LIMESTONE, SHALE PENETRATION RATE EQUATIONS DEVELOPED

Mohammed E. Osman
United Arab Emirates University
Abu Dhabi, U.A.E.

Sabry A. Mohammed
Cairo University
Cairo

Increasing rotary speed has a greater effect on increasing rate of penetration in Abu Dhabi shales and limestones than other drilling parameters, including various mechanical and hydraulic factors.

The graphical presentation of drilling parameters and penetration rate data found that rotary speed is the most important factor in controlling rate of penetration.

Constants for the penetration rate equations were developed from a least square analysis of empirical data. The formulas and design charts can help drilling engineers in predicting the drillability of different formations in the Abu Dhabi Emirate.

The drilling parameters used in the study included formation depth and characteristics, penetration rates, weight on bit, rotary speeds, pump pressures, mud pump dimensions, bit conditions (type, diameter, nozzle configuration), and drilling fluid properties.

Drilling costs are mainly affected by rate of penetration, which is consequently affected by numerous controllable and uncontrollable factors.

A rigorous analysis of drilling rates is complicated by the difficulty of completely isolating the variables under study. Also, interpretation of field data may involve uncertainties because of the possibility of undetected changes in rock properties.

The rate of penetration varies inversely with the compressive strength of the rock drilled.1 The proper choice of bit type for a given formation plays an important role in obtaining the lowest drilling cost.2

Generally, field data indicate that drilling rate increases as rotary speed increases, but the higher the rotary speed the smaller the incremental response.

The mechanical factors of bit weight and rotary speed are linearly related to drilling rate provided that the hydraulic factors are in proper balance to ensure proper cleaning of the hole.3 4

Also, field data indicate that bit hydraulic horsepower is an unimportant variable as long as adequate bottom hole cleaning is provided.5 Proper nozzle configuration and bottom hole pressure reduction because of upward angled jets may contribute to cleaning the hole.6

The ratio of cuttings mass-flow rate/mud-mass flow rate is strongly dependent upon Reynolds number, nozzle height above the bottom of the hole, and cuttings density.7 The effects of certain variables (bit weight, rotary speed, and hydraulics) established in the field have shown a good correlation between field and laboratory results.8

Air, gas, and water are the best drilling fluids, but problems arise because those fluids often cannot be used instead of mud. In some cases drilling rates with water have been 5-15 times those with mud.

However, the water-drilled holes were enlarged and irregular.9 The other drilling fluids properties (such as solids content, water loss, pressure gradient, viscosity, and gel strength) also have an effect on drilling rates.10-12 Further studies presented mathematical models which describe the effect of one parameter or another or combination of them on the penetration rates.13-17

El-Nadi and Osman determined a drilling equation which represents the combined effect of various parameters on penetration rate (Equation 1).17 This equation is supplemented by Equation 2 which calculates the reduction in penetration because of the dullness of the drilling bit (dR).17

The shearing stress of various rocks was found between the following limits:18

Tp = To + 0.9 Pc

and

Tp = To + 2Pc

The value of Pc, the effective confining pressure in psf, is taken as 77.76 x depth.

FIELD DATA

Abu Dhabi Co. for Onshore Operations (ADCO) and the former Department of Petroleum (DOP) of Abu Dhabi provided drilling data from 30 wells drilled in six fields in Abu Dhabi Emirate, The fields included Sahil, Asab, Bu Hasa, Zubbaya, Bab, and Ruwais.

The drilling data were correlated to the depth drilled and classified according to lithology, mechanical data, and drilling fluid properties. The records indicated that most of these wells penetrated limestone, shale, anhydrite, marl, basal shale, and dense limestone.

The most common formations penetrated by these wells are shale and limestone.

The bit mechanical data included size, type, running time, depth in, depth out, dullness, and nozzle size. Soft and medium formation bits were the most common types used for drilling both shales and limestones. The bit sizes ranged from 8 1/2 to 26 in., and the maximum depth drilled in these wells was 9,462 ft.

The bits were graded on a conventional sliding scale from zero (sharp, new) to eight (completely dull). Each increment indicates one-eighth fractional wear of the teeth.

The mechanical data also included weight on bit and rotary speed.

