Abstract
A fast-forward (FF) model for density logging is an essential element for inversion techniques, which may be performed with density data alone or jointly with other measurements. Such models must be both fast and accurate to be of value in the log interpretation process. The environment of high-angle or horizontal (HA/HZ) wells presents a scenario in which forward models have particular promise.
In the 1980s, Watson (1984) developed the technique of differential sensitivity functions to rapidly predict the response of a density logging tool. However, the accuracy of this technique is modest because of the limitations inherent in its linear approximation. In this work, we extend the density sensitivity technique to a second-order approximation. A critical component of this model is the second-order sensitivity functions, which are challenging to calculate. With the aid of the perturbation feature in the MCNP5 code, we use elements of the sensitivity functions at both the first and second orders to approximate the second-order dependences.
We calibrate the model in fully detailed MCNP (Monte Carlo N-particle) simulations of the EcoScope* LWD tool response for a wide range of borehole conditions covering formation electron densities from 1.5 to 3.0 g/cm3; drilling fluids of water, light mud, and heavy barite mud; and standoff values from 0 to 1 in. The maximum deviations between the forward model predictions and MCNP simulations in these diverse borehole conditions are 0.02 g/cm3 for the long-spacing (LS) electron density, 0.03 g/cm3 for the short-spacing (SS) electron density, and 0.04 g/cm3 for the compensated electron density. This combination of accuracy and versatility is a dramatic improvement over the performance of linear sensitivity techniques. We benchmark the model in a simulated HA/HZ well environment and demonstrate performance that is roughly consistent with the calibration. The speed of the improved forward model is almost equivalent to that of the original sensitivity function technique and is six orders of magnitude faster than the Monte Carlo data calculations.
