# Coupled Numerical Method for Modeling Propped Fracture Behavior
## 4 Discussion  
Hydraulic fracturing treatment is used to enhance well productivity, usually drilled in tight or less permeable reservoirs by forming high-conductive channels between the formation and the wellbore. The closure pressure after fracturing indicates a closing action that is prevented by proppant particles placed between the fracture walls and which are bearing a complex stress condition. Even if proppants are enormously strong and the strength of the hydrocarbon-bearing layer is quite high, proppant deformation and embedment take place and may result in a significant reduction of the created fracture conductivity, particularly under high closure pressure circumstances. In this paper, a brand-new method was developed to model in-situ fracture behavior by coupling DEM-FEM-CFD numerical solutions. DEM was applied to generate and randomly place proppants into the fracture; meanwhile, FEM Static Structural module was used to let the proppants be deformed and embedded into the formation, and finally, Computational Fluid Dynamics application was coupled to investigate the permeability and conductivity of the propped fractures. To the best of our knowledge, this research marks the workflow of coupling DEM-FEM-CFD for propped fracture behavior modeling the first time. This research showed that achievable fracture conductivity increases with the increase of proppant size and formation stiffness; however, it decreases with the increment of fracture-aperture-closing stress. Of course, these trends fit the results published by many researchers before, but the absolute value of the simulation results pointed out new perspectives of fracture behavior modeling. As many real factors--such as fracture geometry, uneven proppant and so stress distribution, proppant deformation and embedment, and industrial flow rate--have been integrated in our model, lower conductivity values could be observed, which fact allows one to consider this developed workflow as a more sophisticated approximation of the real phenomenon. Meanwhile, these results also confirm the conclusions drawn by [PERSON] et al. (2019), i.e., proppant conductivity measuring standards may result in overestimated conductivity values compared to achievable ones in the underground. This current work also highlighted some future perspectives in the direction of how to describe the phenomenon more precisely. Following the way of our previous work, the implementation of non-perfect spheres as proppants may make another breakthrough. Figure 19 represents our electron microscopic examination of proppants and DEM clumps approximating proppant particle geometry which is usually characterized by sphericity and roundness indices. Another potential is to consider proppant size distribution and generate proppants with different diameters according to their mesh size and sieve analysis that may result in further conductivity reduction. Figure 18: Fracture conductivity for different formation Young’s modulus. This paper demonstrated the capability of DEM-FEM-CFD coupling for modeling multidisciplinary processes regarding hydraulic fracturing and provided insight into the factors that drive the comprehensive interactions between proppant particles, formation stiffness, and closure pressure. The outcome of this research may advance the fundamental understanding of proppant embedment and deformation and contribute to a broad scale of applied sciences that aim to optimize hydraulic fracturing. Conceptualization, T.L. and A.V. ; methodology, T.L. and A.V. ; software, A.V. and F.S. ; validation, T.L. and A.V. ; formal analysis, T.L. and A.V. investigation, T.L. and A.V. ; resources, T.L. and A.V. ; data curation, T.L. ; writing--original draft preparation, T.L. and A.V. ; writing--review and editing, T.L. and A.V. ; visualization, T.L., A.V., and F.S. ; supervision, T.L. ; project administration, T.L. ; funding acquisition, A.J. All authors have read and agreed to the published version of the manuscript.