A hydraulically valid model with the resultant viscosity predicting algorithms has been developed for lost circulation material (LCM) added to non-aqueous drilling fluids.

Measuring drilling fluid rheology for fluids containing LCM is difficult or impossible with a standard bob and sleeve rheometer because of the interference of the particles with the rotation of the sleeve in the narrow annular gap. A bob and sleeve with a larger annular gap invalidates the fundamental assumption of a constant shear rate across the gap. The ability to predict rheology after LCM addition could be very important in evaluating LCM selection and applications, hole cleaning ability and the equivalent circulating density of the fluid.

Model rheology predictions

The engineering model allows multiple products at different concentrations to be added to a fluid; the program predicts the dial readings.

In Figure 1 (under the caption Starting Fluid), the standard six-speed rheometer dial readings can be input. The algorithm processes the products sequentially under the Added

Products caption and outputs the final dial readings under the Predicted Rheology caption. The predicted dial readings then are used to calculate plastic viscosity (PV), yield point (YP), Herschel-Bulkley model parameters n, k and tau0 for hydraulics along with the new fluid density. Only ground marble, resilient graphitic carbon and a specific fiber are included in the current version. However, the model algorithm has a built in analysis method to determine the constants for other products.

Does particle size affect the result?

A series of tests using GM-5, GM-25 and GM-50 (where the numbers indicate the d50 of the particulate material) ground marble was performed using a 12.0 lb/gal field fluid. Results are shown in Figures 2 and 3. These tests investigated the effect of concentration and particle size of the ground marble. It was concluded that particle size has no significant effect on the final viscosity; only the volume fraction of the added products.

In Table 1 there is good agreement with the model and measured data for 20 lb/bbl additions. For 40 lb/bbl and 80 lb/bbl additions there is a larger variation for the 300 RPM data for the larger particles. This likely indicates measurement problems in the narrow annular gap in the viscometer. Because the gap is narrow, the larger size LCM material will be excluded from the gap, causing the measured viscosity to be low and closer to the base fluid. Regardless of these issues, the data are acceptable for use in hydraulics analysis and are hydraulically conservative. In these data analysis, an equivalent circulating density (ECD) error was calculated

for a test case. This is the ECD error in percentage for an 8.5 by 5 inch annulus with 10,000 ft (3,048.8 m) maximum depth (MD) at 500 gpm (gallons per minute) flow rate. The worst-case scenario is 1.5% error on the 80 lb/bbl addition, which results in a difference of 0.17 lb/gal for the calculated ECD.

For particles that are not highly charged or reactive, it can be assumed that there is little or no effect of particle size on bulk viscosity. Likewise, the application method will compensate for reduced particle size due to "grinding" during the drilling process since a base line rheology measurement is made each time an addition of LCM, and subsequent rheology prediction, is to be done (Table 1).

Testing the model

Resilient graphitic carbon (RGC-50) was added in three different concentrations: 16, 32 and 64 lb/bbl additions. In these tests, the model correlated with the measured results very well. The largest observed error was only 4.6 dial readings, which were on the highest product addition and on the 300 rpm dial reading.

Hydraulically, the error is quite small with the largest computed ECD error for the RGC-50 product being only 0.7 %. It should be noted that the RGC-50 product has a much more non-liner characteristic curve than the ground marble products. Considering the sensitivity of the non-linear curve to volume fraction and the degree to which this product is non-linear, the viscosity prediction is remarkably accurate (Table 2).

Fiber additions

F-35 has the most non-linear characteristic rheology curve of all the products tested when measured on a standard bob and sleeve rheometer. In these tests, the 10 lb/bbl addition measured data agreed quite well with the predicted values, while the accuracy deteriorated dramatically with additions up to 40 lb/bbl. It should be noted that 40 lb/bbl additions of fiber is quite high, since the low specific gravity results in a relatively high volume percent of fiber. In these data, the measured signature appears to have an almost linear viscosity increase with product concentration (Table 3).

Mixing three components

In these tests, the additive assumption is tested using three products: 20 lb/GM-25, 16 lb/bbl RGC-50 and 10 lb/bbl F-35. Very good agreement was observed between the measured and tested data. These multiple component results substantiate the initial assumption that a partial

volume fraction viscosity model for non-reactive solids could be developed (Table 4).

Conclusion

The engineering model developed to include in the drilling fluid hydraulic model was able to adequately predict rheology for LCM additions in non-aqueous drilling fluids with sufficient accuracy, which minimized error on ECD predictions. Also, little or no particle size viscosity effect was observed with ground marble products. Only a volume fraction effect was observed.

The model testing validated the assumption that modeling viscosity increase with product additions can be treated additively. Not only can single product additions be treated additively, but so can multiple product additions. In addition, the model showed that particle shape and/or character can have a dramatic impact on viscosity increase of a suspension at constant volume fraction.

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