Interpretation of Multiple Hydraulically Fractured Horizontal Wells in Closed Systems (2004)

Abstract The fracturing of horizontal wells has recently gained wide acceptance as a viable completion option to maximize the return on investment. This is especially true in the case of tight formations. This paper presents an analytical model for fractured horizontal wells in anisotropic closed or semi-infinite, homogenous or naturally fractured systems. Uniform flux, infinite conductivity and finite conductivity models are considered. The fractures may be of different properties and unequally spaced along the horizontal wellbore. This model is validated using a numerical simulator. It provides us with methods and ideas for designing, interpreting well tests and prediction of the long time performance of the system under study. A log-log plot of pressure and pressure derivative versus test time may reveal the presence of several straight lines corresponding to different flow regimes: bilinear, first linear, biradial, radial, pseudoradial, second linear and pseudo steady state. New equations have been developed describing the unique characteristics of these flow regimes. These equations allow us to calculate: the number of active fractures, equivalent fracture conductivity and total system conductivity, equivalent halffracture length, reservoir directional permeabilities, equivalent skin, the total skin, reservoir width for semi-infinite systems and drainage area for closed systems. Simulated examples have been performed to show the applicability of the proposed technique. Introduction Stimulation of a horizontal well in a low-permeability reservoir may significantly increase the well productivity. Unlike a vertical well, a horizontal well may be fractured at more than one point along the well length. Yost et al.1 presented a case study of a multiply fractured horizontal well intersecting natural fissures. They presented a practical view of the fracturing treatment of a horizontal well in a naturally fractured reservoir. They reported improvement ratios six days after fracturing ranging form 4 to 35 in different zones along the horizontal wellbore. Mukherejee and Economides2 presented a simple procedure to calculate the optimum number of orthogonal transverse fractures in horizontal wells and their sizes Soliman et al.3 investigated the pressure-transient behavior of horizontal well with production taking place through finiteconductivity vertical fractures. For transverse circular fracturethey obtained a Laplace space solution valid for the period when flow in the reservoir can be treated as linear (towards the fracture plane). Among other things, they compared the effectiveness of finite-conductivity vertical fractures intercepting horizontal and vertical wellbore. This comparison is valid for short flowing times. Conlin et al.4 presented a case study of a multiply fractured horizontal well drilled in a low-permeability chalk reservoir producing under solution gas drive. Larsen and Heger5 introduced methods to generate synthetic pressure transient data for MFHW their discussion was restricted to individual or pairs of fractures in unbounded reservoirs in all directions. Roberts et al.6 studied the effect of non-Darcy flow within the hydraulic fractures on horizontal well productivity in tight gas reservoirs. Raghavan et al.7 introduced a new model to compute the pressure transient data of MFHWs. They discussed, also, the long time performance of such a completion.