Analyzing the production data of fractured horizontal wells by a linear triple porosity model: Development of analysis equations Afsar J. Ali, Shahab Siddiqui, Hassan Dehghanpour n University of Alberta, Canada article info Article history: Received 11 October 2012 Accepted 17 October 2013 Available online 14 November 2013 Keywords: hydraulic fracturing shale gas production data analysis fractured horizontal wells abstract Tight reservoirs stimulated by multistage hydraulic fracturing are commonly described by a dual porosity model. This model consists of homogeneous matrix blocks separated by vertical hydraulic fractures. This work hypothesizes that the production data of some fractured horizontal wells may also be described by a triple porosity model. The third medium can be either reactivated natural fractures or thin horizontal beds of higher permeability. We test this hypothesis by extending the existing triple porosity models to develop an analytical procedure to determine the reservoir parameters. We derive simplified equations for different regions of the rate-time plot including linear and bilinear flow regions. These equations can be used to calculate the effective fracture half-length, matrix permeability and length of micro-fractures. We use the proposed model to analyze the production data of two wells drilled in Barnett shale. The results show that a dual porosity model is more appropriate for describing Barnett shale data. Even if the micro-fractures are present they are not inter-connected and the length scale is much smaller than the hydraulic fracture spacing. & 2013 Elsevier B.V. All rights reserved. 1. Introduction Recent advances in horizontal drilling and multistage hydraulic fracturing have unlocked the tight formations such as shale gas and tight oil. Modeling hydrocarbon flow in these fractured systems is challenging since there is a big contrast between matrix and fracture permeability, and also the flow geometry is different from the conventional reservoirs. The previous dual porosity models (Warren and Root, 1963; Kazemi, 1969; Carlson and Mercer, 1991) have been extended for analyzing fractured horizontal wells. Bello (2009) applied the linear dual porosity model developed by El-Banbi and Wattenbar- ger (1998) to do rate transient analysis of fractured shale reser- voirs. This model includes slab matrix blocks separated by vertical hydraulic fractures, which can estimate the half length of the hydraulic fractures by history matching of the measured well production data. However, the induced hydraulic fractures may reactivate pos- sibly existing natural fractures which in turn may result in a complex fracture network (Gale et al., 2007; Dahi-Taleghani, 2009). Under these conditions, the reservoir should be described by a triple porosity model. Mathematical formulations of flow through triple porosity media were first introduced three decades ago (Liu, 1981). Abdassah and Ershaghi (1986) developed a triple porosity model to describe the well test data of fractured reser- voirs with a dual matrix structure. Liu et al. (2003) proposed a triple porosity model to describe the well test data of a reservoir which consists of fractures, rock matrices, and cavities. Wu et al. (2004) used the same model to describe flow in a reservoir, which consists of matrices, large fractures, and small fractures. The linear dual porosity models have been recently extended to account for both hydraulic fractures, and microfractures in hor- izontal wells. Ozkan et al. (2010) presented a transient dual- porosity model for the inner shale reservoir and extended the previous tri-linear model presented by Brown et al. (2009). The combination of these two models is the first triple porosity model proposed for linear fractured systems. Recently, Al-Ahmadi (2010) extended the dual porosity model of Bello (2009) and presented a triple porosity model for the linear systems. Their fully unsteady state model is essentially similar to the model presented by Ozkan et al. (2010), except they assumed slab matrix blocks whereas Ozkan et al. (2010) assumed spherical matrix blocks to derive the transfer functions. Dehghanpour and Shirdel (2011) extended Ozkan et al. (2010) transient model and presented a triple porosity model for the inner shale reservoir. The combination of this model and the tri-linear model presented by Brown et al. (2009) repre- sents a quadruple porosity model which includes a triple fracture system and one matrix system. The existing triple porosity models for fractured horizontal wells assume sequential flow. This means that they ignore fluid Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/petrol Journal of Petroleum Science and Engineering 0920-4105/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.petrol.2013.10.016 n Corresponding author. E-mail address: dehghanpour@ualberta.ca (H. Dehghanpour). Journal of Petroleum Science and Engineering 112 (2013) 117–128