TECHNOLOGY Method reduces errors in oil-based mud hydraulic calculations

Haiwang Sun
Maurer Engineering Inc.
Houston

Density and rheological properties of oil-based muds are more affected by temperature and pressure than in other muds. Because current API recommended drilling hydraulics calculation techniques do not include these parameters, the API calculations are not accurate.

Although literature does mention this problem, no systematic solution has previously been available.

Matching pump pressure

Oil-based muds, by eliminating downhole problems and increasing penetration rate, are ideal for complex drilling operations. Offshore drilling has increased their popularity.

A persistent problem with oil-based muds is the difficulty in matching calculated pump pressures with measured values.¹ This problem is also acute for synthetic-based mud (SBM).²

White, et al.,¹ reported a 1,300 psi difference between predicted and measured pump pressures. This inconsistency has caused many uncertainties in drilling hydraulics design and is mainly due to the failure to correct for temperature and pressure effects on mud properties.

While circulating, some pump pressure is expended in overcoming friction along the circulating path. Friction pressure losses are functions of mud properties, which further are functions of downhole temperatures and pressures. For this reason, accurate prediction of pump pressure requires proper accounting for the effects of temperature and pressure.

Because downhole pressure itself is strongly affected by pump pressure, the calculation involves an iterative procedure. Downhole temperatures, on the other hand, are functions of circulating time, circulating rate, drillstring inlet temperature, surface temperature, and geo thermal gradient. Because this process is complex, a computer program is needed to model pump pressure and its associated parameters.

A good understanding of mud properties at downhole conditions is key to accurately predicting friction pressure losses and pump pressures. Several investigators have tested oil-based muds at elevated temperatures and pressures.^{1 3-5}

A general conclusion from these investigations is that temperature and pressure have significant effects on oil-based muds. Mud density, plastic viscosity, and yield point generally decrease as temperature increases and increase as pressure increases.

The most convenient and accurate density model found in literature is the compositional model described by Peters, et al.⁴ This model has been incorporated into Oilmud (high temperature, high-pressure oil mud hydraulics model) for density correction.

For correcting the effects of temperature and pressure on rheological properties, Houwen and Geehan's exponential model⁵ was found to have a strong theoretical basis and high flexibility for practical application. Their model served in the present study as the basis for deriving mathematical equations for relating mud rheological properties to temperature and pressure.

Data from literature for three types of oil-based muds were examined, including a diesel-based mud, a low-toxic mineral oil-based mud, and an SBM. Although equations were obtained and embedded in the computer model for all three types of oil-based muds, this study focuses on SBMs.

SBM is a promising mud system for offshore drilling because it is environmentally acceptable.² The computer model, however, can also be used for the other two types of oil-based muds. The equations developed for SBMs are as follows (T is temperature in °F. and P is pressure in psi):

 Plastic viscosity:
 PV = (9.172 + 0.000368P)e(199.2 + 0.008473P)/T (1)
 Yield point:
 YP = 10.2e115.4/T (2)
 Flow behavior index:
 n = 0.617e-30.22/T (3)
 Consistency index:
 K = 239.9 e292.2/T (4)

The correlation for YP does not include P, which means that the effect of pressure on YP is negligible. This is similar to the results given by Politte³ for diesel-based muds.

The effect of pressure on the flow-behavior index (n) and consistency index (K) for the power-law model does not follow a clear trend. Therefore, Equations 3 and 4 represent the averages of the two parameters over the pressure range of interest.

In practice, the same SBM system may contain different solids concentrations or may be treated with different additives. In these cases, Equations 1-4 must be corrected with properties measured on site before being used.

This flexibility has been incorporated into the computer model.

To determine pump pressure and its associated hydraulic parameters, the temperature distributions in the drillstring and annulus were first determined using a temperature model called Gtemp. The entire circulating path was then divided into small segments. Each segment was about 100 ft in length and had special pipe ID, pipe OD, and borehole diameter.

These subdivisions provided a way to evaluate flowing pressure, friction pressure loss, and mud properties segment by segment.

Calculation was initiated from the annulus head down to the bottom hole and then back to the surface. This order was used because the outlet pressure of the first segment at the annulus head is a known value (for example, atmospheric pressure). The segment inlet pressure was equal to the sum of the hydrostatic pressure and the friction pressure loss in the segment.

Because the segment pressure loss is a function of the inlet pressure itself through fluid properties, evaluation of this inlet pressure required an iterative process. The same iteration is required for every segment along the circulation path.

For input parameters, White, et al.'s, field experiments provided all tubular and well bore data. Tool joint effects were considered by adding tool joint lengths and representing them with a small section with appropriate IDs and ODs.

Well bore deviation effects were also considered in the pressure calculations. Measured depth was used for calculating friction pressure losses, while the true vertical depth was used for calculating hydrostatic pressures.

In this study, the newly developed computer model, Oilmud, was used along with two existing computer models, including the temperature model (Gtemp) and a hydraulic model (Hydmod).

