A student is presented with a J-function curve for a collection of core samples
ID: 115377 • Letter: A
Question
A student is presented with a J-function curve for a collection of core samples taken from a single formation. The student is asked to measure the capillary pressure of a core from a similar formation with slightly lower porosity and permeability. To do so, he must first estimate the expected-measured capillary pressure to adequately design his measurement procedure. Produce the expected capillary pressure vs. water saturation curve for the new core from the J-function presented below, given the new core has a porosity of 0.27, an absolute permeability 0.500 md, and the fluid system to be utilized is water-oil with an IFT of 50 mN/m and a contact angle through water of 35o.
PNG 405: Rock & Fluid Properties Fall 2017 HOMEWORK ASSIGNMENT No. 6 Due Oct 19 1. A student is presented with a J-function curve for a collection of core samples taken from a single formation. The student is asked to measure the capillary pressure of a core from a similar formation with slightly lower porosity and permeability. To do so, he must first estimate the expected-measured capillary pressure to adequately design his measurement procedure. Produce the expected capillary pressure vs. water saturation curve for the new core from the J-function presented below, given the new core has a porosity of 0.27, an absolute permeability 0.500 md, and the fluid system to be utilized is water-oil with an IFT of 50 mN/m and a contact angle through water of 35° 0.2 0.4 0.6 0.8 Water SaturationExplanation / Answer
Leverett J-Function Capillary pressure data are obtained on small core samples that represent an extremely small part of the reservoir and, therefore, it is necessary to combine all capillary data to classify a particular reservoir. The fact that the capillary pressure-saturation curves of nearly all naturally porous materials have many features in common has led to attempts to devise some general equation describing all such curves. Leverett (1941) approached the problem from the standpoint of dimensional analysis. Realizing that capillary pressure should depend on the porosity, interfacial tension, and mean pore radius, Leverett defined the dimensionless function of saturation, which he called the J-function, as where J(Sw) = Leverett J-function pc = capillary pressure, psi s = interfacial tension, dynes/cm k = permeability, md f = fractional porosity In doing so, Leverett interpreted the ratio of permeability, k, to porosity, f, as being proportional to the square of a mean pore radius. The J-function was originally proposed as a means of converting all capillary-pressure data to a universal curve. There are significant differences in correlation of the J-function with water saturation from formation to formation, so that no universal curve can be obtained. For the same formation, however, this dimensionless capillary-pressure function serves quite well in many cases to remove discrepancies in the pc versus Sw curves and reduce them to a common curve.
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