The falling ball viscometer method was used to measure the viscosity of bitumen and sand mixtures. The viscosity of the slurry was measured over a range of concentrations, but with emphasis on higher concentrations, a regime which is believed to be representative of sand concentration in wormholes during cold production of heavy oil. Non-Newtonian behavior was observed at very high sand concentration.


In developing cold production technology, it is essential to understand the flow behavior of slurries, suspensions of sand grains in bitumen and water, and their geo-mechanical behavior near the transition towards sand. The objective of these experiments is to elucidate the subject by studying the slurry viscosity as a function of porosity. Shear viscosity of a fluid, as a measure of the rate of dissipative transverse momentum transfer due to shear (see, for example, Landau, et al, 1987), is known to be increased by increasing concentration of sand suspensions in the fluid. At very low concentration, the relative viscosity, defined as the ratio of the mixture to the fluid viscosity, increases linearly with concentration (Einstein, 1906, 1911). At higher concentration, the relative viscosity increases further and nonlinearly due to stronger hydrodynamic interactions between sand grains. At even higher concentrations, direct grain-grain contacts become much more frequent, and hence the transverse momentum transfer becomes much easier. In addition, collision induced grain rotations become more frequent, so that a larger amount of linear momentum is transferred to angular momentum of sand grains, leading to higher viscosity and non-Newtonian behavior at high shear (Krieger, et al, 1959). In this regime the sand grains are in discontinuous contact with one another and we expect a sharper increase in relative viscosity for small decreases in porosity. The upper boundary to this regime corresponds to the transition from a slurry to a saturated sand. At the boundary between these two regimes, the contacts are continuous and a sand grain matrix exists. This concentration corresponds to the "maximum porosity" of the sand grains, which for many sands is typically about 0.45.

For saturated sand there exists a narrow range of concentrations (porosities) within which fluid behavior may be observed. This can occur at porosities between the "maximum porosity" and the "critical porosity" when shear stresses are applied rapidly to the sand. As the matrix collapses, pore pressures are increased and effective stresses are decreased. If the mobility of the pore fluid is sufficiently low, the effective stresses can be reduced to zero and the sand loses all frictional strength and behaves as a fluid. This behavior is often referred to as "liquefaction." Figure 1 depicts the concept for a sand suspension. The borders separating these regimes are not necessarily narrow.

Many experimental, theoretical and numerical works for hard sphere suspensions have been conducted at relatively high porosities (Mooney, et al, 1951; Jeffrey, et al, 1976; Vocadlo, 1976; Shook, et al, 1976; Brady, et al, 1985; Ladd, 1990). However, very few experimental and theoretical works have been done at lower porosities, especially near the "maximum porosity."

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