Proper representation of dynamic (propagating) fractures is important for modeling applications in which the fracture is directly coupled to a reservoir simulator. Such a model, while once applied only to unconventional fracturing applications is now being developed for conventional fracturing techniques (such as fracturing in low permeability reservoirs) as a more realistic tool for modeling both fracture growth and post fracture production responses. In an uncoupled model (such as conventional fracturing software) the reservoir coupling is usually simplified to a 1-dimensional leak-off model which lends itself easily to construct dynamic grids for the fracture. However, coupled models will generally require a dynamic fracture propagating through a stationary reservoir/stress grid. This creates a well-known grid effect resulting in oscillation of fracture growth with time, and limiting the stability of the model. In most unconventional fracturing applications, the fracture volume is small compared to injected fluid volume due to high leak-off, which causes a singularity of mass balance constraint or fluid volume in facture. If one were to use a conventional fracturing model with a dynamic grid, this would result in convergence problems due to the high leak off of injected fluid. Also, what is not represented in conventional models is the influence that high leak-off has on the far-field stresses and pressures, which in turn influences the fracturing mechanics. It is believed that the use of a fully coupled dynamic model such as the one being developed here will generate more realistic representions of the fracture/reservoir response. This paper presents numerical techniques necessary for the successful development of such a fully coupled model. Four different methods for representing dynamic fracture propagation were formulated. These four methods take into consideration the mutual influence between dynamic fracture propagation and reservoir flow, treat the fracture as a highly permeable part of the reservoir, and use one (common) grid system to model both dynamic fracture propagation and reservoir flow in a fully coupled manner. The individual methods differ by the algorithms, by which the dynamic modification of the transmissibility for fractured grid(s) is derived, and range from an empirical approach to the use of analytical fracture models. Introduction Proper representation of dynamic (propagating) fractures is important for many reservoir processes such as waterflooding at fracture pressure, produced water re-injection (PWRI), steam injection into heavy oils and oil sands, or waste and sand disposal. Also, modeling propagating fracture is the central issue for the simulation of hydraulic fracturing in a coupled manner with reservoir response. In uncoupled conventional fracturing simulation, the fracture propagation usually is modeled based on mass balance of injected fluid, and the reservoir coupling with fracture is simplified to 1-D or 2-D analytical "leak-off model"1,2,3. In 1980, Settari4 proposed a method for modeling hydraulic fracture probation based on mass balance constraint, by coupling fracture mechanics, fracture propagation, reservoir flow and heat transfer. The reservoir coupling with fracture is obtained by treating fracture flow as a boundary of reservoir flow and numerically solving leakoff of injected fluid. Hagoort et al.5 studied the application of the model for modeling dynamical fracture in waterflood.

The key challenge in unconventional gas plays covering vast geographical areas is locating the regions in the reservoir with the highest combination of reservoir and completions quality. This allows operators to evaluate not only the richness of their resource but also the ability of the reservoir to produce hydrocarbons in commercial quantities. This paper discusses hydraulic fracturing designs targeting tight gas in horizontal wells drilled in the Apollonia tight chalk formation in the Abu-Gharadig basin, Western Desert, Egypt through the integration of laboratory, geological, petrophysical, geomechanical, fracture simulation, and diagnostic fracture injection test (DFIT) analysis. Laboratory testing, which included scanning electron microscopy (SEM) and X-ray diffraction (XRD), was conducted to determine mineralogy and potential damage mechanisms. Fracturing fluid chemistry was tested and optimized using core plugs from representative reservoir rock (fracture conductivity, fracturing fluid compatibility, surfactant type, fracture regain permeability, and scale tendency). Geomechanical rock properties derived from advanced petrophysical analysis of newly acquired high-definition triple-combo full-wave sonic logs and core samples were combined with geological parameters and potential treating schedules to develop sophisticated fracture simulation models. These models were then refined with in-situ reservoir data obtained from DFIT analyses to derive the final fracturing treatment design. The stimulation model was built using a three-dimensional (3D) geological model with multidisciplinary inputs, including formation properties, in-situ stresses, natural fractures, and completion parameters (i.e., well orientation, stage and perforation cluster spacing, fluid volume, viscosity, and proppant volume, size, and ramping schedule). The integration of all available data resulted in an optimized fracture design that helped reduce both cost and formation damage, thus improving flowback, long-term productivity, and profitability from this tight formation.

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