In this paper, we describe a method to estimate, in real-time, the volume of a hydraulic fracture from tiltmeter measurements recorded during the treatment. The resolution of fracture dimensions and orientation is discussed at first. A limit, expressed in terms of the distance between the tiltmeters and the fracture, above which only the volume and orientation of the fracture have an effect on the tilt field is established. The proposed method of analysis takes advantage of this, often neglected, fundamental properties of the elastic kernels (St. Venant principle). We recognize that, in most cases without additional information, only the fracture volume and orientation can be accurately estimated from tiltmeter measurements. The knowledge of the fracture volume estimated from tilt data together with the injected volume at time t furnish the efficiency of the treatment at this time. Furthermore, because the method employed to analyse the tilt data is computationally efficient, the volume and efficiency can be obtained in real time (i.e. as the data arrive) throughout a hydraulic fracturing treatment.
1. INTRODUCTION
Hydraulic fracturing is a technique widely used for the stimulation of oil and gas reservoir (Economides & Nolte, 2000). Fracture orientation must be known to determine well layout and spacing, especially in reservoirs with permeability anisotropy. In some environments, there is considerable uncertainty about whether fractures are growing in horizontal or vertical planes, which can significantly effect the overall size of the fracture formed. Fractures treatment schedule designs which assume a vertical orientation will often fail in execution if the actual fracture is horizontal. Ultimately, the success of a hydraulic fracture treatment depends on placing the correct amount of proppant in the fracture to produce a conductive channel with a size and shape that provides an overall optimal stimulation effect. Fracture olume and efficiency are important in design because these parameters help determine timing and volumes of for pumping clean and slurry fluid stages.
In order to "map" hydraulic fractures, several type of indirect measurements are typically used such as micro-seismic acoustic monitoring, tiltmeter mapping, and treatment pressure analysis. In this communication, our interest lies in the analysis of tiltmeter measurements performed during hydraulic fracturing jobs.
Despite the now common use of tiltmeters to map hydraulic fractures in the petroleum industry (Wright et al., 1999), it is not precisely clear what information on the fracture can and cannot be obtained from such measurements. Based on practical experience, (Cipolla & Wright, 2000) lists some of the fracture quantities better resolved by surface or borehole tiltmeters. In this paper, we present formal results we have recently obtained regarding the issue of determining the geometry of hydraulic fractures from tiltmeter measurements. We then discuss practical implications of these results.
Specifically, we show that due to the elastostatic nature of the problem, the effect of the dimensions of the fracture fades extremely fast spatially such that, in most case, tiltmeters only sample the far-field effect of the hydraulic fracture. This far-field deformation pattern only depends on the orientation of the fracture (anisotropic displacement field) and the volume of the fracture (intensity of the recorded tilts), the two being coupled.
