Since the early 90's, the use of horizontal wells has become increasingly more popular in the development of oil and gas fields. Advances in drilling technology such as Measurement While Drilling (MWD) and Logging While Drilling (LWD) with accumulated knowledge/experience enable cost effective and more sophisticated horizontal wells to be drilled. Nevertheless, drilling a horizontal well that is perfectly parallel to the bedding plane is still distant from reality. All horizontal wells, to a certain extent, follow a sinusoidal trajectory merely because of steering problems, natural undulation of layers as well as presence of non-uniform layer thickness. In horizontal well applications ten to fifteen feet amplitude undulations are often considered as precise placement. Although MWD and LWD procedures minimize the possibility of exiting pay zones, while drilling horizontal wells in relatively thin formations there is always a real possibility to leave the pay zone even for a short period of time.
A number of studies have appeared in the literature for pressure transient analysis of horizontal wells for rapid determination of permeability anisotropy, skin factors and average pressures. However, none of these forward and their accompanying inverse solutions discusses the validity and applicability of the offered protocols if the horizontal well in actuality is undulated. In this study, we analyse pressure transient response of undulating wells using a previously developed numerical model that can accommodate various types of well architectures including undulating wells. Our objective in this paper is to demonstrate when analytical solutions for pressure transient analysis of horizontal wells are still usable and when they become unusable for various undulation configurations studied, and show how numerical well test analysis procedures can be utilized when analytical models are inadequate.
Example scenarios investigated in this paper show that the presence of intensive undulations in well trajectories may significantly shorten and even may overshadow the transient flow period that is already endangered by the presence of wellbore storage affects. Under these conditions the use of a numerical model, with options for undulating well architectures, will be necessary for accurate analysis of pressure transient data.
Introduction
Remaining within the pay zone during drilling of horizontal wells is vital in minimizing loss in productivity. This has become achievable with recent advances in technology and experience that was followed by reports of successful drilling of horizontal wells.1,2 However, lateral drilling is not free of undulation; if not more, ten or fifteen feet of undulation in lateral drilling can easily happen. Also, as an economical alternative to multilateral wells, there are cases reported where sinusoidal wells are purposely drilled to produce maximum drainage radius exposure within low productivity zone in waterflooding3, to maximize exposure to pay zones in layered formations by cutting layers several times4, and to achieve a cost effective recovery in highly faulted, poorly connected sand layers.5
Analytical solutions for pressure drawdown or buildup of lateral wells always assume that wells are perfectly parallel to outer boundaries. Furthermore, whether undulating or not, performances of lateral wells are simulated by most numerical models utilizing a wellbore equation with equivalent wellblock radius approach. This type of analysis for lateral wells might produce inaccurate results, as wellblock radius calculations may not be applicable for lateral wells situated in thin layers. Differently from general practice, the numerical model6 used in this study employs a form of residual equation rather than a wellbore equation to determine flow into (or from) wells. In addition the model offers great flexibility to trace the actual path of wells, and approximates wells as an assembly of fine rectangular cells.
Our discussion here will start out by first comparing pressure responses of horizontal wells obtained from the analytical and numerical models. Each flow regimes encountered while analysing pressure responses of horizontal wells will then be examined. Finally, effects of undulation on the development of each flow regime will be studied for several cases considered.
