The correct selection of drilling fluids should be based on the entire mud circuit, encompassing and integrating both rheological and hydraulic criteria during the design phase, instead of delegating a passive role to drilling fluid properties while placing greater emphasis on mud pump parameters.Roberto Maglione, Alberto Guarneri, Giovanni FerrariENI/Agip Division

Milan

Other important constraints, such as borehole wall erosion, drillstring pressure drop, high viscosity values at the wall of the borehole, and low viscosity values at the bit, are not taken into consideration in the mud planning phase, resulting in the inefficient optimization of the above-mentioned parameters.

In this way, the mud engineer should use different approaches than in the past by selecting rheological and hydraulic parameters to improve penetration rates, hole clearing properties, and circuit integrity.

### Parameter integration

The integrated approach often leads to different operational parameters that serve to satisfy all elements composing the hydraulic drilling circuit, resulting in a huge impact on operational activities.An active optimization process, taking into account all the constraints given by the hydraulic circuit during the drilling process, suggests that this approach is very similar to the functionalist processes used in other fields of scientific research, such as life processes. In these cases, all phenomena involved in the process are located and used to solve arising problems in a dynamic manner.

The problems to be solved are always determined by ever-changing conditions of the constraints involved. Thus, an integrated problem-solving approach is needed to evaluate the best solution for all parameters and for every case.

The rheological model used in this approach uses the well-known three constant parameters, valid for pseudoplastic yield fluids, developed by Herschel and Bulkley and already proved to be the best one in terms of easy use and reliability of the results.^{1 2} The mathematical model relating shear stress and shear rate is shown as Equation 1 (see Equations box [49,588 bytes]).

Recent studies proved that for an optimized drilling mud, two of the three constant parameters are a function of the well and formation properties.^{3} The yield point (t_{o}) and consistency index (k) can be evaluated directly from the well-formation system.

Thus, Equation 1 can be rewritten as Equation 2, having a one constant rheological parameter consisting of the flow-behavior index (n).

### Case study

The optimization procedure used in this study and subsequent theories has evolved through the work of many researchers.^{4-10}

The following discussion highlights an example of hydraulic optimization for a 171/2-in. vertical shallow section. All the calculations made for the new procedure are compared to well program data, utilizing a passive checking method for the drilling mud. Input data and the constraints imposed by the surface equipment, consisting of three triplex mud pumps with 61/2-in. liners, are listed in Table 1 [58,622 bytes].

Taking into consideration the safety margin, the maximum allowable annular circulating pressure drop from the 185/8-in. casing shoe to surface was about 1 bar. The mud density (p_{mud}) for the entire section, determined from a pore pressure-vs.-drilling depth calculation, was 1,100 kg/cu m using a drilling mud yield point of about 15.7 Pa using d_{s} = 0.25 in. and a p_{cut} of 2,550 kg/cu m (for nomenclature, see Equation box).

A pump rate of about 4,500 l./min, using two mud pumps at the maximum flow rate was utilized in the study. This provided an environment of laminar flow in the annular sections, excluding the area around the drill collars, while maintaining a concentration of less than 5% drill cuttings from TD to surface figuring for an average penetration rate of about 15-20 m/hr.^{1 11 12}

The planned drilling mud, as determined by the well program, was based on a passive checking method using the following rheological parameters:

tRunning the optimization procedure based on the above input data, the relationship between the rheological parameters of the optimized drilling mud, satisfying all the restrictions imposed by the drilling hydraulic circuit, can be calculated._{o}= 2.05 Pa

k = 1.46 Pa^{*}s^{n}

n = 0.41

### Fluid behavior

Fig. 1 [44,568 bytes] shows the behavior of the consistency index vs. the flow-behavior index at a constant yield point (t_{o}= 15.7 Pa) and flow rate (Q = 4,500 l./min). In this case, the relationship between k and n is well defined by Equation 3.

This means that by keeping the flow rate and the yield point constant, followed by varying the value of the flow-behavior index, one can find the corresponding value of the consistency index by optimizing all the constraints imposed by the drilling hydraulic circuit.

If the selected best rheological procedure is not accurately followed, one or more of the constraints imposed by the circuit will not be satisfied. Thus, it is very important to follow the relationship as dictated by Equation 3 in order to choose the most optimal mud to safely drilling this section.

In reference to Equations 2 and 3, the relationship for this case is shown in Equation 4. Equation 4 only points out the dependence of the shear stress (t) against the shear rate (y) on the flow-behavior index (n).

