[SOLVED] matlab GENG4405 2019 Assignment 2, Part 4

GENG4405 2019Assignment 2, Part 4
Part 4 of the Assignment: What is change in velocity with position?
Monitoring wells 500 meters and 1000 meters from the production well have been fitted with pressure and flowrate measurement equipment. The fluid velocity 1000 meters from the production well is 1103 ms and the velocity 500 meters from the production well is 2103 ms. What is the instantaneous change in velocity with position 1000 meters form the production well?
Fluid flow, when changes in density and viscosity can be neglected isothermal flow, is often modelled with the NavierStokes Equation:
2
This can be interpreted as mass times acceleration on the lefthand side and the sum of pressure forces, viscous forces and external forces on the righthand side. It is a partial differential equation
For very low Reynolds numbers 1 the viscous forces dominate and the
acceleration term can generally be ignored resulting in Stokes flow equation
02
Which is applicable to flow in porous media, such as liquid moving under a small pressure gradient in a reservoir. In our reservoir water flows toward the well where the pressure is lowest. Near the well velocities are sufficiently high that this model would be invalid however far away from the well the assumptions are reasonable.
Using a cylindrical coordinate system , , , considering flow to be purely radial and with no change in the rate of change of the radial velocity with angleor heightleads to
0 1
Which is a second order, ordinary differential equation. Subject to:
655 kg , 76.5106 Pas, 9.81 , and 12 MPa m3 2
Based on monitoring the pressure in the production well and two monitoring wells

1000.005
Where all pressures are expressed in Pa.
Assignment Question:
20 Write MATLAB code using the shooting method and the boundary conditions based on the velocities at 1000 meters and 500 meters to determine the local velocity gradient at 1000 meters from the production well. Use secondorder RungeKutta to solve the initial value problem and step between the boundaries do not use an inbuilt MATLAB function in your final submission. In the report explain how you changed the BVP into an initial value problem what new equations did you develop? and discus your choice of convergence criteria.