Homework_Assignment_2_Solution

Homework_Assignment_2_Solution - Homework Assignment No. 2...

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Homework Assignment No. 2 January 30, 2010 Due on Thursday, February 4, 2010 @ 2:00 PM PGE368 (Unique No. 19290) Spring Semester 2010 Fundamentals of Well Logging Instructor: Carlos T. Verdín, Ph.D. THE PROCESS OF MUD-FILTRATE INVASION DESCRIPTION: The objective of this homework is to exercise the concept of mud-filtrate invasion by integrating knowledge of petrophysical properties of rocks with fluid flow in porous media. SOLUTION SET
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THE FOLLOWING QUESTIONS ARE INTENDED AS EXAMPLES OF CONCEPTUAL EXAM QUESTIONS. THERE IS NO NEED TO ANSWER THEM! 1. Explain why capillary pressure has an impact on the shape (smoothness) of the radial distribution of fluid saturation after invasion. Assume the case of water-base mud invading an oil- saturated, porous and permeable sand. Answer: When the process of invasion involves the relative displacement of two immiscible fluids (wetting and non-wetting fluid phases) in porous media, there is a force that opposes fluid displacement along throats. The opposing force is inversely proportional to throat radius. When a rock exhibits a distribution of throat sizes, the displacement of fluids will not be spatially uniform: displacement along large throats will encounter less opposition that displacement along small throats. Consequently, for a fixed pressure gradient (overbalance pressure), fluid displacement will achieve longer displacement distances along large throats that along small throats, and the radial distribution of fluid will be smooth rather than sharp. 2. The model of piston-like invasion (sharp radial saturation front) is accurate only for cases of porous and permeable formations with uniform pore-throat sizes, TRUE or FALSE? Explain your answer. Answer: TRUE. When the formation exhibits equal-size pore throats the forces of opposition to fluid displacement will be uniform across all throats and hence, the radial distribution of water saturation will exhibit a piston-like (shock front) behavior (as predicted by Buckley-Leverett model of immiscible fluid displacement). On the other hand, variable throat-size distributions in a formation will result in smooth radial variations of fluid saturation from the borehole wall toward the virgin (uninvaded) zone: some pores and throats will be filled with mud filtrate while others will still be filled with original formation fluid at the same radial distance from the wellbore. 3. According to discussions in class and in the course notes, high
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Homework_Assignment_2_Solution - Homework Assignment No. 2...

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