Hey dear researchers,
Am seeking some resources (no matter what kind e.g. thesis, book, article, and so on) explaining clearly equations governing the fluid flow in fractured reservoirs. I have so far found some, but they are sadly incomplete. I was wondering if one can help me in this way.
Thanks a lot in advance.
I would also recommend to read the SPE papers by Chang and Yortsos, Acuña and Yortsos, Flamenco and Camacho, and the papers:
- Pressure Transient and Decline Curve Behavior in Naturally Fractured Vuggy Carbonate Reservoir, SPE Reservoir Evaluation & Engineering, 2005
- Decline-Curve Analysis of Fractured Reservoirs With Fractal Geometry, SPE Reservoir Evaluation & Engineering, 2008
You may read this reference:
https://www.amazon.com/Fluid-Flow-Fractured-Porous-Media/dp/3039214233
I am going to simultaneously employ the multiscale finite element method and machine learning for modeling the fluid flow in a porous medium with matrix (high porosity and low permeability) and fracture (low porosity and high permeability). As mentioned above, we can model fractures in different ways, such as dual porosity (continuum), dual permeability (continuum) and DFN (discrete). As I want to use finite element (not finite difference nor finite volume), do you think which method is better?
Thanks a lot
Do you mean I have to apply continuum and discrete models separately and in the following compare those with the analytical method?
Thank you.
You can take a look at:
- Fluid Flow in Fractured Porous Media (2019), de Richeng Liu (Editor), Yujing Jiang (Editor), ISBN-13 : 978-3039214235
https://www.amazon.com/Fluid-Flow-Fractured-Porous-Media/dp/3039214233
Also:
- Characterization of naturally fractured reservoirs. SPE 69538. VII Latin American and Caribbean Petroleum Engineering Confrence, Buenos Aires, Argentina, March 25-28, 2001.
https://www.researchgate.net/publication/259802422_Characterization_of_naturally_fractured_reservoirs
- Methodology for permeability tensor determination in naturally fractured reservoirs. 8th European Conference on the Mathematics of the Oil Recovery Proceedings, ISBN 90-73781-24-8, Freiberg, Germany, September 3-6, 2002.
http://dx.doi.org/10.13140/RG.2.1.5054.0968
The Porous Media Group (https://pmg.w.uib.no/) has several works for fluid flow fracture in porous media (https://pmg.w.uib.no/publications/) They also created an open-source framework in python called porepy specialized in that (https://github.com/pmgbergen/porepy). I didn't work with a fracture but one the most relevant paper I'm aware of they have is this one. Article Benchmarks for single-phase flow in fractured porous media
Due to the anisotropic shape, fractures are often incorporated in the mathematical models as lower dimensional objects. Several pertinent suggestions in this sense have already been made above. One question is which model to choose in the reduced-dimensional fracture, and there is no unique answer to this. In fact, the choice of the model depends on how the porosity or permeability ratios (in the fracture and the adjacent blocks) scale with the aspect ratio of the fracture before being reduced to a lower dimensional object. In some situations, one only adds a source term to account for the normal flux over the fracture-matrix interface, but the fracture model remains essentially the same. In other cases, the model becomes an ODE, or you may even have the fracture as an impermeable object.
Related to this topic you can read the following 2 papers:
* Characterization of naturally fractured reservoirs SPE 69538 Article Characterization of naturally fractured reservoirs
* Methodology for permeability tensor determination in naturally fractured reservoirs DOI: 10.13140/RG.2.1.5054.0968 Conference Paper Methodology for permeability tensor determination in natural...
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