Drilling Hydraulics Paper - Shashwat (PE14M013)

DRILLING HYDRAULICS - CALCULATIONS AND OPTIMIZATION Shashwat Sharma Indian Institute of Technology, Madras Chennai, India

ABSTRACT The hydraulics system plays an active role during the drilling operations; so its proper design and maintenance can accelerate the drilling effort and lower the overall well cost. This paper discusses the relevance of the hydraulics system in the optimization of the drilling operations, in the enhancement of penetration rate and reduction in system pressure losses to allow more ‘useful’ pressure loss to occur across the bit. The major requirements of the drilling hydraulics system are discussed, along with the major considerations in each application. A review of commonly used rheological models has been done, with introduction of two recent and more novel rheological models – Herschel-Bulkley and Casson models. Impact of choice of the rheological model on the hydraulics calculations is studied. Finally, a summary of the procedure that is followed during the calculation and optimization of hydraulics parameters is discussed via equations.

Drilling hydraulics reflected by fluid flow and pressure response is a key parameter in the well construction process. It is a factor that is continuously present during drilling and tripping operations. Special attention needs to be paid to the optimization of drilling hydraulics in highly inclined and extended reach wells where stuck and lost pipe situations maybe encountered more easily and frequently.

INTRODUCTION The hydraulics system is the mud system in the wellbore when it is in either a static or a dynamic state. The static system occurs when the mud stands idle in the well. The dynamic state occurs when the mud is in motion, resulting from pumping or pipe movement. The hydraulics system serves many purposes in the well. Since it is centered on the mud system, the purposes of mud and hydraulics are often common to each other. Some of these objectives are listed below:      

Control subsurface pressures Provide buoyancy to drill string and casing Cuttings removal from below the bit Increase penetration rate (ROP) Control surge pressures created during lowering pipe into the well Minimize swab pressures generated during pulling out pipe from the well

The hydraulics system consists of a non-Newtonian suspension (drilling mud) circulated from surface to the bottom hole through the drill column, flowing through the bit nozzle restrictions and returning to surface in the annular region between the borehole and drill column (Figure 1).

FIGURE 1: SCHEMATIC OF THE CIRCULATION SYSTEM; P1 - P5 INDICATE PRESSURES AT NODES

PRESSURE LOSSES The circulating system can be divided into four sections for nodal analysis – surface connections (including standpipe, rotary hose and swivel), tubulars (including drill pipe, heavyweight drill pipe and drill collars), annular areas around the tubular regions, and the drill bit. Hydraulics calculations for drilling aim to calculate the pressure (energy) losses in every part of the circulating system and then find the total system losses. This will then determine the pumping requirements from the rig pumps and in turn the horsepower requirements.

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1.

Surface connection losses: These pressure losses are determined by converting the range of lengths and OD’s of surface equipments such as standpipe, rotary hose, swivel and Kelly to an equivalent length and then using the following general equation to evaluate the pressure loss:

1.

Sufficient cuttings entrainment along the annulus 

Uniform annular velocity profiles:  If turbulent, velocities are constant but two difficulties appear: shear stress close to the wall of the borehole is too high (dangerous for the wellbore stability in soft formations), and pressure circulation losses are high.  If laminar, velocities profile depends on rheological model.



Annular velocity vs. cuttings sedimentation velocity: Annular velocity greater than sedimentation velocity of cuttings is required to prevent balling up or stuck pipe incidents. The cuttings’ sedimentation velocity depends on cuttings density, cuttings shape, cuttings dimensions, mud density, viscosity and rheological characteristics.

(1) where, P1 = pressure loss (psi) E = constant 2.

Pipe and Annular losses: These pressure losses take place due to frictional drag between the pipe material and fluid. The magnitude of these pressure losses depends upon:   

Tubular dimensions (length, OD, ID) Mud rheological properties (density, plastic viscosity and yield point) Type of flow (laminar or turbulent)

2.

Wellbore stability 

Minimum shear stress along borehole wall: Shear stresses close to the wall of the borehole can erode it and cause caving. It strongly depends on the velocity gradient, function of the mud annular velocities curve. Laminar flow regime induces lower velocity gradients and thus lower shear stresses. So, it's recommended, in soft sedimentary formations, to keep a laminar flow regime inside the annulus.



Annulus pressure vs. formation breakdown pressure: The annulus pressure is composed by the static pressure (function of mud density and of depth), and dynamic pressure (function of pressure circulation losses (depending on mud characteristics, annulus dimensions, depth, and mud flow rate). Any increase in this total pressure above the breakdown pressure of the formation will result in leak-off problems.

