A Three-Dimensional Well Planning Method for HDR Geothermal Wells

Abstract

Abstract This paper presents a method for planning sections of directionally drilled wells in three dimensions where azimuth and inclination is specified at the end points. It describes the implementation of the algorithm in a computer code and its use at the Camborne School of Mines Geothermal Energy Project for planning a proposed third well in an existing hot dry rock geothermal reservoir. Introduction A hot dry rock geothermal energy research project is being undertaken by Camborne School of Mines in Cornwall, England. The current phase of work is primarily concerned with the development of a fractured rock geothermal reservoir at a depth of 2 km in the Carnmenellis granite of South West England. The experimental system consists of a pair of directionally drilled wells and following explosive pre-treatment of the lower injection well, a "reservoir" was created by massive hydraulic stimulation. The system was designed to intersect the two sets of dominant near vertical joints in the granite (striking 60 deg and 160 deg) to allow maximum potential access to the fractures in the rock. Opening of the natural discontinuities in the rock mass was expected to develop upwards towards the recovery well. Micro-seismic monitoring of the developing reservoir revealed preferential growth along the direction of maximum principal preferential growth along the direction of maximum principal stress (130 deg - 310 deg) but with predominantly downward growth attributed to the high natural horizontal stress anisotropy. As the position and orientation of the current recovery well provides insufficient return flow rates for a viable geothermal provides insufficient return flow rates for a viable geothermal system, it is proposed to drill a third well during the next phase of the project to investigate further methods of improving the system's performance. The design of the trajectory of this third well has introduced constraints not normally encountered in conventional well planning. In particular the well must intersect the existing reservoir at a precise spatial position and attitude. Additionally, as the existing pumping installation, research data acquisition system and wellheads are located on the floor of a small quarry, the choice of available spud positions is severely limited. These constraints coupled with the difficulty of deviating a well in the hard abrasive granite require a high precision well trajectory to be planned with some intervals of it treated in a full three dimensional manner. Methods are available for calculating well trajectories in 3-D (eg Ref 3), but these constrain the well path vectors at kickoff and target points to be co-planar and reduced to a two dimensional calculation in an oblique plane. In the situation presented here this is not the case and a more general full 3-D presented here this is not the case and a more general full 3-D treatment is required. The problem is analogous to the frequent requirement in computer graphics to produce a smooth curve between data points on a graph on some output device which is only capable of incremental movement (eg a drum plotter), the intermediate positions must be calculated using some form of curve fit. Several positions must be calculated using some form of curve fit. Several methods are available including local spline fits and Bezier curves but the particular method of interest here is to use a parametric description of the well path in three dimensions. MATHEMATICAL ANALYSIS The following analysis uses a method attributed to McConalogue and is in common use in several 2-D computer graphics packages. A simple extension to three dimensions allows the method to be applied to a section of wellpath with specified azimuth and inclination at the end points.