SEMI-ANALYTIC SOLUTION OF THE HORIZONTAL WELL INTERSETED BY MULTIPLE FINITE CONDUCTIVITY FRACTURES (original) (raw)
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Hydraulic fracturing is a stimulation treatment routinely performed on oil and gas wells in low-permeability reservoirs. However, simulating fractured wells is still challenging and impractical using local grid refinement in full-field models with a large number of wells each with multiple fractures. This paper describes a novel modeling technique by which hydraulic fractures are represented as part of the well model, rather than any form of refinement in the simulation grid. In this approach a planar fracture is modeled by the mesh formed from the interconnected branches of a multilateral, multisegment well. The main advantages are: 1) the fracture mesh is made independent of the simulation grid and thus model building is simpler; 2) fractures can be added and altered at any simulation time; 3) fractures can intersect the reservoir grid lines at any angle; 4) fracture geometry and properties can be fully honored. This technique is designed to model long-term pseudo-steady state fracture flows and uses Darcy flow equations in the lateral well branches that represent the fracture. The accuracy, stability, and practicality of this new technique have been investigated using a suite of simulation models ranging from a single well in a homogeneous reservoir to a real field sector model with numerous wells, each with multiple fractures. Where possible, the behavior of a reference model—built using traditional grid-refinement techniques—is compared against the multilateral, multisegment well model equivalent. The results of these experiments presented in this paper show a close agreement between the reference gridded fractures and the well model fractures when the system reaches a pseudo-steady state. They also show that the new approach suffers from a lesser degree of numerical instability when modeling extremely thin and highly conductive fractures. Finally, the results confirm the practicality and flexibility of this approach. Introduction The use of hydraulic fracturing for well stimulation is widespread in the industry. This treatment is particularly prevalent in oil shales and gas shales and tight formations in general, where virtually all production can be attributed to the practice of fracturing. It is also used in the context of tight oil reservoirs; for example, in deepwater scenarios where the costs of drilling and completion are very high and well productivity, which is dictated by hydraulic fractures, is vital. Hydraulic fracturing can dramatically change the flow dynamics of a reservoir, so its correct modeling in reservoir simulation can be critical. However, the presence of hydraulic fractures presents a challenge in flow simulation. This is because these fractures introduce effects that operate on different length and time scales than usual reservoir dynamics. To overcome this problem, a multitude of modeling techniques and workarounds has been developed. These include use of dual-porosity models, enhancement of the productivity index of the fractured wells (Zhang et al. 2012), virtual well perforations to simulate the fractures (Bogachev et al. 2011), and explicit fine-scale gridding. In full-field simulations, where an entire reservoir with complex geometry, multiple wells, and possibly faults is modeled, local grid refinement (LGR) is a popular methodology to represent hydraulic fractures. However, this approach introduces its own set of problems.
Environmental Earth Sciences, 2015
In this paper, numerical and semi-analytical investigations were conducted to understand the hydraulic fracturing operation in the tight gas reservoir only identified by the code A7 in the North German Basin. Two simulators, FLAC3D plus (numerical, full 3D model) and MFrac (semi-analytical, modified model based on the conventional pseudo-3D model), were used to model the fracturing operations including fracture propagation, proppant transport and settling. A comparison of the two simulators was carried out through simulations. Meanwhile, the function of the geological barrier integrity in A7 was also studied and confirmed. The simulations were based on the history matching of the in situ measured well head pressure. At the end of the simulation, a long fracture (length ) height) was modeled by both simulators. Although the results express some differences in the modeled fracture length and width (average), their results for fracture pressure, fluid leak off and proppant distribution are comparable. That means they would provide similar productivity in the later production. Investigation of the geological barrier integrity confirms that the cap rock, formed from rock salt and anhydrite, normally has higher minimum horizontal stress and lower permeability providing enough resistance to prevent the fracture from propagating in the vertical direction of the cap rocks. The case study reveals that, even when the injection volume was increased 10 times the initial volume, the integrity of the cap rocks could not be broken. Despite the presence of interbedded shale formations, in the reservoir as those of the cap rock an impediment function, if their thicknesses are too small to prevent their breakage and the injection volume too large for them to resist fracturing.