Out of the above three factors, the choice of model used to characterize the drilling mud, viz. Power law, HerschelBulkley, Bingham plastic etc. has a major effect upon the pressure loss determined from the conventional equations. 3.

Drill bit losses: Drill bits are provided with nozzles to provide a jetting action required for cleaning and cooling. More often, the nozzles used are a fraction of an inch. Hence, the pressure requirements to pass, say 1000 gpm, through such small nozzles are large. The pressure loss across the bit is greatly influenced by the sizes of nozzles used, and volume flow rate. For a given flow rate, smaller nozzles lead to greater pressure drop and, in turn, a greater nozzle velocity. The pressure drop across the bit is obtained by subtracting Pc (= P1 + P2 + P3 + P4 + P5) from the pump pressure. Drilling hydraulics optimization usually refers to optimization of the bit hydraulics to achieve maximum bit penetration rate through the formation. This can be obtained by increasing mechanical parameters (weight-onbit and rotating speed) and hydraulic parameters. Procedures followed for maximizing bit horsepower, jet impact, and bit nozzle velocity are those presented by Kendall and Goins1 and later modified by Bobo2. These are discussed later using relevant equations.

3.

Optimum bit performance The mud flow rate must be sufficient to cool the bit to temperatures that allow extended functional life at bottomhole drilling conditions. In addition to it, it's important the mud flow rate is sufficient to carry up all cuttings drilled. The cuttings discharge depends on the rate of penetration, the drilled cross-section area (R).

MAIN REQUIREMENTS OF DRILLING HYDRAULICS Drilling parameters such the annulus dimensions, the drilling mud characteristics and the mud flow rate have to be chosen in order to ensure:

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Minimum circulation power consumption

It's important to minimize pressure circulation losses, in order to minimize power consumption. It depends on the mud density, friction factor coefficient, annular velocity and tubular dimensions, including eccentricity. A large Yield stress (in laminar regime) strongly increases the losses if annulus clearance is small. This ratio "YP/Aannulus" is an important parameter about circulation losses and can explain main differences observed between conventional and slim hole drillings. It's possible to define the optimized annulus dimensions to avoid too important pressure losses for a maximum mud flow rate given (by an economic ROP). The rapidity with which chips or cuttings are removed has a considerable effect on ROP. It is the mud velocity that chiefly governs this factor. Figure 2 shows ideally the velocity profiles in the annulus. In laminar flow, there is a much larger velocity variation across the annulus than in turbulent flow. In turbulent flow, overturning effect of flattish chips will not occur due to a much more gradual variation of velocity across annulus width. It has, thus, been concluded (Williams and Bruce3) that low viscosity, low gel strength muds are most efficient cutting lifters since the velocity at which turbulent flow occurs for these muds is lower. Turbulent slip velocities used by Williams and Bruce are determined from the following equation:

DRILLING MUD RHEOLOGICAL MODELS Most drilling fluids are non-Newtonian suspensions exhibiting a characteristic rheogram response. Regular rheological measurements in drilling rigs are made by a coaxial cylinder viscometer at two different speeds (300 and 600 rpm) which only represent the high shear rate region. Since drilling fluids are subjected to very different shear rates, from very low values in the mud pits to very high values through bit nozzles, the rheological parameters estimate based only on two measurements will lead to significant imprecision such as yield point overestimation. Rheological models are useful tools to describe mathematically the relationship between shear stress and shear rate of a given fluid. Traditionally, the oil industry uses the Bingham and Ostwald de Waele models. However, more realistic models have been proposed to represent more adequately the behavior from rheogram. We also consider two other rheological models: Casson and Herschel-Bulkley.

(2) where, vc = cutting clip velocity in turbulent flow (ft/min) tc/dc = thickness to diameter ratio of cutting

FIGURE 3: FLUID RHEOGRAM FOR DIFFERENT MODELS

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Bingham Plastic model: This model describes laminar flow using the flowing equation: (3)

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Ostwald de Waele model: This is essentially a Power law model which provides greater accuracy in determination of shear stresses at low shear rates. The following relation is followed: (4) where, K = Consistency index N = Power law index The “K” value is a measure of the thickness of the mud. It is defined as the shear stress at a shear rate of one reciprocal second. An increase in the value of 'K' indicates an increase in the overall hole cleaning effectiveness of the fluid.

FIGURE 2: COMPARISON OF LAMINAR AND TURBULENT VELOCITY DISTRIBUTIONS IN ANNULUS (AFTER WILLAMS AND BRUCE)

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The value of constant ‘n’ indicates the degree of nonNewtonian behavior over a given shear rate range. If 'n' = 1, the behavior of the fluid is considered to be Newtonian. As 'n' decreases in value, the behavior of the fluid is more non-Newtonian and the viscosity will decrease with an increase in shear rate. 3.

