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Starting with a subexcitable net of FitzHugh-Nagumo elements it is shown that parameter variability (diversity) is able to induce pattern formation. These patterns are most coherent for an intermediate variability strength. This effect is similar to the well-known spatiotemporal stochastic resonance generated by additive noise in subexcitable media. Furthermore, variability is able to induce a transition to an excitable behavior of the net. This transition strongly depends on the coupling strength between the elements and it is found only for strong coupling. For weaker coupling one observes a lifetime lengthening of waves propagating through the medium, but the net stays subexcitable.

Erosion of sand control screens in oil and gas wells can lead to catastrophic completion failures, substantial production losses and damage to downstream facilities. Screen erosion can be caused by a number of completion design and environmental factors. However, the dominant failure mechanism is production of small solids through the screen openings, leading to development of localized high-velocity hot spots in the screen filter media and subsequent failure of the media. The current work discusses a detailed screen erosion study conducted to evaluate screen flow parameters leading to erosion and to provide safe operating guidelines for wells completed using cased hole perforated frac-pack (CHFP) and cased hole perforated gravel-packed (CHGP) completions with premium wire-mesh sand control screens. The erosion study consisted of both experimental work to determine erosion damage in screen samples and computational fluid dynamic (CFD) simulations to help visualize particle flow paths through the metal-mesh sand control media and determine local flow velocities and erosion-induced wear patterns. The experimental erosion tests and CFD modeling were performed on a specific screen configuration used in a number of subsea gas wells subject to high velocity flow conditions and associated high screen erosion potential. An empirical erosion model was then developed to translate short-term, high-velocity laboratory test results into field erosion predictions and well flow guidelines to minimize erosion potential. This paper presents results of the experimental work and associated CFD modeling as well as completion flow guidelines developed for field operation of subsea gas wells.

The influence of variability on the response of a net of bistable FitzHugh-Nagumo elements to a weak signal is investigated. The response of the net undergoes a resonancelike behavior due to additive variability. For an intermediate strength of additive variability the external signal is optimally enhanced in the output of the net (diversity-induced resonance). Furthermore, we show that additive noise strongly influences the diversity-induced resonance. Afterwards the interplay of additive and multiplicative variability on the response of the net is investigated. Starting with asymmetric bistable elements the enhancement of the signal is not very pronounced in the presence of additive variability. Via symmetry restoration by multiplicative variability the resonance is further enhanced. We call this phenomenon doubly diversity-induced resonance, because the interplay of both, additive and multiplicative variability, is essential to achieve the optimal enhancement of the signal. The restoration of symmetry can be explained by a systematic effect of the multiplicative variability, which changes the thresholds for the transitions between the two stable fixed points. We investigate the response to variability for globally and diffusively coupled networks and in dependency on the coupling strength.