Homework_Assignment_8_Solution

# Homework_Assignment_8_Solution - Homework Assignment No. 8...

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Homework Assignment No. 8 Solution Set April 15, 2010 Due on April 22, 2010 @ 2:00 PM PGE368 Spring Semester 2010 Fundamentals of Well Logging Instructor: Carlos T. Verdín, Ph.D. PETROPHYSICAL INTERPRETATION OF RESISTIVITY LOGS DESCRIPTION: The objectives of this homework are: (a) To exercise the conceptual understanding of electrical resistivity logs, (b) To calculate the electrical resistivity of connate water from resistivity logs, and (c) To calculate hydrocarbon saturation from resistivity logs. GUIDELINES FOR THE PREPARATION OF HOMEWORK REPORTS: (A) YOUR REPORT SHOULD BE CLEAN, NEAT, AND WELL ORGANIZED. DESCRIPTIONS SHOULD BE LEGIBLE AND READABLE. (B) ALL FIGURES AND TABLES SHOULD BE LABELED AND PROPERLY ANNOTATED WITH A CAPTION. PLOTS SHOULD BE DISPLAYED WITH THEIR AXES, VARIABLES, AND MEASUREMENT UNITS. (C) ALL RELEVANT RESULTS AND QUANTITIES SHOULD BE WRITTEN WITH THE CORRESPONDING MEASUREMENT UNITS. (D) ATTENTION SHOULD BE PAID TO NUMBER OF DECIMAL FIGURES USED TO DISPLAY RESULTS. (E) SPREADSHEETS ARE NOT SELF-EXPLANATORY NOR ARE LOOSE FIGURES. (F) CLEARLY INDICATE THE NUMBER OF THE PROBLEM THAT YOU ARE ANSWERING EACH TIME. (G) CIRCLE YOUR NUMERICAL ANSWERS. (H) ANSWER QUESTIONS IN ORDER (IF THE ANSWERS ARE ON LOGS, KEEP THE ORDER AND GIVE THE REFERENCE TO THE PAGE NUMBER WITH THE PLOT), (I) IF YOU DID NOT HAVE TIME TO FINISH THE HOMEWORK, YOU SHOULD CLEARLY INDICATE WHICH QUESTIONS YOU DID NOT ANSWER. POINTS WILL BE DEDUCTED FROM HOMEWORK THAT DOES NOT ADHERE TO THE ABOVE PRESENTATION RULES.

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The following question is worth 10 points: 1. For a=1, m=2, and n=1.5 in Archie’s equations, a. With everything else being equal, a 5% change in porosity will cause what percent change in the rock’s electrical resistivity? We know that 1 21 . 5 2 1 . w t w R RC S φ == i , where 1 1.5 w w R C S = 1 3 2 2 t t t dR Cd d dR R ⇒= = So a 5% change in porosity will cause 2( 5%) 10% t t dR R ±= ± c hange in the rock’s electrical resistivity b. Using the same parameters, a 5% change in water saturation (with everything else being equal) will cause what percent change in the rock’s electrical resistivity. Similarly, we know that 2 . 5 1 . 5 1 . w t ww R SS i , where 2 2 w R C = 2 2.5 1.5 1.5 wt w t w CdS dR dS dR SR S −− = So a 5% change in water saturation will cause 1.5( 5%) 7.5% t t dR R ± c hange in the rock’s electrical resistivity The following questions are worth 15 points: 2. Consider the case of oil-base mud invading water-bearing sand. The sand has a porosity of 18%, and exhibits a combined clay-bound and capillary-bound water saturation of 15%. Salt concentration in the water sand is 140,000 ppm. The sand’s temperature is 130 degF. Assume that a=1, m=2, and n=2 in Archie’s equations. a. Construct QUALITATIVE plots of water saturation and salt concentration as a function of radial distance into the sand starting from the center of the well. Pay attention to units in your plot.
0 1 2 3 4 5 6 7 8 9 10 0 10 20 30 40 50 60 70 80 90 100 Water Saturation, % Radial Distance, ft Water Saturation vs. Radial Distance Mudcake Capillary bound saturation reduced due to overbalance pressure

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## This note was uploaded on 02/13/2012 for the course PGE 368 taught by Professor Staff during the Spring '08 term at University of Texas at Austin.

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Homework_Assignment_8_Solution - Homework Assignment No. 8...

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