WORKING GUIDE TO RESERVOIR ROCK PROPERTIES AND FLUID FLOW TAREK AHMED AMSTERDAM. BOSTON· HEIDELBERG· LONDON NEW YORK· OXFORD· PARIS' SAN DIEGO SAN FRANCISCO' SINGAPORE. SYDNEY. TOKYO ElSEVIER Gulr Prf..""""1 I'IIblitbinll'" an inlrm' of F.1o 0.01, or 0 1 162:6 Q B m o o1 oA pi pwf total at Well 1 ¼ @ kh 2 0 1 3 0 1 kt 70:6Q B m o o2 oA A 3:23 þ 0:87s5 @ 4
[email protected] fmct r2w kh 2 3 0 1 2 3 2 2 948fmc r 70:6 Q B m 948fmc r t 15 @ t 25 o3 o o A 4 Ei Ei 4 kt kh kt where Qo1, Qo2, and Qo3 refer to the respective producing rates of Wells 1, 2, and 3. This computational approach can be used to calculate the pressure at Wells 2 and 3. Further, it can be extended to include any number of wells flowing under the unsteady-state flow condition. It should also be noted that, if the point of interest is an operating well, the skin factor s must be included for that well only. Example 3-21 Assume that the three wells as shown in Figure 3-29 are producing under a transient flow condition for 15 hours. The following additional data are available: Qo1 ¼ 100 STB/day Qo2 ¼ 160 STB/day Qo3 ¼ 200 STB/day pi ¼ 4500 psi Bo ¼ 1.20 bbl/STB ct ¼ 20 10 6 psi 1 (S)Well 1 ¼ 0.5 h ¼ 20 ft f ¼ 15% k ¼ 40 md rw ¼ 0.25 ft mo ¼ 2.0 cp r1 ¼ 400 ft r2 ¼ 700 ft 214 3. FUNDAMENTALS OF RESERVOIR FLUID FLOW If the three wells are producing at a constant flow rate, calculate the sand face flowing pressure at Well 1. Solution Step 1. Calculate the pressure drop at Well 1 caused by its own production by using Equation 3-145: ð162:6Þð100Þð1:2Þð2:0Þ ð40Þð20Þ 2 0 1 3 ð40Þð15Þ A 3:23 þ 0:87ð0Þ5 4
[email protected] ð0:15Þð2Þð20 10 6 Þð0:25Þ2 ðDpÞWell 1 ¼ ¼ 270:2 psi Step 2. Calculate the pressure drop at Well 1 due to the production from Well 2: ð70:6Þð160Þð1:2Þð2Þ ð40Þð20Þ 2 3 2 6 ð948Þð0:15Þð2:0Þð20 10 Þð400Þ 5 Ei 4 ð40Þð15Þ ðDpÞdue to Well 2 ¼ ¼ 33:888½ Ei ð 1:5168Þ ¼ ð33:888Þð0:13Þ ¼ 4:41 psi Step 3. Calculate the pressure drop due to production from Well 3: ð70:6Þð200Þð1:2Þð2Þ ð40Þð20Þ 2 3 2 6 ð948Þð0:15Þð2:0Þð20 10 Þð700Þ 5 Ei 4 ð40Þð15Þ ðDpÞdue to Well 3 ¼ ¼ ð42:36Þ½ Ei ð 4:645Þ ¼ ð42:36Þð1:84 10 3 Þ ¼ 0:08 psi Step 4. Calculate the total pressure drop at Well 1: ðDpÞtotal at Well 1 ¼ 270:2 þ 4:41 þ 0:08 ¼ 274:69 psi Step 5. Calculate pwf at Well 1: pwf ¼ 4500 274:69 ¼ 4225:31 psi SECTION 3.11 215 PRINCIPLE OF SUPERPOSITION Effects of Variable Flow Rates All of the mathematical expressio