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Comparison of analytical models for hydraulic fracture conductivity

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Abstract

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.

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Abbreviations

C :

the Carman–Kozeny constant, dimensionless

D 1 :

Proppant diameter, mm

D 2 :

core thickness, mm

E 1 :

Young’s modulus of the proppant, MPa

E 2 :

Young’s modulus of the rock, MPa

F RCD :

fracture conductivity, μm2 cm

f 1 :

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

f 2 :

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

h :

embedment depth, mm

H :

fracture height, m

k :

permeability, μm2

K :

distance coefficient, dimensionless

k n :

normal fracture stiffness, MPa/cm

L :

fracture length, m

N :

number of proppants in the model, dimensionless

n 1 :

number of proppants in each layer, dimensionless

n 2 :

number of proppant layers, dimensionless

p :

closure pressure, MPa

p max :

maximum contact pressure, MPa

R :

proppant radius, mm

r 0 :

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

R s1 :

proppant distance ratio, dimensionless

R s2 :

proppant distance ratio, dimensionless

w f :

fracture width, mm

w f0 :

initial fracture width, mm

ν 1 :

Poisson’s ratio of sphere 1, dimensionless

ν 2 :

Poisson’s ratio of sphere 2, dimensionless

η :

proppant crushing rate, dimensionless

β :

proppant deformation, mm

α:

change in fracture width, mm

σ n :

normal stress, MPa

τ :

degree of tortuosity, dimensionless

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Funding

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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Authors and Affiliations

  1. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, 610500, China

    Yuxuan Liu, Dilin Wen, Jianchun Guo & Jiandong Wang

  2. CNOOC China Limited, Zhanjiang Branch, Zhanjiang, 524057, China

    Xin Wu

  3. Sinopec Shengli Oilfield Company, Shengli, 257001, China

    Jiandong Wang

Authors
  1. Yuxuan Liu
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  2. Dilin Wen
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  3. Xin Wu
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  4. Jianchun Guo
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  5. Jiandong Wang
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Corresponding author

Correspondence to Yuxuan Liu.

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Editorial handling: Liang Xiao

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Cite this article

Liu, Y., Wen, D., Wu, X. et al. Comparison of analytical models for hydraulic fracture conductivity. Arab J Geosci 12, 479 (2019). https://doi.org/10.1007/s12517-019-4639-y

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