Quantifying Rock Capillary Strength Behavior in Unconsolidated Sandstones

Abstract Changes in water saturation or rock wettability can lead to rock instability and sand production. The effects of saturation on rock strength have two origins - chemical sensitivity and changes in capillary forces. In this paper, a detailed study of capillary rock strength behavior after water breakthrough is carried out for four different models. These four models account for particle-particle interactions and include spherical particles in tangential contact, differently sized spheres in tangential contact, squeezed contacts, and detached spheres. The effects of fluid properties (e.g. contact angle and surface tension), rock properties (e.g. particle size, size ratio, contact fabric), and deformation of loaded rock on capillary strength have been mathematically expressed and quantified. The model calculations indicate:For all the models, capillary strength increases linearly with increasing surface tension between fluid phases.Contact angle influences both the magnitude of capillary strength and its variation with saturation. The larger the contact angle, the lower the magnitude (under the same water saturation) and the faster its decrease with increasing saturation.If the particle size is uniform, small particle size results in high capillary strength. If particles have different sizes, the size ratio of the particles has a similar influence on capillary strength as does fluid contact angle: it affects both the magnitude of capillary strength and its variation with water saturation. However, the relationships are different: the smaller the size difference, the higher the magnitude and the slower its decrease with saturation.For the detached and squeezed models the capillary force (or strength) firstly increases with water saturation, then decreases after a critical saturation, in contrast to the tangential contact model where capillary force always decreases with water saturation.Through the introduction of the strain concept into the capillary models, they can be used to describe capillary strength variations with rock deformation. It is found that capillary strength more-or-less reaches a maximum when spheres are tangentially contacted, and decreases in both the squeezed and detached states, but decreasing much faster with increasing deformation in the squeezed state. These improvements in the micromechanical modeling of sands will be used to build our understanding of sand production in very weak or unconsolidated rocks, clarifying how sand production is affected by changes in saturation. Introduction Extensive experiments have been carried out to study the effect of water saturation (or moisture content, humidity, etc.) on the strength and elastic properties of shale1,2, chalk3,4,5, and sandstone1,6,7,8,9,10,11. In summary, those experiments found that:Strength reduction with increased saturation is generally found for all rock samples, with a strength reduction of from 8%6 to 98%7, depending on rock texture, mineralogy, fluid chemistry, etc.;Most of the strength decrease occurs after only a slight increase of water saturation (or moisture content) from the dry state6,7,12. Further increases in moisture content have little effect on rock strength and properties;The value of the friction coefficient appeared to remain unaltered in many cases1,11,13, but some researchers4,14 found it varies with water saturation (up to 10°4) if the rock surface chemically reacted with water, thus causing a change in the surface smoothness; and,Young's modulus decreases with water content increases, sharing the same trend as rock strength. Poisson's ratio may increase or decrease slightly before a general increase takes place6,15 at higher saturations.