By K. Aziz
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Extra info for Petroleum Reservoir Simulation
Eqn. 42). For reasons that will become clear when we consider an arbitrary spacing, the effect of the source term is proportional to the volume of the boundary block, which is larger (exactly twice for same Ax) for the block-centred grid. 104) Similar equations arise in the treatment of individual wells and aquifers (see 75 PETROLEUM RESERVOIR SIMULATION FLOW OF A SINGLE FLUID IN ONE DIMENSION Chapter 9). In the point-distributed grid, eqn. 108b) is not used, because aU/dx is approximated at N - $ and 3.
L MODEL MODEL I So, ~ 0 . 1 5 Sp II '1 Sw = l so= I FIG. 12. Sw=I MODEL I[ So=l Sw=I Sw=l' So=l Three-phase k , calculated by Stone's Model I and 11. 1 1 . Three-phase k , calculated by Stone's Model I and 11. Model II This model tends to predict higher So, compared to eqn. 119). Also, it gives incorrect values for small krocwsince lim kro = co as krocw-+ 0. Therefore eqn. 1 19) is a more reasonable model. 10 give examples of two-phase rock properties. Two examples of three-phase krocalculated by eqns.
42) we have utilised the fact that A2 is a linear operator. 42) illustrates the important relationship between local errors and errors of solution: The errors ofsolution ei satisfy the difference equation for ui with the source q, replaced by the local error, - R,. Note that consistency is a property of the difference operator and not of the solution. 2 Convergence Let ei be the error in the approximate solution at i, , This is called the error of the solution or the global discretisation error.