Table 1 [11713 bytes] lists basic input for all three models. Drillstring inlet temperature, geothermal gradient, flow rate, surface plastic viscosity, and yield point were directly obtained from White, et al.'s, field study.¹ Pump rated horsepower and maximum pump pressure were based on field practices.

The 24-hr effective circulating time was obtained by trial and error using the computer models until the modeling results most closely matched measured values. This circulating time appeared to be much longer than White, et al.'s, circulating time (4-8 hr) during their field experiments. However, it is almost certain that the mud had been circulated in the well for an extended period during drilling operations prior to their experiments.

The model looked at variations of temperature and mud properties with well depth, friction pressure losses in the drillstring and annulus, pump pressure, effect of drillstring inlet temperature on drilling hydraulics, and effect of temperature and pressure on equivalent circulating density (ECD).

Variations with depth

Fig. 1 [13245 bytes] shows the temperature distributions in the drillstring and annulus from Gtemp with a 24-hr effective circulating time and a 400 gpm pump rate. The downhole temperatures in both the drillstring and annulus were much higher than the drillstring inlet temperature or the surface temperature, even after circulating for 24 hr.

Also shown is that these downhole temperatures were much less than the formation temperature. This means that neither the surface temperature nor the formation temperature can adequately represent the temperatures in the drillstring and annulus.

Because fluid properties are important functions of temperature and pressure, they change correspondingly with well depth. Fig. 2 [11677 bytes] shows the variation of plastic viscosity (PV) with depth in both the drillstring and annulus, as calculated with Oilmud.

The significant changes in plastic viscosity (Fig. 2 [11677 bytes]) highlight the need for temperature and pressure corrections in drilling hydraulics design.

Friction in drillstring

Friction pressure losses in the drillstring were predicted using Oilmud (Fig. 3 [17678 bytes]). During the analysis, flow rate was varied from 50 to 700 gpm, which covered the flow rate range used by White, et al.

Fig. 3 [17678 bytes] shows that the predicted drillstring pressure losses closely matched the measured values over the entire flow rate range. This indicates that the method described in this article accurately predicts drillstring friction pressure losses. It also indicates that the Bingham plastic model with temperature and pressure corrections is valid for this prediction.

It is interesting to note that API calculations without corrections overestimated the friction pressure losses at lower flow rates and underestimated them at higher flow rates. The overestimation is primarily as a result of using fluid properties obtained at surface conditions.

As shown in Fig. 2 [11677 bytes], plastic viscosity measured at surface conditions was much larger than at downhole conditions. The same is true for yield point, YP, of the Bingham plastic model and the consistency index, K, of the power-law model.

Underestimation at high flow rates was mainly caused by failing to include the effect of pressure on fluid properties. High flow rates result in high system pressure, and high pressure increases fluid plastic viscosity, yield point, and mud density, which further increase friction pressure losses.

Fig. 3 [17678 bytes] also shows that at high flow rates, the predictions given by White, et al., fell far below their measured values. The main reason for this discrepancy was that their calculations failed to include the appropriate downhole temperature and the pressure effect.

As shown in Fig. 4 [14361 bytes], drillstring temperature decreases dramatically as the pump rate is increased. The average temperatures at 700 gpm are about 60° F. lower than the value used by White, et al. (150° F.).

From

Fig. 3 [17678 bytes], the maximum error for predictions with a single temperature of 150° F. was as high as 1,000 psi, while predictions without temperature and pressure corrections diverged by less than 300 psi.

Therefore, corrections based on improper conditions are no better than results obtained without corrections.

Friction in annulus

Figs. 5a and 5b [50142 bytes] compare predicted friction pressure losses in the annulus with the Bingham plastic model and power-law model, respectively.

Fig. 5a [50142 bytes] shows that the predicted friction pressure loss both with and without corrections are far from the measured values. The corrections reduced the errors by only 30%.

The significant differences between predicted and measured values indicate that the Bingham plastic model is not valid for annular flow because the Bingham plastic model tends to overestimate shear stresses at low shear rates.

By contrast, corrected friction pressure losses in the annulus predicted with the power-law model were relatively close to measured values (Fig. 5b [50142 bytes]), although the predicted trend is different from the trend in the measured data. This means that the power-law model with corrections can be applied to annular flow with reasonable accuracy.

It is believed that the difference between the trends for the predicted and measured data was caused by imperfect fitting of the power-law model with the data from rheological measurements.

Pump pressure

Pump pressure is the sum of friction pressure losses in the drillstring, annulus, and surface pipe system, plus the pressure drop at the drill bit. Therefore, the error in pump pressure is a combination of errors in the four elements.

Because, in general, pressure drop at the bit and in the surface pipe system can be evaluated fairly accurately, errors in pump pressure consists primarily of errors from friction pressure losses in the drillstring and annulus. This is true for pump pressures predicted from both the Bingham plastic and power-law models (Figs. 5c and 5d).

Fig. 5c shows that the predicted pump pressures with temperature and pressure corrections fall in the middle between the predicted pump pressures without corrections and the measured values over the entire flow rate range. This means that the corrections reduced the errors by 50%.

