Practical Drilling Technology OGJ SPECIAL Virtual rheology and hydraulics improve use of oil and synthetic-based muds

Mario Zamora
M-I Drilling Fluids LLC
Houston

When combined to form the core of a unitized suite of software modules, they provide new technology which is a step improvement over conventional approaches to calculate equivalent circulating densities (ECDs) and pump pressures for oil and synthetic-based muds (OBMs and SBMs).

More-accurate predictions are now possible for downhole mud rheology, circulating and static densities, frictional pressure losses, and pump pressures.

High-temperature/high-pressure (HTHP), deepwater, and extended-reach applications can especially take advantage of this new approach. The benefits from this method include reduced incidence of lost circulation, improved drilling performance, fewer drilling problems, and better information for effective decision-making.

While the concepts are not new in the strictest sense, neither has been fully exploited and implemented until now. The first concept, virtual hydraulics (VH), subdivides the well into short depth segments and combines variable downhole rheology with localized downhole conditions for hydraulics calculations. This permits a unique downhole perspective of hydraulics and rheology at a single point in time.

The second concept, virtual rheology (VR), takes full advantage of available field and lab data for the specific mud in use to determine downhole rheological properties as a function of temperature and pressure.

Virtual hydraulics and virtual rheology represent refinements of existing technology seeded by two projects involving field measurements. The significance of these studies, conducted 20 years and over 6,000 miles apart, is that they form the foundation for a practical, logical, and systematic approach for analysis of mud hydraulics and rheology. A third project has provided valuable field data to fine-tune the technology.

The "virtual" designations are appropriate for two reasons:

• First, virtual hydraulics satisfies the conditions of analysis in a 3D space in real time.

• Second, virtual rheology software uses rheological data taken at the well site and in the laboratory to create a "virtual" viscometer capable of making realistic predictions over a wide range of temperatures and pressures. Virtual rheology can use otherwise conventional rheological models and data which routinely are already measured for SBMs and OBMs in critical applications.

Impact of SBMs

The emergence of SBMs has single-handedly raised the importance of hydraulics and rheology to current high levels. While their remarkable field performances and reusability have helped to lower overall drilling costs dramatically, SBMs still are more expensive per barrel than other muds.¹ As such, SBMs are rarely used if severe lost circulation is expected or likely. Lost circulation is the "Achilles' heel" for SBMs. Minimum ECD levels are necessary, and accurate ECD predictions are needed for planning and operational adjustments. Similar concerns are raised for oil-based muds, although the adverse consequences of lost circulation are not as severe.

All types of pressure calculations involving SBMs and OBMs have always been a problem. While their sensitivity to temperature and pressure is well known, the lack of quality field data has limited development of consistent models. It has been possible to underestimate actual pump pressures by 25% on one well, and overestimate pressures on another well by a similar margin.

Pre-existing technology

Mud properties change as the mud is circulated downhole. In 1974, Fontenot and Clark were among the first to correlate field measurements to pressure-loss calculations using variable downhole mud properties.² They reported improved pressure calculations for tests involving 17.5-ppg oil-based mud and 14.2-ppg water-based mud, despite not having access to test equipment and computer power that is available today. Fontenot and Clark assumed oil-mud rheology variations paralleled that of the base fluid (diesel).

Today, better results can be obtained by measuring properties on an HTHP viscometer such as the Fann Model 70, the industry de facto standard.

In 1994, a Fann Model 70 viscometer (a lab instrument) was used on a rig during the drilling of an HTHP well in the U.K. sector of the North Sea.³ A dedicated operator measured the OBM rheology daily across a predetermined range of temperatures and pressures. The data were entered into two different computer programs for analysis and comparison to pressure-while-drilling (PWD) measurements.

The large volume of high-quality, almost real-time rheological data significantly improved the accuracy of ECD predictions. Another major goal of this project was to model downhole density, appropriately called the equivalent static density or ESD. Interestingly, Fontenot and Clark did not consider the effects of temperature and pressure on density in their work.

