Borehole Electromagnetics –Diffusive and Propagation Transients - Wave Propagation in Drilling, Well Logging and Reservoir Applications - page 340

Problems for inclined beds are typically formulated and hosted on
Cartesian or rectangular grid systems using “staircase grids” as shown at the left
of Figure 8.1. Uncertainties and numerical noise associated with grid aspect
ratio and density are often introduced by such mesh systems - an improvement
is the locally oriented grid suggested at the right of Figure 8.1 in which layer
interfaces are aligned with one set of coordinate axes.
Staircase grids Boundary conforming grids
Figure 8.1. “Staircase” versus “boundary conforming” grids for layered media.
A second limitation with conventional formulations is the use of “dipole”
representations for coil transmitters (dipoles are mathematical representations
for very small diameter coils in uniform media valid only at large receiver
distances). While point source idealizations are acceptable for MWD mud
pulsers or sonic sources in acoustic logging tools, both of which form isolated
hardware units acting in uniform background media, borehole electromagnetic
problems provide unique challenges. For one, transmitter and receiver coils on
MWD resistivity tools wrap around metal drill collars, typically several inches
in diameter; also, it is not uncommon for coils to reside across multiple thin
geological layers in many exploration scenarios. A transmitter (or receiver)
representation that does not accommodate these features will not provide
accurate forward simulations for hardware design or inverse results for well log
interpretation. We solve this problem by introducing “non-dipolar” transmitter
coils, as shown in Figure 8.2. Here, the coil is shown as a circle; in fact, in
Electromagnetic Well Logging , other possibilities, e.g., ellipses, squares and
rectangles are considered (hundred feet diameters are also permissible for
surface environmental applications). As indicated in Figure 8.3, we expand our
variable meshes far away from the source, where high physical resolution is not
required. As further suggested in Figure 8.4, our coil may reside across multiple
layers, for both (no mandrel) wireline and metal-mandrel MWD applications -
the relevant coefficients in Maxwell's equations are simply evaluated using local
values. Borehole eccentricity effects, arising from the horizontal drilling
environment, as well as contamination effects due to mud filtrate invasion, can
also be simulated as suggested in Figure 8.5 and discussed in the new topic.