The weight on bit ranged from 30,000 to 55,000 lb for drilling limestone and from 32,500 to 60,000 lb for drilling shale. The rotary speed ranged from 70 to 120 rpm for drilling limestone and from 50 to 120 rpm for drilling shale.

ADCO also provided information on circulation pressures and rates as well as mud pump dimensions. Rates of penetration were calculated from bit running time, depth in, and depth out.

The important properties of drilling fluids, such as mud weight, plastic viscosity, solid contents, and water loss, were included in the drilling data. The mud weight ranged from 57 to 75 lb/cu ft, and the plastic viscosity ranged from 8 to 19 cp.

These data corresponded to different values of bit teeth wear.

To take into account the effect of bit teeth wear, a correction for penetration rate is obtained from the use of Equation 2. The value of dR is then combined with the actual field data, resulting in a penetration rate that corresponds to that of a new bit.

Some experimental data had to be obtained for shear strength at atmospheric pressure (po) for both limestone and shale; these data were necessary to calculate the reduction in drilling rates expressed by Equation 2.

ADCO provided eight cylindrical core plugs (two from shale zones and six from limestone zones) for source material for the compressive strength tests. Table 1 shows the results of the failure load experiments on each of the core plugs. The shear strength is equal to one half of the normally applied failure load divided by the cross sectional area of the plugs.

Limestone Samples 4, 5, and 6 had extremely low shear strengths, which may have been caused by some fissures found in the plugs. These results were ignored in the calculations of the average shear strength of limestone.

The average shear strengths were determined from the data in the last column in Table 1: 4.7 x 105 lb/sq ft for the limestone formations and 4.2 x 105 psf for shale formations.

PENETRATION RATE EQUATION

The drilling data were used to evaluate the Constant K and Exponents a, b, and c in Equation 1 for both shale and limestone formations.

Applying the least square method resulted in Equations 3 and 4.17 It should be noted that Equations 3 and 4 are valid assuming that the following have negligible effects on drilling rates:

Variations in mud properties except mud weight and plastic viscosity
Variations in bottom hole assembly, depth, temperature, and characteristics of a particular formation from one well to another
Variations in some unrecorded factors that had only a small effect on penetration rate.

It should be understood that the constant and the three exponents for each equation interrelate in a complex manner. The exponents in these two equations indicate that the effect of rotary speed on drilling rates is high and the effect of weight on bit on drilling rates is low.

Although the exponent of weight on bit is small because of small variations in weight on bit data, the importance of the weight on bit parameter is reflected in each equation constant.

The exponents of the Reynolds number parameter in each equation indicate that bottom hole cleaning was more effective in the shale zones drilled than in the limestone zones.

Fig. 1 presents the drillability of shale and limestone (Figs. 1a and 1b, respectively) as a function of weight on bit for different values of rotary speed and a constant Reynolds number of 10.5

As the weight on bit increases, the drilling rate increases but with decreasing rate of change. Note that the decreasing rate of change is greater for shale than for limestone.

The two graphs also indicate the effect of higher rotary speeds on drilling rate. Higher rotary speeds produce higher rates of penetration.

Fig. 2 shows the correlation between Reynolds number and penetration rate for shale and limestone formations (Figs. 2a and 2b, respectively). For these two graphs, the weight on bit was kept constant at 500 lb/in. The increase in Reynolds number results in an increase in rate of penetration, but with a decreasing rate of change.

As in the case with varied weight on bit, the decreasing rate of change is greater for shale than for limestone.

Bit hydraulics and mud properties, expressed in the form of Reynolds number, have a greater effect in drilling limestone than shale. This indicates that bottom hole cleaning has been more effective while drilling in shale than in limestone.

Equations 3 and 4 have been transformed into the nomographs shown in Figs. 3 and 4, respectively. These nomographs can be used as design charts to help drilling engineers predict the drillability of both shale and limestone. With any three of the four parameters known (weight on bit, Reynolds number, rotary speed, and penetration rate), the fourth parameter can be easily obtained from the design charts.

These two equations were developed to express the drillability of both limestone and shale formations common in Abu Dhabi Emirate. It is recommended to use the two equations for similar zones and within the range of field data used.

ACKNOWLEDGMENT

The authors wish to express their appreciation to ADCO and DOP of Abu Dhabi for providing drilling data and core samples. Also, thanks are extended to Mr. Ahmad Dhaqan for handling numerous computer runs.

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