The comparison of Figs. 3, 5a, and 5c reveals that the remaining 50% of the predicted errors was mostly the result of annular friction pressure calculations. This is because the Bingham plastic model is invalid for annular flow where shear rates are small.

Similar analysis in Figs. 5b and 5d shows that the power-law model was not as effective as the Bingham plastic model in predicting pump pressures and friction pressure losses in the drillstring, especially for high flow rates. This is because the equations correcting the power-law parameters (Equations 3 and 4) do not include a pressure term. Therefore, a better rheological model is as important as temperature and pressure corrections for accurately predicting pump pressure.

Inlet temperature

Without special thermal isolation or heating systems, drillstring inlet temperature generally reflects ambient temperature. If ambient temperature is close to standard temperature, 75° F., the effect of inlet temperature on drilling hydraulics is negligible.

In many cases, however, ambient temperature can vary widely from standard conditions. For example, the temperature in a desert area can be as high as 110° F. during the day and as low as 40° F. during the night. In deepwater drilling, the temperature at the ocean floor may also fall to around 40° F. In these cases, the effect of inlet temperature on pump pressure becomes critical in drilling hydraulics design.

Fig. 6a [14600 bytes] shows the impact of inlet temperature on pump pressure. Above 65° F., drillstring inlet temperature does not have significant effect on pump pressure. Below 65° F., however, pump pressure sharply increases as the drillstring inlet temperature decreases.

A 25° F. decrease in drillstring inlet temperature from 65° F. results in a 1,600 psi increase in pump pressure. In many cases, drilling operations cannot be maintained with a pressure increase of this magnitude. Failing to account for this situation may cause serious downhole problems.

The dependence of annular friction pressure losses on drillstring inlet temperature is shown in Fig. 6b. These data show that a 25° F. decrease in drillstring inlet temperature resulted in a 250 psi increase in annular friction losses. This increase may cause lost circulation in weak formations or formation damage in pay zones.

Equivalent circulating density

Accurately predicting equivalent circulating density (ECD) is important during any drilling operation. Low ECD may lead to gas kicks or even blowouts, while high ECD may result in lost circulation or formation damage.

Because downhole temperatures reduce rheological parameters and friction pressure losses, they further reduce the total pressures and ECD. Fig. 7 [12988 bytes] compares the ECD distributions along the well bore with and without corrections.

For the conditions shown in the figure, the bottom hole ECD with corrections was 11.70 ppg, which is very close to the actual ECD calculated with the measured bottom hole pressure of 11.68 ppg.

The ECD without corrections, however, was 12.00 ppg, which is 0.32 ppg higher than the actual value. This is equivalent to a 182 psi difference in bottom hole pressure.

In practice, this overestimation of ECD may cause field engineers to prepare a mud much lighter than actually required. This may explain why gas and oil kicks are a common problem with oil-based muds.

Drilling hydraulics

The purpose of drilling hydraulics design is to determine optimum pump rate, maximum bit hydraulic horsepower or jet impact force, and optimum total flow area or bit nozzle size.

To analyze the effect of temperature and pressure on these parameters, the plastic viscosities and yield points obtained from Oilmud were averaged along the circulation path. These averaged values were then input into Hydmod.

Table 2 [42402 bytes] lists the optimum values with and without corrections. Mud density was assumed to be constant. Results from Oilmud showed that mud density did not change significantly along the well bore.

As shown in Table 2, temperature and pressure effects will allow drilling engineers to increase the total flow area, optimum pump rate, jet impact force, and bit horsepower by about 10%. This means that with the same pump and pump rate, the jet impact force can be increased by about 10% when temperature and pressure effects are considered. This increase can significantly improve bottom hole cleaning efficiency as well as increase penetration rate.

As mentioned earlier, temperature and pressure effects only account for 50% of the predicted errors. The other 50% was caused by an improper rheological model.

If both error sources are considered, the designed drilling hydraulic parameters with conventional methods can be 20% off their optimum values.

Acknowledgments

The author thanks John Cohen and Greg Deskins of Maurer Engineering Inc. for their help in preparing this article.

References

1. 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. IADC/SPE 35057, IADC/SPE Drilling Conference held in New Orleans, Mar. 12-15, 1996.

2. Growcock, F.B., and Frederick, T.P., "Operational Limits of Synthetic Drilling Fluids," SPE Drilling and Completion, September 1996.

3. Politte, M.D., "Invert Oil Mud Rheology as a Function of Temperature and Pressure," Paper No. SPE/IADC 13458, SPE/IADC Drilling Conference, New Orleans, Mar. 6-8, 1985.

4. Peters, E.J., Chenevert, E.J., and Zhang, C., "A Model for Predicting the Density of Oil Muds at High Pressures and Temperatures," SPE Drilling Engineering, June 1990.

5. Houwen, O.H., and Geehan, T., "Rheology of Oil-Based Muds," Paper No. SPE 15416, SPE Annual Technical Conference and Exhibition held in New Orleans, Oct. 5-8, 1986.

Bibliography

1. Raymond, L.R., "Temperature Distribution in a Circulating Drilling Fluid," JPT, March 1969.

The Author