Since the paper by Cleary and Fonesca in 1992, there have been several attempts to determine if convection is an important factor in proppant placement. Papers by Clark and Courington, Clark and Zhu, and Barree and Conway have provided important clues, but the primary question remains unanswered. To address these questions, we have returned to the question of scaling in models. As mentioned in JPT paper (March 1995) by Clark and Zhu, scaling in a slot-flow model is difficult because each of the possible scaling factors (Reynolds number, velocity, shear rate and pressure drop) have a different dependence on width. Because of this, our initial laboratory model was scaled on shear rate and therefore flowing viscosity. Further examination of the problem lead us to believe that the ratio of the forces available to push the fluid in the horizontal and vertical directions is extremely important in determining whether or not convection is observed. This paper will discuss the development of two dimensionless groups that can be used to predict convection and the experimental evidence that validate these dimensionless group.
Hydraulic fracturing is used as a primary stimulation technique for oil and gas wells. During a fracturing treatment, fluids are pumped under pressure through perforations in the pipe and into the formation. At some point the formation fails and the resulting crack is usually vertical and normally propagates away from the wellbore as two cracks 180 apart. A propping agent, such as sand, is pumped with the fluid to hold the crack open after the fracturing treatment is completed. When discussing fractures, the literature usually only deals with one wing of the fracture. A schematic of one wing of a fracture is shown in Figure (1).
Often the fracture is higher than the producing interval. When the fracture height is much higher than the perforated interval (see Figure (1)), the flow into the fracture can be classified as flow into a slot from a point source. In 1992, Cleary and Fonseca postulated that, in point-source fractures, gravity driven motion of the slurry, which they termed convection, will dominate Stokes type settling in the placement of the propping agent (Figure (2)). This is important because the placement of proppant within the productive interval determines, in part, the amount of production increase.
Unfortunately, while the speculation by Cleary and Fonseca was not supported by creditable experimental evidence, it was accepted almost without question by the industry. Since the concept of convection was proposed by Cleary and Fonseca, there have been a number of papers published on the subject. Clark and Courington published some initial results from a small slot-flow model. This work was followed by a more extensive study by Clark an Zhu and Barree and Conway.