Calibrating to Ogbon-1
Learning objectives
- State the calibration discipline: choose a model family, fit its free parameters to the well, read the misfit, then trust predictions
- Read the Ogbon-1 brine sand target: mean Vp 3.378 km/s at mean porosity 0.260 over the interval 6150 to 6240 m
- Fit the soft-sand model by adjusting the critical porosity and coordination number, and watch the root-mean-square misfit fall
- Read a residual misfit honestly: when the friable line stays too soft, the sand belongs nearer the stiff-sand trend
From a Model Family to This Reservoir
Parts 5 and 6 handed over families of models, not answers. The soft-sand line is a family: fix the mineral and it still has free parameters, the critical porosity where the grains lock up and the coordination number , the average contacts per grain. Different values draw different curves. Calibration is the step that picks the values, and it does so by making the model account for a rock you have actually measured. The discipline is fixed: choose a family, fit its free parameters to the well, read how well the fit did, and only then trust the model to predict a porosity or a fluid effect you have not measured. Skip the reading of the misfit and you have a curve that happens to pass near your data; do it honestly and you learn whether the family was the right one at all.
The Ogbon-1 Target
Ogbon-1 gives a clean target. Over the brine-saturated main sand from 6150 to 6240 m, the same interval Part 4.6 fluid-substituted, the sonic and density logs read a mean P-wave velocity of km/s at a mean porosity of 0.260, with a bulk density of 2.221 g/cc. Start the soft-sand model at a plausible first guess, a quartz frame with , , at 20 MPa, and evaluate it at that porosity. It returns km/s. The model is too soft by 0.540 km/s, a misfit of sixteen percent, and it is worth seeing where the miss lives. The predicted density, 2.229 g/cc, matches the log to within 0.01, because density is only bookkeeping and the mineral and porosity are right. It is the stiffness that is wrong: the friable frame carries the load through too few, too compliant contacts for this rock.
Reading the Misfit
Now turn the knobs. Raising the coordination number adds load paths and stiffens the frame; raising the critical porosity lengthens the road down to the mineral and stiffens it too. Push both up together, to and , and the model climbs to km/s, the misfit shrinking to 0.247. Push to 16 and it reaches 3.205, a residual of 0.173. The misfit is falling, but watch what it costs: to close the last of the gap and land on 3.378 the coordination number has to run past 20, and a real grain pack has between eight and eleven contacts per grain. That is the calibration telling you something the eye would miss. The soft-sand line is the lower bound, the friable end of the sand story, and the Ogbon-1 main sand is stiffer than any friable sand can be at this porosity; its true home is up near the stiff-sand line of Part 5.4, where early cement and consolidation have begun to stiffen the contacts. A fitted that runs off the physical scale is not a better fit, it is the model refusing, and the honest reading is to change the family rather than force the knob. Calibration, done properly, both pins a model to a reservoir and warns you when the model was the wrong one. With a calibrated, physically honest model of this sand in hand, the next section turns it into a chart that reads porosity and fluid at a glance.
References
- Dvorkin, J., & Nur, A. (1996). Elasticity of high-porosity sandstones: Theory for two North Sea data sets. Geophysics, 61(5), 1363-1370.
- Avseth, P., Mukerji, T., & Mavko, G. (2005). Quantitative Seismic Interpretation. Cambridge University Press.