Improved hydraulics field data

The lack of field data has been the root cause of difficulties associated with predicting hydraulics with OBMs and SBMs. Field data are particularly valuable because HTHP field conditions cannot easily be duplicated in laboratories or shallow test wells.

In February 1995, a major project was initiated to measure and collect hydraulics data on a live well in the Gulf of Mexico at 12,710-ft measured depth in 420 ft of water.⁴ The operator was committed to using SBMs and required verification of pressures for internal risk analysis.

Fig. 1 [46842 bytes] summarizes the project with the annular temperatures and pressures superimposed over the 36-hr testing time line. The data proved to be a great source for understanding and evaluating downhole rheology and hydraulics. This well was chosen because calculated ECDs for the 11.5-ppg, polyalpha olefin (PAO) based SBM were considered abnormally high, although lost circulation was never imminent. Concerns for ECD were magnified because calculations using American Petroleum Institute (API) equations were significantly lower than actual.

The primary goal of this project was to resolve discrepancies concerning pump pressures and ECDs. Secondary objectives included measuring and evaluating ESD, surge/swab pressures, bit pressure loss, and mud temperature profile.

Multiple sensor packages were installed on the drill pipe to minimize rig time and to take simultaneous measurements at different depths to improve data quality. Temperature and pressure readings were taken in the annulus and inside the drillstring. The test program included surge/swab measurements (plus trip in and out), pressure/flow measurements, static tests, and several special tests. Several million data points were collected from 15 downhole gauges and a fully instrumented surface data acquisition system.

API calculated and measured pump pressures are compared in Fig. 2 [25832 bytes]. The calculated pump pressure at 665 gpm was about 2,400 psi; the actual pump pressure was nearly 3,700 psi. The significant variation was caused by inaccurate calculation of turbulent-flow losses in the drillstring. Actual pressure losses in the annulus were about 40% less than those calculated using API equations. From a practical sense, this was a best case scenario.

Virtual hydraulics

Hydraulics analysis can be improved by first subdividing a well into short depth segments. Mud rheological properties, density, temperature, well geometry, well bore angle, eccentricity, etc., are then defined for each segment in the annulus and drillstring. This approach provides great flexibility and structure and works very well if downhole rheological properties can be estimated properly.

The importance of correcting SBM and OBM density for temperature and pressure cannot be overstated. It is nonsensical to calculate annular pressure loss with four-decimal accuracy and then add it to uncorrected hydrostatic pressure to determine the ECD. On some HTHP wells, mud density at the bottom of the hole can exceed surface-measured density by more than 0.5 ppg. Fig. 3 [26600 bytes] compares measured and calculated static density for the SBM used in the Gulf of Mexico well. The measured annular temperature profile is also shown.

Temperature and pressure effects on density can be predicted accurately using models published in the literature if quality PVT (pressure-volume-temperature) data are available for the base fluid (internal phase).⁵ The Huxley-Bertram HTHP viscometer, which uses a floating piston to monitor volume changes during testing, can provide reliable data on base fluids to 15,000 psi and 450° F. Figs. 4 [32180 bytes] and 5 [30259 bytes] demonstrate the effects of temperature and pressure on the density of a PAO-based fluid and an 11.51-ppg SBM (at 72° F.) as measured on the Huxley-Bertram device. Fig. 6 [16571 bytes] compares measured and predicted ESD values for an internal olefin (IO) based SBM used in the Gulf of Mexico.

PVT analysis can provide the "local" density under given temperature and pressure conditions, but the ESD profile requires a numerical integration of local densities. Individual depth segments from 50 to 100 ft work well for most situations.

Virtual rheology

Rheological properties measured on the mud in use are always better than those modeled from general trends and laboratory studies. Ironically, most of the rheological data collected during a typical drilling operation are never used. Fann Model 35 viscometers used at the well site (maximum of 180° F. and atmospheric pressure) typically provide the rheological data input for computer analysis.