Fig. 2 [48,720 bytes] shows the rheological behavior-shear stress vs. shear rate-of the planned drilling mud and the optimized drilling mud for two values of the flow-behavior index (n=0.5 and n=0.1).

Figs. 3-6 show the behavior of the most important operational parameters against the drilling depth, from 400 m to 1,200 m TD, for different values of the flow-behavior index of the optimized mud and for the planned mud to be used in the field.

Fig. 3 [69,474 bytes] shows the behavior of the pressure drop inside the drillstring, considering flow for both the planned and the optimized mud at different values of the flow-behavior index. It can be shown that using the planned mud with a pump rate of about 4,500 l./min will produce pressure drop variations between 51.5 bar (bit at the casing shoe) and 87.3 bar (bit at the bottom of the hole).

Using the optimized mud, it can be shown that, more or less, the same pressure drop is given by the value of the flow behavior equal to 0.4, corresponding to a consistency index of the optimized mud of about k=0.622 Pa - s^{n}.

Below this value (for n<0.4), the optimized drilling mud flowing inside the drillstring gives lower and lower pressure drops until it reaches very low values (for n=0.1), varying from 9.3 bar at the casing shoe to 17.5 bar when the bit gets the bottom of the hole.

Since the pressure drop inside the drillstring can normally take a large drop in total circulating pressure, with no positive impact on drilling performance (beyond that of transporting fluids to the bit), it is normal thinking to reduce this pressure as much as possible, for instance by changing drill-bit nozzles, to better exploit the total pressure drop of the circuit. This results in increased hhp at the drill bit.

In this case, an optimized drilling mud, having a flow-behavior index value less than 0.4, becomes acceptable. It can be stated that the lower the flow-behavior index of the optimized mud, the lower will be the pressure loss of the mud inside the drillstring.

Fig. 4 73,729 bytes] shows the behavior of the available bit-pressure drop vs. drilling depth in relation to different values of the flow-behavior index (of the optimized mud), including most of the important optimization procedures used in the practice (for the planned mud).^{11 13 14}

The optimization procedures taken into account are based on the maximum jet impact force at the bit, the maximum hhp at the bit, and the exploitation of the maximum pump pressure/flow rate supplied by the mud pumps.

In reference to Figs. 3-6, New A, New B, and New C were developed by Aadnoy as a generalization of two theories based on the maximum hhp at the bit and the maximum jet impact force.^{15} Max P/Q is a method that exploits the maximum available pump rate and pressure supplied by the mud pumps.^{15}

Looking at Fig. 4, it can be shown that the available pressure drop at the bit, considering the planned mud, is minimal using the optimization methods such as New A, New B, New C, and the maximum jet impact force. Using the maximum hhp at the bit method, the pressure drop increases until it achieves the maximum using the maximum pump pressure/flow rate supplied by the mud pumps (Max P/Q), reaching a value of about 181.4 bar.

As far as the optimized mud is concerned, the lower values of the available pressure drop at the bit can be found for high values of the flow-behavior index, until they reach values of about n=0.4, approaching that of the Max P/Q method (about 180.8 bar).

Maximum values are reached for flow-behavior index less than 0.4 to a high of n=0.1 at about 252.7 bar. In this case, it can be asserted that optimized drilling mud, having a flow-behavior index value less than 0.4, provides the best performances in terms of available pressure drop at the bit. In other words, the lower the flow-behavior index of the optimized mud, the higher will be the fraction of the total circulating pressure drop of the circuit spent at the drill bit.

### Fluid flow behavior

Fig. 5a [143,731 bytes] shows the behavior of the hhp at the bit vs. drilling depth for different values of the flow-behavior index (optimized mud) and for the more important optimization procedures used in the practice (planned mud).In this plot, it can be shown that the hhpbit, considering the planned mud, is very poor using Aadnoy's methods (New A, B, and C), fairly poor for the method based on the maximum jet-impact force, slightly higher for the method based on the maximum hhp, and quite high at for the maximum pump pressure/flow rate supplied by the mud pumps (Max P/Q).

Considering the optimized mud, one can see high values for the upper values on the flow-behavior index and even higher hhpbit values for a flow-behavior index greater than 0.4, reaching the highest value of n=0.1 with 2,537.1 hp. In this case, the situation is similar to that shown in Fig. 4.

It can also be stated that the influence of the flow-behavior index of the optimized mud is very high for operational parameters such as hhp at the bit (hhp_{bit}), where the lower value is the flow-behavior index of the optimized mud and the higher value is the hhp at the drill bit.