Casson model: This model considers the variation of shear stresses with the square roots of shear rate and Yield stresses in a fluid under laminar regime. The relation is as follows:

(5) 4.

Herschel – Bulkley model: It is a Yield – Power law model which uses a Yield stress value in addition to the Power law relation to describe the rheological behavior more accurately than any other model:

(6) The model is very complex and requires a minimum of three shear stress/shear rate measurements for a fluid. It, however, can be reduced to the Bingham Plastic model when n ≈ 1 or to the Power law model when τ0 = 0. However, as already discussed, the first two models tend to represent inaccurately the drilling fluids behavior, especially at medium and low shear rate ranges. Casson model can surpass this shortcoming, but it’s a two parameter model that is somewhat simplistic in nature for oilfield applications. The Herschel-Bulkley model presents more adequate rheological parameters as compared to traditional calculations involving Newtonian shear rates. However, the most adequate model for a particular application is always determined by the minimum standard error deviation value for the experimental results.

For a given length of drill string (drill pipe and drill collars) and given mud properties, pressure losses P 1, P2, P3, P4 and P5 (Figure 1) will remain constant. However, the pressure loss across the bit is greatly influenced by the nozzle size, which directly needs to reflect the cleaning requirements and chip transport requirements from the drilling mud. Features such as extended nozzles and varying the number of nozzles have been shown to affect drill rate. Attempts have been made to optimize certain bit hydraulics variables to cause perfect cleaning. The variables most commonly optimized are impact force, hydraulic horsepower, or jet velocity. Each optimized variable yields different values of bit pressure drop and, in turn, different nozzle sizes. Thus, it’s a difficult engineering decision over which criterion should be used and optimized. Moreover, in most drilling operations the flow rate for each hole section has already been fixed to provide optimum annular velocity and hole cleaning. This leaves only one variable to optimize: the pressure drop across the bit, Pb. Both criteria are directly dependent on the bit friction loss, and consequently maximum bit friction loss is desired. The bit friction loss is calculated by the following equation:

(8) where ∆Pparasite is the energy dissipated by fluid circulation through the drilling column and the annular region. Since the surface pressure is limited by pumping equipments, the maximum bit pressure loss can occur when ∆P parasite is minimized. The two criteria most commonly used are maximum bit hydraulic power and maximum jet impact force. These are discussed below: 1.

Bit Hydraulic Power: The general relation for hydraulic power can be written for the drill bit as:

(9) Using calculus, the equation relating surface (pump) pressure and bit pressure loss can be optimized to show that:

HYDRAULICS CALCULATIONS Drilling hydraulics aims to maximize the rate of penetration of the bit through the formation. To optimize hydraulics the pressure relationships throughout the well must be defined. A nodal analysis of pressure at different points in the circulating system gives us the following relation:

(10) where ‘m’ is the flow exponent, with values between 1.75 to 2. Keeping m=2 on a conservative approach, it can be seen that:

(7) where, Pp = Pump pressure PF = Sum of all pressure drops except bit loss ∆Pb = Bit pressure loss

(11)

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In other words, for optimum hydraulics, the pressure drop across the bit should be 65% of the total available surface pressure.

2. Jet Impact Force: The general relation for jet impact force for the drill bit can be written as:

(12)

It has been generally agreed in the literature that better hydraulics increases the penetration rate by cleaning the hole bottom to prevent regrinding of cuttings. In addition, increased weight and rotary speed may be applied to the bit before bit balling occurs. However, since the rate of bit wear increases as bit weight and rotary speed increase, there exists an optimum weight and rotary speed even in a perfectly clean hole. Once the optimum cleaning needs have been obtained, there is no additional advantage to a further increase in hydraulics.

Using calculus, the descriptive equation for impact force by the jet can be maximized and resolved as:

(13) With the value of ‘m’ as 2, the relation reduces to:

(14) This implies that 50% of the pump pressure must be expended at the bit for optimum impact conditions. The optimum flow rate for both criteria must be searched inside a range defined by the minimum flow rate required to transport the solids cut by the bit to the surface and the maximum allowed by the pumping equipment. The optimum flow rate corresponds to either the maximum hydraulic power or impact force. Once calculated the optimum flow rate, the bit nozzle diameters are calculated by:

FIGURE 4: BIT HYDRAULIC POWER OBTAINED BY MAXIMUM EQUIPMENT AS COMPARED TO CONVENTIONAL JET PROGRAM (AFTER KENDALL AND GOINS)

(15)

The nozzle velocity (in ft/s) is given by:

(16)

SUMMARY OF PROCEDURE FOR HYDRAULICS CALCULATIONS The procedure for calculating the various pressure losses and hydraulics parameters for a circulating system is summarized below:

The total flow area from the nozzles (in sq. inches) is given by:

1. 2.

