Abstract
In this paper, a semi-analytical solution of the pseudosteadystate
(PSS) productivity index under non-Darcy flow condition is
proposed. Based on the model, a new method of optimization of the
fracture conductivity has been developed for non-Darcy flow in the
fracture. Meanwhile, the effects of the Reynolds number, the proppant
number and the fracture conductivity on the dimensionless productivity
index have been discussed in detail.
Results show that: (1) the classic UFD (Unified Fracture Design) curves
of the Darcy-flow model underestimate the effect of the proppant number
and are unsuitable for the non-Darcy-flow fracture optimization. Our
discretized model provides a new tool to obtain the optimal fracture
parameters for the case of non-Darcy flow condition. (2) for a given
penetration ratio, the non-Darcy flow behavior exerts a strong influence
on the productivity index with the dimensionless fracture conductivity
CfD= 0.1 -1000 and a considerable productivity index drop can be
observed. For the extremely low (CfD<0.1) or high (CfD>1000)
dimensionless fracture conductivity, the effect of non-Darcy flow becomes
negligible. (3) the effect of the non-Darcy flow on the productivity
index becomes pronounced at large value of proppant number, Np. For a
given proppant number, the optimal fracture conductivity is slowly
increasing as the Reynolds number increases. However, the magnitude of
the effect on the productivity index is gradually declining. At the
Reynolds number less than 5, the non-Darcy flow has a relatively strong
impact on the productivity index and an apparent fall of the maximum
productivity index can be noticed, especially for a large proppant
number. Beyond the value of 5, the declining trend of the maximum
productivity index gradually slows down as the Reynolds number increases.
Original language | English |
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Pages (from-to) | 714-725 |
Number of pages | 12 |
Journal | Journal of Petroleum Science and Engineering |
Volume | 146 |
Early online date | 9 Jul 2016 |
DOIs | |
Publication status | Published - Oct 2016 |
Bibliographical note
This work was supported by the National Natural ScienceFoundation of China No. 51204148 and the Fundamental Research Funds for the
Central Universities
Keywords
- productivity index
- non-Darcy flow
- vertically fractured well
- optimization of the fracture parameters
- rectangular reservoir