# Coupled Numerical Method for Modeling Propped Fracture Behavior
###### Abstract
[6] derived empirical equations based on experimental data to determine the parameters influencing proppant embedment, such as proppant concentration, size, distribution, rock type, etc. [PERSON] et al. [7] carried out experimental research on proppant embedment in non-tight reservoir cores; therefore, the results can be interpreted as limited ones. Nevertheless, the results showed that the most critical factors that have a relevant impact on proppant embedment were closure pressure, proppant size, and fluid properties. Therefore, [PERSON] et al. [8] also developed a computer-controlled measurement that determined proppered-fracture width and proppant embedment as a function of closure pressure, the concentration of proppant paving, proppant size, core mechanical characteristics, etc. [PERSON] and [PERSON] [9] investigated the proppant embedment in core samples experimentally. They also found that the fracture width could be remarkably reduced because of the proppant embedment, especially in soft formations. They examined the experimental data of proppant embedment at different conditions, and they published empirical equations that can determine the proppant embedment as a function of formation pressure, the elastic modulus of the core, and proppant concentration. Further experimental studies of proppant embedment and fracture conductivity were published by many researchers [10; 11; 12; 13; 14]. However, these empirical or semi-empirical solutions could provide interpretations in limited conditions. Others [15; 16; 17; 18] also conducted experimental research about fracture conductivity. However, the exactness of these developed models considering the prediction of in situ fracture behavior may not be satisfactory due to the artificial conditions from which they have been derived. The lack of a comprehensive analytical model was fulfilled by [PERSON] et al. [19], who developed an analytical approach based on the Hertzian Contact Theory to investigate the effect of proppant deformation and embedment on fracture conductivity. Their research was derived from two mutually squeezed spheres and considered only mathematical and physical principles; therefore, it was found to be a valuable method to gain information about conductivity influencing factors. Their approach could provide results for proppant embedment, change in fracture aperture, deformation, permeability, and conductivity for single- and multi-layer patterns. Furthermore, their equations are completely analytical, resulting in an elegant solution for fracture behavior modeling. However, it also has limitation because some random factors, like non-regular proppant shape, uneven proppantplacement, uneven stress distribution, and complicated fracture geometry, cannot be described analytically. After all, it can be stated that the detailed description of a propped fracture behavior requires a numerical solution due to the random character of the phenomenon. Therefore, a few numerical approaches have already been developed. For example, [PERSON] et al. [20] investigated the impact of high-quality prop proposed fracture but also to include the effect of proppant deformation. Our pursuit was to develop a coupled numerical model to describe the hydraulic fracture behavior under the in-situ condition as precisely as possible. Finally, we invented a complex workflow that simulates random and uneven proppant placement, the closing action of the formation considering the rock and proppant as elastic bodies, and involves fluid dynamics at typical fractured well flow rates. Sensitivity test results were matched with published data, and the correctness of the method was verified. The findings of underground achievable fracture conductivity, which is much less than expected from proppant technical datasheets, showed the potential of DEM-FEM-CFD coupling for modeling multidisciplinary processes in respect of hydraulic fracturing.