Practical aspects of coupling a fracture-mechanical finite-element code to a reservoir simulator for hydraulic fracturing applications are discussed. Three essential components of the coupling are the stability control algorithm, the fracture permeability model, and the pressure corrector. Stability is controlled by specifying the minimum and maximum numbers of finite elements that are allowed to fail at each timestep. Trial runs with varied timesteps are performed in order to keep the number of failing elements within the prescribed range. The fracture permeability model links the permeability of failed finite elements to displacement discontinuities (rather than to effective stresses.) A pressure corrector is applied to maintain mass balance in the system. Failed elements in the fracturing code create new porosity that is exported to the flow code. If no pressure correction is applied, this effectively means that mass will be artificially produced in the model when fracturing starts. In order to correct for this, the density of the fluid in failed elements is adjusted to maintain the mass balance. This is achieved by introducing a correction to the fluid pressure in failed elements.


Depletion of easily producible hydrocarbon reservoirs calls for a steadily increasing share of low-permeability reservoirs in the global fuel portfolio. Such reservoirs include e.g. shale gas reserves and tight gas sands. Also extracting more oil from conventional reservoirs remains high on the agenda. These current challenges require that stimulation techniques used to increase well productivity in low-permeable and/or complex reservoirs be improved and optimized to ensure a stable production over long time.

Hydraulic fracturing is a widespread technique used for well stimulation in conventional and unconventional reservoirs [1]. A fluid, or a sequence of different fluids, is injected form a well into the formation in order to create a hydraulic fracture. With regard to the vertical extent of the hydraulic fracture, treatments are usually designed to contain the fracture within the productive zone and avoid its penetration into the under- and overburden. The fracture length should ensure an economical increase in the well productivity without e.g. jeopardizing the integrity of the neighboring wells. This turns design of a hydraulic fracturing treatment into an optimization exercise. It calls for robust and compute-efficient numerical models that can predict fracture growth in a mechanically and hydraulically heterogeneous, and often naturally fractured, rock.

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