# An Elrod–Adams-model-based method to account for the fluid lag in hydraulic fracturing in 2D and 3D

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## Abstract

An efficient method to model the fluid lag in hydraulic fracturing has been developed based on the Elrod–Adams model. The main feature of this method is the absence of the need to explicitly track the free end of the fracturing fluid, but rather, the fluid front is obtained by solving the pressure field (zero for the lag) and an auxiliary field for the entire fracture. An important advantage of this method is that no change of formulation, and hence no contact detection, is needed when the fluid reaches the fracture tip. Moreover, the method works for both the injection phase and the liquid withdrawal phase. Based on the latter case studies can be developed to investigate the quantity of the remaining fluid after the fracturing process in order to assess the environmental impact of fracturing. The method applies to both 2D and 3D problems.

## Keywords

Hydraulic fracturing Elrod–Adams model Fluid lag Lubrication equation## Notes

### Acknowledgements

The authors would like to acknowledge the helpful discussion with Gustavo Buscaglia from University of São Paulo. This work is supported by the National Natural Science Foundation of China with Grant No. 11402146. YS also acknowledges the financial support by the Young 1000 Talent Program of China.

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