The analytical solution for radial flow and constant production rate during infinite acting flow at sufficiently...
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The analytical solution for radial flow and constant production rate during infinite acting flow at sufficiently long times is equal to: PD == In 41, where, y = 0.5772 is Euler's constant. The terms P, 1, and r, are the dimensionless pressure, time, and radius, respectively. OP OP дрrо Pand 8² P a. Calculate the analytical derivatives to = 10³ and r = 1. b. Evaluate the backward, forward, and centered finite-differences approximation of the 1st-order partial derivatives at t = 105, r=1 using A, = 0.2, 0.1,0.01, 0.001 and Evaluate the derivatives at At, 1,10, 10², 10. Evaluate the relative error in percentage. List your results in a table. c. Evaluate the centered finite-differences approximate of the 2nd order partial derivative at tp=10³, rp=1 Arp = 0.2, 0.1,0.01, 0.001. Evaluate the relative error in percentage. List your results in a table. d. Plot the relative error of approximate -and app 0² Po orp calculation as a function of Ar, from 104 to 0.5. Make sure to get smooth and continuous curves by selecting appropriate Ar increments. Compare the three finite-differences schemes of the 1st-order derivative (backward, forward, and centered). You must use MATLAB to compute and plot your data. (The MATLAB code "*.m" must be uploaded). The analytical solution for radial flow and constant production rate during infinite acting flow at sufficiently long times is equal to: PD == In 41, where, y = 0.5772 is Euler's constant. The terms P, 1, and r, are the dimensionless pressure, time, and radius, respectively. OP OP дрrо Pand 8² P a. Calculate the analytical derivatives to = 10³ and r = 1. b. Evaluate the backward, forward, and centered finite-differences approximation of the 1st-order partial derivatives at t = 105, r=1 using A, = 0.2, 0.1,0.01, 0.001 and Evaluate the derivatives at At, 1,10, 10², 10. Evaluate the relative error in percentage. List your results in a table. c. Evaluate the centered finite-differences approximate of the 2nd order partial derivative at tp=10³, rp=1 Arp = 0.2, 0.1,0.01, 0.001. Evaluate the relative error in percentage. List your results in a table. d. Plot the relative error of approximate -and app 0² Po orp calculation as a function of Ar, from 104 to 0.5. Make sure to get smooth and continuous curves by selecting appropriate Ar increments. Compare the three finite-differences schemes of the 1st-order derivative (backward, forward, and centered). You must use MATLAB to compute and plot your data. (The MATLAB code "*.m" must be uploaded).
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Answer a Analytical derivatives OPD tp JPD ard 1 2tp 1 rD 5 106 a PD 1 2 b Finitedifference approxim... View the full answer
Related Book For
Fundamentals of Heat and Mass Transfer
ISBN: 978-0471457282
6th Edition
Authors: Incropera, Dewitt, Bergman, Lavine
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