Decline curve analysis for horizontal wells

Abstract

The completion of horizontal wells has become popular as a means to provide larger contact with the reservoir to enhance well productivity or infectivity or to overcome problems associated with gas and water coning. In this study we develop a novel solution for the case of a horizontal well in an anisotropic reservoir. Decline curve analysis is one of the most commonly used tools in reservoir engineering for the analysis of production data, where we use production rates versus time compared to a theoretical model. However, conventional type curves for decline curve analysis are based either on a vertical well model or on a vertically fractured well model, both of which are insufficient to describe the transient and transition to boundarydominated flow behavior for horizontal wells. We derived a line source solution for a horizontal well from the point source solution, which assumes reservoir isotropy in the horizontal plane, single phase fluid flow in the reservoir, no gravity forces, and we assume that permeability is independent of location in the reservoir. We define an anisotropy factor that can be combined with formation thickness to yield an effective formation thickness. We also introduce a pseudoskin function for a horizontal well which represents the difference of pressure drop between the vertically fractured and horizontal well solutions. We developed new type curves in this work for an infinite-conductivity horizontal well where these type curves can be used for decline curve analysis. These type curves represent the dimensionless rate response and other auxiliary rate functions which are the solutions for production at constant bottomhole pressure and for closed rectangular outer boundary conditions. For the type curves, the well is assumed to be located at the center of a square reservoir. The integral and derivative of the integral functions are useful for the selection of transient stems as well as to interpret the boundary dominated flow portion of the data.Our type curve correlating approach involves the following parameters: shape factor for a horizontal well, [ ]; horizontal well penetration ratio, [ ]; dimensionless horizontal well half-length, LD; anisotropy ratio, [ ] vertical location of the well, [ ]; wellbore radius of the horizontal well, [ ]; Pore volume of the reservoir. Simultaneously matching the flow rate and the auxiliary functions provides more confidence in the match and aids in selecting the correct transient and depletion stem. The auxiliary data functions are particularly useful for matching boundary-dominated flow data due to the uniqueness of the these trends. Finally, the analysis procedures we presented are especially designed for a horizontal well. The material balance method is introduced for the analysis of data from wells with variable bottomhole pressure and variable rate production histories. The value of our new method is illustrated in a field case that matches one of the new type curves very well but the data are not modeled well during the transient flow regime by conventional radial flow type curves.