Hydrodynamic simulation of horizontal wells by multi-stage hydraulic fracturing of a formation taking into account pressure losses due to streamline convergence
UDC: 622.276.66.001.57
DOI: 10.33285/0207-2351-2023-2(650)-26-28
Authors:
KOVALENKO IGOR V.
1
1 Gazpromneft, Scientific Technical Center, Saint Petersburg, Russia
Keywords: hydraulic fracture, streamline convergence, well, hydrodynamic modeling
Annotation:
Hydraulic fracturing of a formation is simulated by various techniques application in hydrodynamic simulators, the main of which are local grid refinement around the well with setting the properties of a hydraulic fracture in the central refined cell, or with setting a recalculation skin factor that increases the productivity factor of a virtual vertical well in a cell that is crossed by a fracture by the equivalent value.
Local grid refinement, being the most accurate solution, is not the most optimal way to simulate hydraulic fractures due to the fact that, firstly, the number of calculated cells increases significantly, and secondly, there occurs a significant difference in size between the cells. The speed of the entire calculation depends on the volume of the smallest cells, which significantly increases the time of calculations.
There are various additional methods to increase the speed of calculations, one of which is to reduce the accuracy when iteratively selecting a solution in a numerical scheme by setting the requirements for calculations using special keywords in the file with the initial data for the hydrodynamic simulator. On the one hand this technique brings speeding up of calculations, but on the other hand – to accuracy decrease.
There is another way – modeling a fracture with increased thickness to increase the size of the simulated cells, but with a reduced permeability by the same amount to maintain the dimensional conductivity of the hydraulic fracture. This method makes it possible to get away from extremely small sizes of the simulated cells in the hydrodynamic simulator while maintaining the acceptable accuracy of calculations. But this does not change the situation essentially.
Modeling using recalculated skin factor in the simulator cell is a more practical method for hydraulic fracture modeling. Firstly, a sufficiently high accuracy of calculations is preserved, and secondly, there is no need to model cells of a small dimension. This method is implemented in many software products and is widely used in hydrodynamic simulation of hydraulic fractures. This modeling method is legitimate due to the fact that the hydraulic fracture actually reduces the convergence of streamlines in the near-wellbore zone, which can also be described in the calculation cell using a negative skin factor.
The article considers the issues of modeling fractures of infinite and finite conductivity, longitudinal and transverse geometry, which causes the convergence of streamlines in the fracture.
Bibliography:
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2. Prats M. Effect of vertical fractures on reservoir behavior. Incompressible Fluid Case // SPE J. – 1961. – Vol. 1, Issue 2. – P. 105–118. – URL: http://doi.org/10.2118/1575-G
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