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I'm trying to calculate the amount of fluid that would flow through an area dependant on the amount of pressure that there is. I'd also like to know the rate at which it would flow.

Essentially I have a very basic model of a well drilling system. At the moment the variables / parameters for each of the objects in question are defined by the user but may be set to constants to enable testing.

The assumptions I'm working on are:

The viscosity of the oil / hydrocarbons is set to constant. Once drilled the area of the hole will not change (there will be no collapse etc). The well is never ending so constant pressure.

If someone could point me in the right direction I'd be very thankful. Some of the assumptions may be way off so guidance in general is also appreciated, many thanks.

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    $\begingroup$ Have you considered assuming poiseuille flow as a first approximation? $\endgroup$ – Michiel Jan 13 '14 at 12:57
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I must write at least 30 characters to post, so this should cover it. What I believe you are looking for is Darcy's Law - http://infohost.nmt.edu/~petro/faculty/Engler524/PET524-5-fluidflow.pdf

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    $\begingroup$ The reason for the character limit is that we generally do not like "link-only" answers. The link can die and invalidate the answer. Also, I don't see why Darcy's law is relevant here, you will have to explain that. $\endgroup$ – Bernhard Jun 22 '14 at 8:18
  • $\begingroup$ @Bernhard Permeability is a measure of the ability of a porous media to transmit fluids. It is a critical property in defining the flow capacity of a rock sample. The unit of measurement is the darcy. Darcy’s Law is applicable for steady state, laminar flow of an incompressible fluid, for a homogeneous and isotropic porous media. Darcy's Law is an empirical expression of the relationships among the variables involved in the flow of fluids through porous media. Darcy’s Law is a limiting case, restricted to low volumetric fluxes. The law can be integrated to fit wellbore geometery, OP's question $\endgroup$ – Armadillo Jun 23 '14 at 16:40
  • $\begingroup$ I know what Darcy's law is, I only don't see why it is relevant here, and also with your explanation I don't see it. $\endgroup$ – Bernhard Jun 23 '14 at 18:08
  • $\begingroup$ @Bernhard OP "would like to calculate the amount of fluid that would flow through an area (open hole completion) dependant on the amount of pressure that there is". Darcy's law would provide him the flow rate based on his inputs of differential pressure, permeability, viscosity, drainage radius, wellbore geometry, formation geometry, and formation volume factor. Knowing Darcy's law, what do you find wrong with its use in petroleum engineering and estimation of flow rate? What do you suggest OP use for his estimation? $\endgroup$ – Armadillo Jun 23 '14 at 19:24
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    $\begingroup$ I only saw the date of the post only after I commented, but I am just trying to trigger you to add some more explanations. I don't think the OP will ever visit again... $\endgroup$ – Bernhard Jun 23 '14 at 20:36

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