Comparison of analytical models for hydraulic fracture conductivity

  • Yuxuan LiuEmail author
  • Dilin Wen
  • Xin Wu
  • Jianchun Guo
  • Jiandong Wang
Original Paper


The purpose of hydraulic fracturing is to establish a highway for oil and gas transportation, and the fracture conductivity reflects the highway’s transport capacity. Scholars have proposed several methods for calculating the conductivity, including both numerical and analytical methods. The analytical methods have received widespread attention as their calculation processes are simple and easy to use. However, the differences between the analytical models and between the models and experimental results are not clear, which prevents the selection of the optimal model. Therefore, this study compared these differences. In this study, comparative analysis was conducted for four analytical models from four aspects, including the factors considered by the models, input parameters, model calculation results, and the differences between the models and the experimental results. By conducting this comparison, there are some differences between the factors, input parameters, and calculation results of the four models. There are also some differences between the predicted values of the models and the experimental results. For practical application, the model must be corrected by fitting the test data. The current model does not fully reflect the interaction mechanism between a proppant and a rock. It is recommended that further research on analytical modeling is conducted.


Fracture conductivity Hydraulic fracturing Model Comparison 



the Carman–Kozeny constant, dimensionless


Proppant diameter, mm


core thickness, mm


Young’s modulus of the proppant, MPa


Young’s modulus of the rock, MPa


fracture conductivity, μm2 cm


function related to the closure pressure, Young’s modulus, and Poisson’s ratio of proppant, dimensionless


function related to the closure pressure, elastic moduli, and Poisson’s ratios of proppant and rock, dimensionless


embedment depth, mm


fracture height, m


permeability, μm2


distance coefficient, dimensionless


normal fracture stiffness, MPa/cm


fracture length, m


number of proppants in the model, dimensionless


number of proppants in each layer, dimensionless


number of proppant layers, dimensionless


closure pressure, MPa


maximum contact pressure, MPa


proppant radius, mm


radius of pore throat when the closure pressure is equal to zero, μm


proppant distance ratio, dimensionless


proppant distance ratio, dimensionless


fracture width, mm


initial fracture width, mm


Poisson’s ratio of sphere 1, dimensionless


Poisson’s ratio of sphere 2, dimensionless


proppant crushing rate, dimensionless


proppant deformation, mm


change in fracture width, mm


normal stress, MPa


degree of tortuosity, dimensionless


Funding information

This study received financial support from the National Natural Science Foundation of China (No. 51804266; No. 51525404; No. 51874250), the Young Scholars Development Fund of SWPU (201599010084), and the National Science and Technology Major Project (No. 2016ZX05002-002).


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Copyright information

© Saudi Society for Geosciences 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Oil and Gas Reservoir Geology and ExploitationSouthwest Petroleum UniversityChengduChina
  2. 2.CNOOC China LimitedZhanjiangChina
  3. 3.Sinopec Shengli Oilfield CompanyShengliChina

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