The increase of hhp_{bit}, and consequently drill-bit jet velocity, inevitably improves the desegregating force of the fluid against the formations at the bottom of the hole. In addition, as the jet velocity increases, the flow of the drilling mud around the bit improves bit cleaning in the area close to the wall of the formation, avoiding problems with bit balling.

All these statements together lead to an increase in penetration rates, becoming more evident in soft formations such as clays and sands than in hard formations such as sandstones and limestones.

Fig. 5b shows the behavior of the hhp/sq in. against the drilling depth for different values of the flow-behavior index (optimized mud) and for the most important optimization procedures used in the practice (planned mud). This figure is similar to Fig. 5a in that the hhp/sq in. is obtained from the hhp_{bit} behavior by simply dividing the hhp_{bit} data by the bottom hole area.

In this figure, it can also be shown that the hhp/sq in.:

- Reaches lower values using the New A, New B, New C, and maximum jet impact force methods
- Reaches medium values for the maximum hhp at the bit method
- Reaches high values of about 7.58 hhp/sq in. for the method exploiting the maximum pump pressure/flow rate supplied by the pump (Max P/Q).

The same consideration can be shown for the previous plots, showing that an optimized drilling mud having a flow-behavior index value equal to or less than 0.4 provides the best performances in terms of hhp/sq in. at the drill bit.

In more general terms, the lower the flow-behavior index of the optimized mud the higher will be the hhp/sq in. at the drill bit. An operational consequence of this result is a higher penetration rate because of the same phenomena discussed with Fig. 5.

### Changes in optimization

Fig. 6 [68,204 bytes] shows the behavior of the apparent viscosity of the drilling mud at the drill bit nozzles vs. jet velocity (flow velocity of the drilling mud at the bit nozzles). It can be shown, considering the planned mud, that as the apparent viscosity decreases, it changes the optimization used for the New C, New B, New A, maximum jet impact force, and maximum hhp methods to a method that exploits the maximum pump pressure/flow rate supplied by the mud pump.In this way, the value of the apparent viscosity varies between 4.357 cp and 1.784 cp. As far as the optimized mud is concerned, the viscosity decreases while the flow-behavior index decreases, passing from a maximum of about 3.815 cp for n=0.70 to 0.045 cp for n=0.10. It can be shown that the minimum value of the viscosity at the bit is obtained for the lowest flow-behavior index value of the optimized mud.

This point is of utmost importance from an operational standpoint. In fact, studies concerning the influence of the apparent mud fluid viscosity at the drill bit report that lowering the mud viscosity at the bit will increase penetration rates in a proportional manner, assuming that all the other parameters-such as formation type, flow rate, geometries, drill bit, weight on bit, and drillstring rotational velocity-remain constant.^{16 17}

Thus, it can finally be concluded that the lower the flow-behavior index of the optimized mud, the lower will be the apparent viscosity of the mud at the drill bit nozzles. From an operational point of view, the lower the apparent viscosity of the mud flowing through the drill bit nozzles, the higher the penetration rates, assuming homogeneous formations and constant drilling parameters.

### Acknowledgment

The authors wish to thank ENI/Agip for permission to publish this article.### References

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- Hemphill, T., Campos, W., and Pilehvari, A., "Yield-power law model more accurately predicts mud rheology," OGJ, Aug. 23, 1993, pp. 45-50.
- Maglione, R., and Romagnoli, R., "The Role of the Rheology Optimization in the Drilling Mud Design," GEAM Bulletin of the Polytechnic of Turin, Vol. XXXV, June-September 1998.
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### The Authors

Roberto Maglioneis a senior R&D drilling engineer working in ENI/Agip's drilling and completion technologies department in Milan. He began working for AGIP in 1988 as a drilling superintendent on both onshore and offshore rigs before joining the research department in 1991. Since 1998, Maglione has worked as a coordinator for the optimization of drilling and completion operations. He has authored over 50 technical papers. Maglione holds an MS in mining engineering from Politecnico di Torino. He is also a registered professional engineer in Italy and an SPE member.

Alberto Guarneripresently works for ENI/Agip R&D in its well drilling and completion operations. He is responsible for underbalanced drilling, drilling, and completion projects. He has a degree in chemistry. Guarneri has worked for Agip since 1977 as a mud and cementing engineer in Italy, Nigeria, and the U.S. He is a co-author of several papers on drilling fluids.

Giovanni Ferrariis presently technical leader for cement, drilling, completion fluids, and relative waste management working for ENI/Agip's drilling and completion technologies department in Milan. He began working for Agip in 1977 as a mud and cementing engineer on onshore and offshore rigs for both domestic and foreign operations. Ferrari holds a BS in chemistry and is an SPE member.

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