficiency by decreasing fluid loss to the formation, to prevent fracture growth into formations other than the desired formation, and to produce maximum propped fracture length and permeability. During the actual treatment, designed procedures frequently are adjusted to compensate for the effects of unexpected formation heterogeneities, spatially varying stress and equipment malfunctions. Because of the complexity of the treatment and the setting upon which the treatment is applied, a need exists for determining the final effect of the treatment.A number of authors have published models which define the final fracture geometry by using the treatment parameters [e.g., Advanti et al., 1985; Ahmed, 1984; Geertsma and De-Klerk, 1969; Nolte, 1983; Perkins and Kern, 1961; Settari and Cleary, 1984]. These models are strongly dependent upon assumed formation characteristics and their interactions with actual treatment parameters. As a result, techniques for delineating the final fracture or fractures which are independent of formation and treatment assumptions or procedures...

On an effective two-phase model of a medium with cracks of finite length

“…A low-velocity wave is observed experimentally after a hydraulic fracture in an interhole region in the zone of fracture [8]. The velocity value of this wave proves to be smaller than all velocities in the media of an interhole region.…”

“…The layers in which a hydraulic fracture has arisen are described by the effective model mentioned above, but the media surrounding them remain elastic. In such a system the normal waves propagate with small velocity v3, which were recorded in [8].…”

“…This model allowed us to elucidate a number of important peculiarities of wave propagation in cracked media [4][5][6] and has received support in experiments [7,8]. In deriving this model several assumptions on the form of cracks are made.…”

On an effective model of an elastic block medium with slide contacts on the interfaces

“…For this medium a four-phase effective model is deduced in several ways. This model is a generalization of the effective layered models of [1][2][3][4], which were experimentally confirmed in [5,6]. By using the equation of the deduced fourphase model, the wave fronts and velocities of wave propagation along axes are determined for this model and compared with the data presented in [4].…”

The equations of the effective two-phase cracked model with finite length cracks

“…On the base of similar assumptions and by means of the matrix method and the method of layer averaging, a two-phase effective model of the cracked medium was derived specifically in the case where the cracks are filled with liquid [1,2]. The study of this model showed a good coincidence of results of model theory with experimental data [3][4][5]. For luther development of effective models, it is useful to get rid of the assumptions made.…”