General-purpose models have attempted to account for downhole conditions with varying success. For HTHP applications, however, SBMs and some OBMs are routinely tested in the laboratory using the Fann Model 70 rated at 20,000 psi and 450° F. Also, pump pressures and flow data are always available at the well site but are rarely used in rheological or hydraulics modeling.

Downhole rheological behavior can be characterized better if all of the available data are considered and integrated into a single 3D data cube (data cubes are similar to the Rubik's cube which was popular some years ago). Fig. 7 [22879 bytes] illustrates this concept. The data cube incorporates field measurements and HTHP lab data over a wide range of conditions. Shear-stress values are determined by interpolation based on pressure, temperature, and shear rate.

The main advantages of the data cube include its ability to be used with any common rheological model and its ability to extrapolate values, within reason, beyond the measured pressure, temperature, and shear-rate limits. If current HTHP data are unavailable, field viscometer readings taken at multiple temperatures can be combined with pressure trends from the most recent HTHP matrix. If HTHP data are not available for the drilling fluid in use, field readings must be used with models based on historical data.

Data cubes are particularly useful for deepwater drilling. Rheological changes caused by temperatures approaching freezing can significantly affect circulating and surge/swab pressures. Measurements can be made at low temperatures by using a modified Fann 70. Circulating coolant can lower test mud temperature to just above freezing. Table 1 [18868 bytes] shows the impact of cold temperatures on the rheology of 13.8-ppg SBM. The first row of data was taken using a field viscometer; the last two rows with a Fann 70 modified for cold temperatures. In practice, these data would be incorporated into a data cube generated for high temperatures and pressures.

Perhaps the most interesting use of the VR data cube is to generate graphs of rheological properties vs. depth at a single point in time. Fig. 8 [35245 bytes] shows the plastic viscosity and yield point graphs for the same well. The left hand side of Fig. 8 was plotted conventionally-the data were plotted on a daily basis. The right hand side of Fig. 8 was generated using the VR data cube on the day the well reached total depth. The latter is an example of 4D analysis (vs. time).

Despite the value of data cubes, they cannot provide miracle solutions. Poor or incomplete data can yield unsuitable results. The best results are achieved if the test temperatures and pressures cover the expected ranges for the mud. While extrapolation is possible, mud rheology at 35° F. may not be effectively predicted from data taken between 120° and 300° F.

Temperature profiles

Even with the data cubes, downhole mud rheology cannot be predicted accurately unless downhole conditions are known in the annulus and drillstring, from surface to total depth. Downhole pressure is much easier to estimate than temperature. Surprising to some, an accurate mud temperature profile is the cornerstone of quality hydraulics predictions.

A wide range of software temperature simulators is available, and some are better than others. Appropriate heat-transfer coefficients are difficult to establish, so best results normally are obtained from computer programs which can be adjusted to match field data. If possible, the program also should handle dual geothermal gradients for deepwater situations.

Pressure calculations

Laminar pressure losses can be calculated by any of the different techniques and rheological models available in the literature. Data cubes contain shear-stress values for the six standard shear rates, so that any of the common models can be used. The Bingham plastic, power law, yield power law, and API dual power law are the most widely used.

The yield power law and the current API equations are the most consistent for matching measured data. One advantage of these models is that they are generalized and can handle changing rheological behavior. For example, a mud might match power-law behavior at the surface and act like a Bingham plastic at total depth.

If possible, pipe eccentricity, pipe rotation, and cuttings-loading effects should be considered when the annular pressure loss is calculated. Full eccentricity can reduce the concentric-case pressure loss by as much as 60%.

Turbulent pressure-loss calculations are a particular problem. Very little data are available on the turbulent behavior of drilling fluids of any type. The pump-pressure variations encountered during the Gulf of Mexico project were clearly related to miscalculation of drillstring losses in turbulent flow.⁴ One reason for the discrepancy was the restricted tool joints on the 5-in. drill pipe.

