LAUSR

A novel method to map asymmetric hydraulic-fracture propagation using tiltmeter measurements is presented. Hydraulic fracturing is primarily used for oil-and-gas well stimulation, and is also applied to precondition rock before mining. The geometry of the developing fracture is often remotely monitored with tiltmeters— instruments that are able to remotely measure the fracture-induced deformations. However, conventional analysis of tiltmeter data is limited to determining the fracture orientation and volume. The objective of this work is to detect asymmetric fracture growth during a hydraulic-fracturing treatment, which will yield heightgrowth information for vertical fracture growth and horizontal asymmetry for lateral fracture growth or detect low preconditioning-treatment efficiency in mining. The technique proposed here uses the extended Kalman filter (EKF) to assimilate tilt data into a hydraulic-fracture model to track the geometry of the fracture front. The EKF uses the implicit level set algorithm (ILSA) as the dynamic model to locate the boundary of the fracture by solving the coupled fluid-flow/fracture-propagation equations, and uses the Okada half-space solution as the observation model (forward model) to relate the fracture geometry to the measured tilts. The 3D fracture model uses the Okada analytical expressions for the displacements and tilts caused by piecewise constant-displacement discontinuity elements to discretize the fracture area. The proposed technique is first validated by a numerical example in which synthetic tilt data are generated by assuming a confining-stress gradient to generate asymmetric fracture growth. The inversion is carried in a two-step process in which the fracture dip and dip direction are first obtained with an elliptical fracture-forward model, and then the ILSA-EKF model is used to obtain the fracture footprint by fixing the dip and dip direction to the values obtained in the first step. Finally, the ILSA-EKF scheme is used to predict the fracture width and geometry evolution from real field data, which are compared with intersection data obtained by temperature and pressure monitoring in offset boreholes. The results show that the procedure is able to satisfactorily capture fracture growth and asymmetry even though the field data contain significant noise, the tiltmeters are relatively far from the fracture, and the dynamic model contains significant “unmodeled dynamics” such as stress anisotropy, material heterogeneity, fluid leakoff into the formation, and other physical processes that have not been explicitly accounted for in the dynamic ILSA model. However, all the physical processes that affect the tilt signal are incorporated by the EKF when the tilt measurements are used to obtain the maximum likelihood estimates of the fracture widths and geometry. Introduction Hydraulic fracturing has been used for oil-and-gas well stimulation since the late 1940s (Montgomery and Smith 2010), and is also used as a preconditioning method to promote earlier and more-continuous caving in underground coal and metal mines (Jeffrey et al. 2013). The goal of hydraulic-fracture design is to optimize the treatment such that a fracture length and fracture conductivity are achieved that maximize productivity while minimizing cost. Hence, information about the fracture geometry and fracture height, width, and orientation is required to study the efficacy of a fracturing treatment and to further optimize future treatments. Most conventional hydraulic-fracture design models assume symmetric/lateral fracture growth about the wellbore. In real treatments, the fracture growth can be asymmetric. Asymmetric fracture geometry develops when the fracture grows preferentially in one direction with respect to the wellbore. In the case of vertical fractures, asymmetric fracture growth may develop with unequal lateral growth or unequal vertical growth or both. Unequal vertical growth is common because the vertical growth occurs through rock layers with contrasting properties and containing contrasting confining stresses. Such vertical growth or height growth not only leads to a less effective stimulation but can also result in the fracture growing into water-bearing formations that may be affected by the treatment or by the later production of the well. Asymmetric growth is often associated with reduced fracture conductivity over the pay zone, and may also lead to a proppant screenout, further reducing the effectiveness of the fracturing treatment (Bennett et al. 1983; Jeffrey 1996). Asymmetry in the lateral growth of a fracture is attributed to interaction with adjacent, previously placed hydraulic fractures that impose an additional compressive stress in the reservoir rock around the fracture. A new fracture will then tend to avoid these more highly stressed areas, leading to asymmetric growth and less-complete stimulation of the reservoir. Because the fracture asymmetry can have a significant effect on the effectiveness and efficiency of a hydraulic-fracturing treatment, it is useful to have methods to monitor asymmetric fracture growth. Fracture-monitoring techniques map hydraulic-fracture geometry indirectly with remote-monitoring methods applied at the wellsite, which provides helpful guidance for controlling the treatment and for optimization of future hydraulic-fracturing designs. Microseismic-event location and tilt measurements are two commonly used techniques to monitor fracture growth. Tiltmeters are instruments that can measure small rotational movements with respect to the gravity vector along two orthogonal directions. The opening and shearing of the hydraulic-fracture surfaces result in rock deformations, which, in turn, cause small rotational movements at the tiltmeter location. The induced movements are picked up by these instruments located either close to the surface Copyright VC 2017 Society of Petroleum Engineers