The fracturing of horizontal wells has recently gained wide acceptance as aviable 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 understudy. 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, pseudo radial, 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 half-fracture length, reservoir directional permabilities, 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 horizontalwells and their sizes. Soliman et al.3 investigated the pressure-transient behavior of horizontal well with production taking place through finite-conductivity vertical fractures. For transverse circular fracture they 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. Larsen and Heger8 presented a comprehensive of the flow periods exhibited by single- and MFHW. They assumed circular fractures. Lateron9, they presented methods to determine the productivity of such a completion. Hegre10 presented a detailed discussion of the simulation of MFHWs. He investigated the effect of both grid cell size and fracture conductivity the have on the transient pressure behavior. Chen and Raghavan11 further extended our ability to understand the behavior of a MFHW by including the effect of lateral boundaries. They emphasized on the computational aspect of the problem. Wan12 introduced the effect of partially penetrating fractures intercepting a horizontal well in a bounded reservoir. This work presents a rigorous solution to a MFHW in closed anisotropic reservoirs.

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.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractHorizontal wells are ideal in tight reservoirs where economic production cannot be achieved by conventional vertical wells. One of the advantages of a horizontal well over a vertical well is that it can be fractured at a number of positions along its horizontal section. Tight reservoirs generally produce in transient state for a considerable part of their producing life. Therefore accurate transient inflow models are required, not just for well testing purposes, but also for production forecasting. The objective of this study is to determine the number and characteristics of the producing fractures along the horizontal segment of the well.A new analytical model is developed to describe the transient pressure response of a horizontal well intersected by several fractures in anisotropic reservoirs. The fractures along the horizontal wells are assumed to be rectangular and vertical, and either transversal or longitudinal relative to the well direction. They are also of finite conductivity, infinite conductivity, or uniform flux type. It is further assumed that the fractures are fully penetrating (2D Model) or partially penetrating (3D Model), the well is either open or perforated only at fractures.A new set of type curves are developed that include five flow regimes: Bilinear, Linear, Radial, Biradial, and Pseudoradial. New equations have been developed describing the unique characteristics of the five flow regimes. These equations allow us to calculate: the number of active fractures, equivalent fracture conductivity and total system conductivity, equivalent half-fracture length, reservoir directional permeabilities, equivalent skin, and the total skin of the system without using type-curve matching. A step-by-step procedure is provided for calculating reservoir parameters of a multiple hydraulically fractured horizontal well and practical applications are carried out by solving some simulated examples.

Horizontal wells are thought to be necessary in formations with low-permeability to increase the recovery and reduce the risk of drilling a dry hole. The horizontal well may cross natural fissures. Although hydraulically fracturing horizontal wells in such formations is a risky job, it may be necessary in order to achieve commercial production. This is especially true for naturally fractured gas reservoirs with matrix permeability in microdarcies and where natural-fracture network does not contribute considerably to the flow from the reservoir into the wellbore. This study investigates the transient pressure behavior of a multiply fractured horizontal well (MFHW), as well as the long time performance of such a completion in an anisotropic naturally fractured reservoir of infinite extent. Combining boundary element method and Laplace transform, single-fracture solution is considered first as it constitutes the core part of the multiple-fracture model. Then, a solution to multiply fractured horizontal wells is presented, which assumes fractures of distinct properties, it allows for unequal spacing between fractures, and permits the perforation of portions of the interval between fractures. Furthermore, it allows the juxtaposition of any number of perforated intervals and any number of fractures. The pseudo-steady state is considered to account for the fluid transfer between the matrix blocks and the fracture network. Due to its simplicity, accuracy, and reliability, procedures for using the new technique referred to as "Tiab's Direct Synthesis" have been developed to analyze the transient pressure and pressure derivative behavior of a MFHW in a naturally fractured reservoir. Individual fracture properties can be determined if individual flow rate contributions are measured, otherwise an average conductivity and half-length is determined. 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 Economides[2]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 finite-conductivity vertical fractures. For transverse circular fracture they 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. Their 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 Heger[5]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. Larsen and Heger[8]presented a comprehensive discussion of the flow periods exhibited by single- and MFHW. They assumed circular fractures. Later on[9], they presented methods to determine the productivity of such a completion. Hegre[10]presented a detailed discussion of the simulation of MFHWs. He investigated the effect of both grid cell size and fracture conductivity the have on the transient pressure behavior.

No abstract