# TAMU PETE 662 - 662_HW1_soln (17 pages)

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## 662_HW1_soln

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- Pages:
- 17
- School:
- Texas A&M University
- Course:
- Pete 662 - Production Engineering

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PETE 662 Spring 2014 Problem 1 Homework 1 Vertical Well Performance 1 21 14 1 28 14 PETE 662 Spring 2014 Homework 1 Vertical Well Performance 1 21 14 1 28 14 PETE 662 Spring 2014 Homework 1 Vertical Well Performance 1 21 14 1 28 14 PETE 662 Spring 2014 Homework 1 Vertical Well Performance 1 21 14 1 28 14 PETE 662 Spring 2014 Problem 2 Homework 1 Vertical Well Performance 1 21 14 1 28 14 PETE 662 Spring 2014 Homework 1 Vertical Well Performance 1 21 14 1 28 14 PETE 662 Spring 2014 Homework 1 Vertical Well Performance 1 21 14 1 28 14 Problem 3 Table Given Data Parameter Calculate Value Oil flow rate bbl day 500 WOR 1 5 Gas gravity 0 71 Oil gravity API 32 Reservoir Temperature F 150 GOR 500 Seperator Temperature F 100 Seperator Pressure psig 100 in terms of reservoir pressure P Calculate oil formation volume factor Calculate as a function of P PETE 662 Spring 2014 Plot Homework 1 Vertical Well Performance 1 21 14 1 28 14 as a function of P 1500 Liquid Flow rate bbl day 1450 1400 1350 1300 1250 0 500 1000 1500 2000 2500 Pressure psia 3000 3500 Matlab Code Qo 500 bbl oil day WOR 1 5 water oil ratio GOR 500 gas oil ratio gas gravity 0 71 gas gravity oil gravity 32 oil gravity in degrees API T 150 degrees Farenheit P 0 2 4336 A oil gravity T 460 Rs gas gravity P 1 187 56 06 10 10 393 A F T 60 oil gravity gas gravity Bo 1 4 67 10 4 Rs 0 11 10 4 F 0 1337 10 8 Rs F Ql Qo WOR Bo plot P Ql xlabel Pressure psia ylabel Liquid Flow rate bbl day 4000 4500 PETE 662 Spring 2014 Problem 4 Homework 1 Vertical Well Performance 1 21 14 1 28 14 PETE 662 Spring 2014 Homework 1 Vertical Well Performance 1 21 14 1 28 14 PETE 662 Spring 2014 Homework 1 Vertical Well Performance 1 21 14 1 28 14 Problem 5 Given Data Parameter re ft Pwf psi Gas gravity k Reservoir Temperature F h Pi psi Value 1490 3000 0 65 0 17 180 78 4613 We are told to assume the gas reservoir is under pseudosteady state and so we take to be Equation 4 47 can be rearranged into Equation 4 50 We can use the quadratic equation to solve for the flow rate at each new reservoir pressure Remember that is decreasing at or psi per day for three years Also realize that the temperature is constant isothermal process but the pressure is changing meaning that the viscosity and the Z factor will only change with pressure I will present how to calculate the Z factor and the viscosity as a function of pressure PETE 662 Spring 2014 Homework 1 Vertical Well Performance a Case 1 S 0 3000 Flow rate Mscf day 2500 2000 1500 1000 500 0 0 200 400 600 Time days 800 1000 1200 0 200 400 600 Time days 800 1000 1200 0 200 400 600 Time days 800 1000 1200 5 18 x 10 16 Cumulative Production Mscf 14 12 10 8 6 4 2 0 2 3 2 2 2 1 Mscf psi 2 1 9 1 8 1 7 1 6 1 5 Cumulative production after 3 years 1 21 14 1 28 14 PETE 662 Spring 2014 Homework 1 Vertical Well Performance b Case 2 S 10 1400 1200 Flow rate Mscf day 1000 800 600 400 200 0 0 200 400 600 Time days 800 1000 1200 0 200 400 600 Time days 800 1000 1200 0 200 400 600 Time days 800 1000 1200 5 9 x 10 8 Cumulative Production Mscf 7 6 5 4 3 2 1 0 1 0 98 0 96 Mscf psi 0 94 0 92 0 9 0 88 0 86 0 84 0 82 Cumulative production after 3 years 1 21 14 1 28 14 PETE 662 Spring 2014 Homework 1 Vertical Well Performance 1 21 14 1 28 14 c At what flow rate is the non Darcy flow effect on production reduction equal to the effect of skin factor of 10 These calculations will be made with the average reservoir pressure equal to 4613 psi Set this change in production equal to the change in production when flow rate changes Solve for q that would make non Darcy effect on production reduction the same decrease in production rate from an increase of skin factor from zero to ten You can also plot residual as a function of q and see at what q the residual is zero 1000 500 X 1 43e 04 Y 0 03959 residual 0 500 1000 1500 2000 2500 0 1 2 3 4 5 6 Flow rate Mscf day Flowrate 7 8 9 10 4 x 10 PETE 662 Spring 2014 Homework 1 Vertical Well Performance 1 21 14 1 28 14 Matlab code for Problem 5 Problem 5 3 4 PPS 2nd edition re 1490 drainage radius ft rw 0 328 wellbore radius ft Pwf 3000 flowing bottom hole pressure psi T 180 reservoir temperature degrees Farenheit p 4613 average reservoir pressure psi t 1 1 365 3 this is the time vector well is produced 1095 days gas gravity 0 65 gas gravity k 0 17 permeability md h 78 reservoir height ft D 10 3 non Darcy coefficient Mscf d 1 S 0 skin factor pvec vector will be used to collect average reservoir pressure q vec vector will be used to collect the daily flow rate Qg 0 used for first summation in the loop Q total vec vector will be used to collect the cumalative flow rate Loop calculates daily flow rate as the average reservoir pressure decreases Gas properties viscosity and Z factor are calculated at each new reservoir pressure for i 1 length t pvec pvec p stores average reservoir pressure z rho g mu g Bg gas properties gas gravity p T calls gas properties function to calculate z density viscosity a 1424 mu g z T D k h used to solve quadratic c 1 p 2 Pwf 2 used to solve quadratic b 1424 mu g z T k h log 0 472 re rw S used to solve quadratic q b sqrt b 2 4 a c 2 a quadratic equation q vec q vec q stores flow rate into vector Qg Qg q cumulative production Q total vec Q total vec Qg stores cumulative production into vector p p 500 365 new average reservoir pressure decreases by 500 365 psi day end PETE 662 Spring 2014 Homework 1 Vertical Well Performance 1 21 14 1 28 14 Gas Properties function this will be useful for your project function z rho g mu g Bg gas properties gas gravity p T pseudocritical temperature and pressure for gas Tpcg 168 325 gas gravity 12 5 gas gravity 2 degrees R Ppcg 677 15 gas gravity 35 7 gas gravity 2 psi Tpco 187 330 gas gravity …

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