Effect of Dynamic Fracture Conductivity during Production
Authors: Jia Xinli , Zhang Feifei , Filippov Andrey 
Published: April 2016

Abstract
Hydraulic fracturing has been successfully employed for unconventional oil and gas recovery for decades. The fracturing process is realized by injecting fluid, which contains the proppant materials used to keep the fracture open and productive, into a well at a high enough rate and pressure to crack open the formation.
Hydraulic fracture-stimulated production plays an important role in unconventional hydrocarbon production. The distribution and transport of proppant significantly affect fracture conductivity and, in turn, the production rate and decline. It is widely recognized that the effective placement of proppant in a fracture has a dominant effect on a well's productivity, yet it is greatly underestimated owing to a lack of knowledge and practical means to deal with the transient proppant settling process inside the fracture. Existing hydraulic fracture models mostly simplify the proppant transport process or even totally neglect the effect. A common assumption is that the average proppant velocity is equal to the average carrier fluid velocity, and the settling velocity is calculated using Stokes' law, while some important forces exerting on proppant particles are not taken into account, which often leads to the overprediction of the effective fracture length by up to 300%. To effectively simulate the dynamic proppant settling inside the fracture requires the consideration of such factors, including the wall-effect lift force, drag, and leakage of the fluid into the formation.
A numerical model has been developed to predict the transient transport and settling of proppants during hydraulic fracturing treatments and production to improve fracture conductivity.
The model presented in this paper includes three stages. The initial stage simulates the homogenous phase behavior with a previously developed fracture injection and production model (FIPM) developed elsewhere. The FIPM can alternate between injection and production modes, with gas, oil, and water phases included, and gas-oil phase transition allowed. Therefore, leakoff and production into the formation are simulated based on the pressure and phase saturation fields, with gravitational, drag, and lift forces taken into account. During the final stage, a fracture-stimulated horizontal well in the Eagle Ford is used to validate the model, both for injection-induced water damage and production.
During the initial proppant injection stage, the distribution of proppants can be considered to be homogenously dispersed in the injection fluid. Shortly after the injection started, because of geothermal effects, leakoff of injection fluid, and gravity, the proppant particles will settle, and the initial fracture conductivity profile is formed during this stage. This conductivity profile has a significant effect on the early-stage production rate. As production continues, the proppant particles will be shifted dynamically and will result in a change in the effective fracture length, width, and conductivity distribution over time.
During the second stage, the leakoff and evaporation of the liquid phase is simulated as flow through porous media, taking the thermal gradient and evaporation latent heat into consideration. The settling and transport of transient solid proppant particles are modeled using the upstream scheme, accounting for the forces of gravity, drag, and wall-lift forces on the particles. Both injection and leakoff of fluids help determine the size and conductivity of fractures, as well as the water-envelope damage in the near-fracture region inside the formation. These can significantly impact the transient depletion of the reservoir, particularly during early production time. This effect is studied in terms of reservoir permeability, production rate, and phase distribution.