# Coupled Numerical Method for Modeling Propped Fracture Behavior
###### Abstract  
Hydraulic fracturing is a well-known production intensification technique in the petroleum industry that aims to enhance the productivity of a well drilled mostly in less permeable reservoirs. The process's effectiveness depends on the achieved fracture conductivity, the product of fracture width, and the permeability of the proppant pack placed within the fracture. This article presents an innovative method developed by our research activity that incorporates the benefit of the Discrete--and Finite Element Method to describe the in situ behavior of hydraulic fractures with a particular emphasis on fracture conductivity. DEM (Discrete Element Method) provided the application of random particle generation and non-uniform proppant placement. We also used FEM (Finite Element Method) Static Structural module to simulate the elastic behavior of solid materials: proppant and formation, while CFD (Computational Fluid Dynamics) module was applied to represent fluid dynamics within the propped fracture. The results of our numerical model were compared to data of API RP-19D and API RP-61 laboratory measurements and findings gained by publishers dealing with propped fracture conductivity. The match of the outcomes verified the method and encouraged us to describe proppant deformation and embedment and their effect as precisely as possible. Based on the results, we performed sensitivity analysis which pointed out the impact of several factors affecting proppant embedment, deformation, and fracture conductivity and let one be aware of a reasonable interpretation of proppped hydraulic fracture operation. However, DEM-CFD coupled models were introduced regarding fracturing before, to the best of our knowledge, the developed workflow of coupling DEM-FEM-CFD for modeling proppant-supported fracture behavior has not been applied yet, thus arising new perspectives for explorers and engineers. hydraulic fracturing; proppant; embedment; deformation +
Footnote †: journal: Applied Sci. 0000-0001-99681-9999/0000-0000-0000-0000-00000-00000-00000-00000-00000-00000-000000-00000-00000-000000-00000-00000-000000-000000-00000-000000-000000-0  
high porosity, is mixed with the fracturing fluid to prop the fracture and prevent formation closure that would result in an ineffective stimulation [3]. The phenomenon investigated in this research occurs after fractures are created, and hydraulic pumps are stopped entailing the hydraulic fluid pressure to drop below the formation closure pressure. At this point, there is no more extra pressure energy to hold the fractures open, which leads to a closing action of the formation, which is prevented by proppant particles that carry the stresses of formation closure [4]. The primary indicator, which characterizes the fracturing treatment, is the fracture conductivity calculated as the product of fracture width and proppant pack permeability. Since the above-described situation affects fracture conductivity significantly, it is crucial to model the problem comprehensively. Several earlier studies deal with proppant embedment; [PERSON] and [PERSON] [5] derived an equation based on the knowledge of proppant concentration and overburden load to compute proppant embedment. It is a semi-empirical model containing two characteristic constants, which could be determined by fitting the results with experimental data. They performed relevant experiments to prove the capability of this equation, and they found that proppant embedment is a more relevant phenomenon than proppant crush under formation pressure. The factors affecting proppant embedment were determined by the formation's competency, the proppant's size, the concentration of the proppant, and the overburden pressure. They concluded that a stiffer, tougher material would be a better propping agent than sand because sand would crush rather than embed under the overburden pressure. [PERSON] et al.