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Horizontal wells with multiple hydraulic fractures have become a common occurrence in the oil and gas industry, especially in tight formations. Published models assume the hydraulic fractures are vertical and symmetric. However, recent studies have shown that fractures are asymmetric and inclined with respect to the vertical direction and the axis of the wellbore. This paper introduces a new technique for interpreting the pressure behavior of a horizontal well with multiple hydraulic fractures. The hydraulic fractures in this model could be longitudinal or transverse, vertical or inclined, symmetrical or asymmetrical. The fractures are propagated in isotropic or anisotropic formations and are considered as having different dimensions and different spacing. This technique, based on pressure and pressure derivative concepts, can be used to calculate various reservoir parameters, including directional permeability, fracture length, skin factors, and angle of inclination. The study has shown that early radial flow might develop when the spacing between fractures is significantly long. This paper also suggests new applications for the well test analysis in the hydraulically fractured reservoirs. These applications are focusing on: 1) Evaluating the performance of the fractures, 2) Determining whether one or more hydraulic fractures do not perform properly as designed (closed) and 3) Locating the malfunctioning fractures. A type curve matching technique has been applied using the plots of the pressure and pressure derivative curves. A set of type curves, which will be included in the paper, have been generated for the inclined transverse and longitudinal hydraulic fractures associated to the horizontal wells with different inclination angles from the vertical direction. A step-by-step procedure for analyzing pressure tests using these type curves is also included in the paper for several numerical examples.

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Summary This paper introduces a new approach for studying productivity-index (PI) behavior of fractured oil and gas reservoirs during transient-and pseudosteady-state conditions. This approach focuses on the fact that PI derivative could vanish at a certain production time, indicating the beginning of pseudosteady state, wherein the PI demonstrates constant value. The reservoirs in this study are considered depleted by horizontal wells intersecting multiple hydraulic fractures where Darcy flow and non-Darcy flow may control flow patterns in the porous media. The PI is calculated assuming constant production rate and considering pressure profile for early- and intermediate-production time when transient condition dominates fluid flow and late-production time when pseudosteady state is reached. The outcomes of this study can be summarized as understanding PI behavior at early- and intermediate-production time when transient flow is dominant in the porous media and late-production time when pseudosteady-state condition is reached; indicating the effect of reservoir configuration on PI and the time when this index approaches constant value; and introducing a study for the influence of non-Darcy flow in the PI. The most-interesting points in this study are the following. First, that PI reaches constant value when the rates of change with time for the two pressure drops—transient and pseudosteady state—are equal. Second, the time for approaching constant PI in a small drainage area is faster than for a large area. Third, that PI is affected by non-Darcy flow at early- and intermediate-production time; however, the effect is not seen at late-production time. Last, that PI could exhibit constant behavior for severe non-Darcy flow at early- and intermediate-production times even though transient-state condition dominates fluid flow in the porous media.

Summary Reservoir performance of hydraulically fractured tight and shale-gas formations is affected by an extensive range of parameters. Non-Darcy flow is one of these parameters, characterized by a significant effect on near-wellbore pressure drop for horizontal wells and near-fracture tips for hydraulic fractures (HFs). Non-Darcy flow develops in porous media when the velocity of reservoir fluid becomes extremely high because of continuous narrowing in the cross-sectional area of flow and the convergence of flow streamlines. As a result, the inertial forces could be considered the major contributor to the total pressure drop required by fluids to move from the outer drainage area toward the wellbore. Pressure drop, caused by non-Darcy flow, is described by the Forchheimer (1901) equation, wherein the deviation from Darcy's law is proportional to the inertial factor (β), which in turn is a function of porous-media characteristics such as permeability and porosity. This paper investigates the effect of non-Darcy flow, represented by the non-Darcy-flow coefficient (D) and/or the rate-dependent skin factor (DQsc), on pressure profiles, flow regimes, and productivity indices (PIs) of multiple HFs that propagate in tight and shale-gas reservoirs. This paper also introduces a new simplified technique for estimating both DQsc and D by knowing bottomhole flowing pressure and cumulative production at any time. For this purpose, a multilinear-flow-regime model was generated and modified for the existence of non-Darcy flow. A comparison for reservoir performance with and without non-Darcy flow was conducted for different reservoir configurations, including the reservoir-drainage area (2xe and 2ye), fracture conductivities, fracture dimensions, and fracture-propagation ratios. A set of plots has been developed for estimating the rate-dependent skin factor depending on production time with respect to cumulative PI. The outcomes of this study can be summarized as understanding the conditions at which non-Darcy flow could have considerable effects on reservoir performance; estimating the deviation in PI caused by the existence of non-Darcy flow from the cases where Darcy flow is the dominant; and introducing a new technique to estimate DQsc and D. The most interesting points in this study are the ability to estimate these two parameters without the need for experimental studies or use of an empirical model; that all flow regimes expected to develop in the entire life of reservoirs are not affected by non-Darcy flow, unlike pressure behaviors and PI; and that the PI is constant for high values of DQsc at early-time production and sharply declines at later production time.