Newton Convergence and Material Balance

Part 12, Chapter 12: Running a Simulation, History Matching, and Forecasting

Solving the Nonlinear Step

A fully implicit step is a nonlinear system. Newton iteration linearizes the equations, solves, and updates, driving the residual toward zero.

Newton convergence and material balancetol 1e-5Newton iteration ->residual (log)Each pass squares the residual, the signature of quadratic convergence, so the step converges in 4 iterations; a too-large timestep would diverge instead.

Quadratic Convergence and Its Limit

Near the solution the residual roughly squares each pass, the signature of quadratic convergence, so a few iterations suffice. But a timestep too large leaves the first guess outside the convergence radius and Newton diverges; the simulator then cuts the step and retries.

Material Balance

A separate global check, the material-balance error, confirms the converged step neither created nor lost mass. A drifting material balance is a red flag even when Newton reports convergence.

This page is prerendered for SEO and accessibility. The interactive widgets above hydrate on JavaScript load.