Engineering Commons^™

Numerical Simulation Of Individual Wells In A Field Simulation Model, Ali Mohammed Akbar

Doctoral Dissertations

"Conventional numerical simulation of hydrocarbon reservoirs is inadequate for the prediction of bottom-hole pressures at production wells. This problem can be overcome by using a special mathematical model which combines individual well simulation with reservoir simulation. Severe computational instability is commonly encountered in the radial models due to the relatively small grid-blocks and high fluid velocities in the vicinity of the well bore. This instability is found to be more pronounced during depletion of the reservoir when the pressure near the well bore is below bubble-point pressure. A new technique is introduced here for saturation calculations in the critical region …

Convergence Of Material Balance In Mathematical Simulation Of Petroleum Reservoirs, Abdul Rashid Merchant

Doctoral Dissertations

One criterion for determining the precision of pressures calculated by a simulation model is the accuracy of the material balance. A high degree of precision in the calculated pressures is a necessary condition for elimination of error in prediction of fluid migration in the reservoir. However, this condition is not sufficient to guarantee accuracy of the simulation, since inaccuracies are introduced by truncation errors, machine round-off errors, and by the use of finite difference approximations to represent nonlinear partial differential equations.

A new procedure called Error Matrix Technique has been developed for reduction of material balance errors. This reduction is …

An Application Of Residual Relaxation To Mathematical Simulation Of Petroleum Reservoirs, Grufron Achmad

Doctoral Dissertations

"Stability and convergence have long been primary concerns in the application of numerical techniques to the simulation of petroleum reservoir performance. An iterative method based on sequentially reducing the residual to zero at each grid point has been developed. It has been shown analytically that this residual relaxation method is stable, convergent, and consistent.

A three-phase areal model was developed to simulate a hypothetical homogeneous petroleum reservoir, and various computational methods were tested with this model. The residual relaxation method developed in this study (RELAX) was found to converge as rapidly as SIP, and much faster than either LSOR or …