While the VR data cube is basically limited to laminar flow, valuable rheological correlations are easily determined from rig data. For example, turbulent behavior can be estimated from pump pressures taken at two or three flow rates. The flow rates should be on the high end to ensure turbulence in the drillstring. Pressure losses in the annulus, across the bit, and through surface connections are first calculated using the best available computer program. The sum of these results is then subtracted from the actual pump pressure to estimate the drillstring losses. The final step is to plot the drillstring pressure losses vs. flow rate on a log-log graph and determine the slope of the straight line passing through the points. The slope is the turbulent equivalent of the power-law behavior index. Values should range from about 1.8 down to about 1.6. Slopes can approach 2.0 for drill pipe with constricted tool joints.

Field comparisons

The VH and VR concepts have been used successfully on wells around the world, including the North Sea, Gulf of Mexico, Southeast Asia, and Alaska. Most applications have involved SBMs, but excellent results have also been achieved for OBMs.

The accuracy of most hydraulics programs can only be determined by how well the calculated pump pressures match actual values. In this regard, VH has consistently calculated values within 5%. However, the software is structured so that most modules can be run independently. This also allows the accuracy of these modules to be evaluated independently. Individual validation tests have been conducted for the temperature profile (circulating and static), density profile, rheological properties, and ECD modules. For example, downhole density predictions have been validated by formation tests (Fig. 6).

The temperature module does an adequate job for most cases, even though the model used is not highly sophisticated. Adjustments based on surface measurements can increase the accuracy. Best temperature profile results are obtained if bottom hole temperature values are provided by measurement-while-drilling tools. Excellent results have even been achieved in geo thermal wells in Southeast Asia.

Rheological predictions depend highly on data quality. Fann Model 70 viscometers appear to provide good, consistent measurements, but data-cube quality suffers if the temperature and pressure ranges are too narrow. Loss of accuracy can also occur if there is an insufficient number of different pressures at a given temperature, and vice-versa. This is common when Fann Model 70 temperature/pressure settings are chosen to match predetermined temperature and pressure profiles. A superior technique involves taking measurements at all combinations of five temperatures and five pressures (square matrix).

Results

• Step improvements in drilling hydraulics calculations can be achieved if the well is subdivided into many short depth segments, each containing key parameters such as rheological properties, temperature, pressure, density, eccentricity, geometry, etc. (virtual hydraulics).

• Data cubes generated by combining all available rheological data can accurately define mud rheology at different temperatures and pressures (virtual rheology).

• Better results are achieved by measuring rather than modeling temperature/pressure effects on mud rheology.

• The temperature profile is the cornerstone of any effective hydraulics/rheology analysis.

• Hydraulics of synthetic-based muds and oil-based muds cannot ignore the effects of temperature and pressure on downhole density.

• Recent analytical improvements in drilling fluid rheology and hydraulics can be attributed, in part, to better downhole field measurements.

References

1. Collins, G.J., and White, W.W., "Improved Practices, Synthetic Mud Drive Record 24-hr Drilling," World Oil, May 1995, pp. 35-39.

2. Fontenot, J.E., and Clark, R.K., "An Improved Method for Calculating Swab and Surge Pressures and Circulating Pressures in a Drilling Well," Society of Petroleum Engineers Journal, October 1974, pp. 451-62.

3. Baranthol, C.B., Alfenore, J., Cotterill, M.D., and Poux-Guillaume, G., "Determination of Hydrostatic Pressure and Dynamic ECD by Computer Models and Field Measurements in the Directional HPHT Well 22130C-13," paper No. 29430, presented at the Society of Petroleum Engineers/International Association of Drilling Contractors Annual Drilling Conference, Amsterdam, Feb. 28-Mar. 2, 1995.

4. White, W.W., Zamora, M., and Svoboda, C.F., "Downhole Measurements of Synthetic-Based Drilling Fluid in Offshore Well Quantify Dynamic Pressure and Temperature Distributions," paper No. 35057, presented at the SPE/IADC Annual Drilling Conference, New Orleans, Mar. 12-15, 1995.

5. Peters, E.J., Chenevert, M.E., and Zhang, C., "A Model for Predicting the Density of Oil-Based Muds at High Pressures and Temperatures," SPE Drilling Engineering, June 1990, pp. 141-48.

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