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
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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 20 106 psi1 (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
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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 106 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 33:888½Ei ð1:5168Þ 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 ð42:36Þ½Ei ð4:645Þ ¼ ð42:36Þð1:84 103 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
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PRINCIPLE OF SUPERPOSITION
Effects of Variable Flow Rates All of the mathematical expressio