(17)

3.

The main advantage of the jet bit is its higher efficiency in removing rock cuttings from the hole. In order to utilize the full potential of the jet bit, a proper nozzle size and pump pressure must be used. Figure 3 illustrates the large increase in bit hydraulic power that can be achieved by the selection of a proper hydraulics program of bit nozzle size and pump operating conditions. Large increases in penetration rate and thus decreases in the cost per foot of hole drilled have been achieved through optimizing bit hydraulics.

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Calculate surface pressure losses using equation (1). Determine the rheological model that suits the condition under study most adequately – Bingham Plastic/Power law/Herschel-Bulkley. Calculate the pressure drops inside the drill pipe and drill collars:  Calculate critical flow velocity (vcritical)  Calculate average flow velocity (vavg)  Determine whether flow is laminar or turbulent:  If vavg < vcritical - flow is laminar  If vavg > vcritical - flow is turbulent  Use appropriate equation to calculate pressure drop.

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5. 6. 7.

Divide the annulus around drill collars and drill pipe into open and cased sections and calculate annular flow for both cases. Add the values for pressure losses obtained from above steps. This is termed system pressure loss. Determine the pressure drop available for bit using equation (8). Determine the nozzle velocity, nozzle size and total flow area using equations (15) through (17).

CONCLUSION There is considerable potential for performing much of the drilling operations more efficiently. This would imply lower cost and better use of available energy. Drilling hydraulics is the key area of focus when it is required to optimize the penetration rate into the formation, eliminating lost time to the greatest possible degree by maximizing cutting removal and improving energy dissipated at bit for rock removal. Hydraulics calculations are rooted in accurate determination of rheological models. However, as the mud is subject to a wide range of shear rates during circulation, it is imperative to perform specific non-linear regression numerical methods so that shear stress vs. shear stress behavior is more representative. In addition to this, it must be stressed that simplified formulations must not be used which restrict hydraulics calculations to inaccurate values. More realistic rheological models and friction loss prediction correlations must be used for this purpose.

REFERENCES 1. Kendall, H. A. and Goins, W. C., Jr.: “Design and Operation of Jet Bit Program for Maximum Hydraulic Horsepower, Impact Force, Jet Velocity”, Trans., AIME (1960) 219, 238. 2. Bobo, R. A.: “Application of Hydraulics to Rotary Drilling Rigs”, presented at 1963 Spring Meeting of API Division of Production Southern District, New Orleans, Louisiana. 3. Williams, C.E., Jr., and Bruce, G.H.: “Carrying Capacity of Drilling Muds”, Trans. AIME, Vol. 192, (1951), p. 111. 4. Kendall, H. A. and Goins, W. C., Jr.: “How Drilling Rate is affected by Hydraulic Horsepower”, Oil and Gas Journal, (1972). 5. Bourgoyne, A.T., and Kimbler, O.K.: “A Critical Examination of Rotary Drilling Hydraulics”, Society of Petroleum Engineers of AIME, Dallas (1969) 6. Bourgoyne. Jr., A.T., Chenevert, M. E., Milheim, K.K. and Young Jr., F. S., “Applied Drilling Engineering”, S.P.E. Print., Richardson, Texas, USA. (1986). 7. De Sa, C.H.M., Martins, A.L., and Amaral, M.S.: “A Computer Programme for Drilling Hydraulics Optimization Considering Realistic Rheological Models”, Society of Petroleum Engineers paper 27554, presented at European Petroleum Computer Conference, Aberdeen (1994) 8. Rabia, H “Rig hydraulics” Textbook, Entrac (1989)

NOMENCLATURE ROP O.D. I.D. ρm ρc Q PV, µp P τ τ0 γ

= rate of penetration (ft/s) = outer diameter (in.) = inner diameter (in.) = mud density (ppg) = cuttings density (ppg) = mud flow rate (gpm) = plastic viscosity (cP) = pressure (psi) = shear stress (lb/100ft2) = Yield point (lb/100ft2) = shear rate (s-1)

Cd Q

= nozzle discharge coefficient = mud flow rate (gpm)

dj nj vn vcritical vavg

= nozzle diameter (in.) = number of nozzles = nozzle velocity (ft/s) = critical flow velocity (ft/s) = average flow velocity (ft/s)

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