Non-Newtonian fluids are common in drilling and oil production. Examples include drilling fluids, heavy oils and fluids used in hydraulic fracturing. A review of the state of the art indicates that our current knowledge of non-Newtonian fluid flow in rough-walled fractures is fragmented, and many assumptions used in numerical simulations are not properly justified. This is unlike Newtonian fluid flow in fractures where a considerable progress has been made over the last 30 years. Open questions and topics that need further investigation are identified based on the review.


A Newtonian fluid is a fluid in which the shear stress is directly proportional to the shear rate. A non-Newtonian fluid is a fluid in which such proportionality does not exist (Figure 1). For instance, in a yield stress fluid, there is a threshold shear stress called yield stress. As the shear stress remains below the threshold, the fluid behaves like a solid material. When the shear stress exceeds the yield stress, the fluid behaves like a liquid. Even when there is no yield point, i.e. the yield stress is zero, a fluid can exhibit non-Newtonian behavior if the shear stress is a nonlinear function of the shear rate. Examples are provided by power-law fluids, with the shear stress given by some power function of the shear rate.

Many fluids used in petroleum industry exhibit non-Newtonian behavior. For instance, drilling fluids are usually designed so as to have a yield point in order to prevent cuttings from settling when circulation stops. Above the yield point, the rheological behavior of the drilling fluid can be quite complex, with the shear stress being a nonlinear function of the shear rate (Majidi et al. 2010). When the non-linearity above the yield stress can be neglected, the drilling fluid rheology can be represented as a Bingham fluid, with the shear stress being a linear function of the shear rate above the yield point (Lavrov 2006).

If a natural fracture network is hit during drilling, the drilling fluid may escape into fractures, and special measures need to be taken in order to prevent the loss of the drilling fluid. Understanding the behavior of the yield stress fluid as it enters a natural rough-walled fracture is crucial for designing the additives used to stop the fluid loss.

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