Simulation of Three-Dimensional Propagation of a Vertical Hydraulic Fracture

Thiercelin, M.J. (Dowell Schlumberger) | Ben-Naceur, K. (Dowell Schlumberger) | Lemanczyk, Z.R. (Dowell Schlumberger)



This paper describes a laboratory and numerical study of contained hydraulic fracture propagation via a preexisting stress gradient. This study was conducted in order to improve current knowledge of three-dimensional geometry. Laboratory tests were performed using prefractured polymethylmethacrylate (PMMA) beams prefractured polymethylmethacrylate (PMMA) beams which were subjected to a stress gradient in the minimum principal stress direction. The fracture propagation was studied as a function of fluid propagation was studied as a function of fluid rheology, flow rate and state of stress. The numerical approach consisted of a pseudo-three-dimensional model, developed to handle any type of boundary condition.

Results show that fracture-shape evolution is close to radial propagation at initiation, but becomes more and more contained as the length increases. A good prediction is achieved once the assumptions of the model are validated, i.e., once the fracture is sufficiently elongated.


The last four years have seen the development of numerous models for predicting the complete geometry of hydraulic fractures. They differ from previous classical models (e.g., Perkins and Kern, Khristianovich and Zheltov) in that they no longer require a constant fracture height to be imposed. This complete determination of the fracture shape allows prediction of containment on the basis of the fluid behavior, the pumping schedule, the fluid-loss to the formation, the in-situ state of stress and, in some of the models, the variation in mechanical properties in the boundary layers. properties in the boundary layers. These models are either pseudo-three-dimensional, or fully three-dimensional.

In general, assumptions are introduced to simplify the physics, making the problem tractable within a reasonable amount of computer time. Such assumptions have to be validated and their limits of application determined.

Field validations are certainly one important procedure; however, they suffer from several major procedure; however, they suffer from several major limitations, including the following.

Uncertainty in the knowledge and variability of the mechanical properties of the layers and the state of stress in the formation.

Behavioral complexity of some rock types which cannot be handled by current fracture propagation models (i.e., plasticity, major preexisting discontinuities).

Inadequate knowledge of the behavior of the fracturing fluid in the fracture.

Difficulty in measuring the evolution of the fracture geometry as a function of time (the only parameters recorded during a usual fracturing job being the rate, the density of the fluid and the pressure, often recorded at the wellhead).

In order to validate the principal assumptions of some of these models, laboratory experiments can be an important tool. Quantitative experiments on fracture propagation have been performed, but they only deal propagation have been performed, but they only deal with radial fracture propagation or constant height fractures. Until now, the only experiments on containment have been relatively qualitative.

A new experimental procedure has been developed, in order to quantitatively study the fully three-dimensional propagation. The experiment presented in this paper deals only with containment related to a gradient acting in the minimum principal stress direction, using a homogeneous impermeable sample. The model used for validation is quasi-three-dimensional and has the advantage over other existing models, of accommodating any type of stress distribution, as opposed to step functions.

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