Drilling Problems & Drilling Optimization

Drilling Problems & Drilling OptimizationDrilling ObjectivesDrilling Objectives

The goals of any drilling venture are safety, minimized cost and a usable completion. Companies may have different ideas ofhow best to attain these goals, and drilling practices may vary according to location, rig type, hole conditions or other factors.But the goals themselves are always the same.

Safety is the primary concern in drilling an oil or gas well. Protection of personnel supersedes all other well objectives, even when it means altering the well plan, incurring unexpected costs or delaying operations. Failure to make safety the top priorityon a rig can and does result in accidents, disabling injuries and deaths. The second priority in drilling is to protect the well and the surrounding environment. We must anticipate potential problems and include provisions in the well plan for minimizing blowout risks or other dangers, and we must continually monitor operations once the rig moves on location.

Environmental issues are having an ever-growing impact on all oil and gas operations. In California and other parts of the United States, for example, public opposition--usually based on environmental concerns--has curtailed or even halted drillingand production activities. Those projects that are allowed to proceed are governed by a maze of complex regulations, many ofwhich carry severe penalties for non-compliance.

Brown (1992) provides an excellent summary of environmental issues in the petroleum industry. Although his article focuses onU.S. regulations, his basic premise--that environmental management must be an integral part of daily oil and gas operations--applies anywhere. As energy and the environment become matters of public policy throughout the world, the bestthings that engineers or rig supervisors can do are to work closely with their companies' environmental specialists, becomefamiliar with applicable regulations and make sure that their operations are in compliance.

Minimized cost is the basis for most drilling optimization efforts. When looking at this objective, we must consider the total wellcost--it does no good to save money on one procedure if the result is a more expensive well. Effective cost control involves establishing a balance among well objectives. While we should never jeopardize safety in an effort to keep costs down, neither should we spend money unnecessarily. By the same token, while we must provide a usable well, we have to do so within realistic budget constraints.

Whether or not an expense is justified is something the engineer must decide for each well. Intermediate casing strings thatmight be necessary in one field, for instance, may be wasted expenditures in another field. Concentrated well-planning andcareful monitoring of rig operations can reduce costs without compromising safety standards or completion requirements.

A usable completion should be the outcome of any drilling operation, whether the well is a producer, an injector or simply a source of information. Even a safely drilled, low-cost well is not entirely successful if it does not meet the needs that led to it being drilled in the first place. As a minimum standard, a well should have: no irreparable damage to the hole or producing formation ;

a sufficiently large hole diameter for running completion equipment or carrying out other post-drilling activities. We may look at our basic drilling goals from two perspectives: dealing with drilling problems and optimizing normal operations.

A drilling problem is any occurrence or condition that stands in the way of well objectives. It could involve anything from weather to transportation delays to blowouts. In this discussion, we concentrate on problems that occur as part of the drilling process itself.

A comprehensive, thoroughly researched well plan is our best defense against hole problems. Every aspect of the plan, from pre-spud activities to completion procedures, should be designed to anticipate and control these problems. An effective wellplan requires thorough research and data collection, and a careful analysis of these data. Data sources may include:

bit records

mud records

mud logs

IADC drilling reports ("tour sheets")

scout tickets

log headers

production histories

seismic studies

well surveys

geologic contours

databases or service company files

The engineer should use all available sources to identify and plan for potential hole problems. Each source may containimportant information not available elsewhere.

The preparation and effort that goes into well planning should carry over into daily operations. Rig personnel must continuallymonitor drilling performance for early indications of problems and make sure that the appropriate problem-solving tools,materials and technical expertise are either at the rig or available on short notice.

Drilling optimization involves using available resources to minimize overall cost, subject to safety and well completionrequirements. Part of this, of course, entails preventing or successfully solving hole problems. But optimization efforts alsoencompass "normal" operations. The key measure of performance in this area is the cost to drill a given interval.

To optimize drilling operations, we must do three things:

Establish criteria for evaluating drilling performance.

Identify the variables that affect this performance.

Determine how to control these variables to our advantage.

Drilling Rig HydraulicsDrilling hydraulics

When hole problems occur when we are trying to optimize drilling performance we should look first to the drilling mud and the circulating system. This makes sense when we consider that the muds functions include:

controlling subsurface pressures

stabilizing the wellbore

supporting part of the drill string and casing weight

removing and transporting drilled cuttings

suspending cuttings in the annulus when the pumps are shut down

transmitting hydraulic energy to the bit

cooling and lubricating the bit and drill string

minimizing formation damage

collecting formation data

Looking at this list, it is easy to see why most drilling textbooks devote a good deal of discussion to the mud system and rig hydraulics.

Wellbore and Formation Pressure

Drilling mud exerts a hydrostatic pressure (P) that we can describe using the well-known relationship

where r = fluid density

g = acceleration of gravity

h = height of fluid column in wellbore

In field units,

(2)

where P = pressure, psi

MW = mud weight or density, lbm/gal (U.S.)

TVD = true vertical depth, ft

When expressed in SI units (with pressure given in kPa), 0.052 becomes 0.00980.

This hydrostatic pressure, which we control by adjusting the mud weight, is our primary means of counteracting formation, or pore pressure.

Equation 2 is adequate for determining the pressure of a static, homogeneous mud column. In many instances, however, the mud is not static; circulation and pipe movement can significantly affect wellbore pressure. Nor is the mud column necessarily homogeneous; during cementing operations or mud changeovers, for example, the well contains fluids of different densities. To determine the actual wellbore pressure, we have to account for these variables. We can simplify our task by defining equivalent mud weight (EMW) or equivalent circulating density(ECD):

(3)

(4)

where EMW = equivalent mud weight, lbm/gal (U.S.)

ECD = equivalent circulating density, lbm/gal (U.S.)

Pwell = sum of hydrostatic and applied pressures, psi

Pann = the frictional pressure loss in the annulus. This corresponds to the pump pressure minus the pressure losses through the surface equipment, drill string and drill bit.

TVD = True vertical depth, ft

When expressed in SI metric units (with pressure given in kPa), 0.052 becomes 0.00980.

Example 1: Equivalent Circulating Density

Determine the Equivalent Circulating Density and the effective wellbore pressure for the following conditions:

Mud weight = 12.5 lbm/gal

TVD =11,300 ft

Calculated annular pressure loss = 150 psi

Solution:

Pore pressure is normally equal to the formation depth times the pressure gradient of the native formation water:

(5)

where = formation fluid density, lbm/gal (U.S.)

= fluid pressure gradient, psi/ft

TVD = True Vertical Depth, ft

When expressed in SI units (with pressure given in kPa), 0.052 becomes 0.00980.

The fluid pressure gradient g typically ranges from 0.433 psi/ft [9.80 kPa/m] for fresh water to 0.465 psi/ft [10.54 kPa/m] or higher for brine.

Example 2: Determining pore pressure

Determine the pore pressure of the following formation.

Normal pressure gradient = 0.46 psi/ft

Measured depth = 12,500 ft

TVD=10,000 ft

Solution:

In many instances, we may encounter abnormal pore pressures, which deviate from established area trends.

Differential pressure (P) is simply the difference between wellbore an dformation pressure:

(6)

When the wellbore and formation pressures are approximately equal, P is zero. We refer to this condition as balanced ( Figure 1 ).

Figure 1

Example 3: Balancing formation pressure

What mud weight at static conditions is required to balance the formation pressure calculated in Example 2?

(Round up to the nearest 0.1 lbm/gal.)

Solution:

This pressure of 4,600 psi is pushing from the formation to the well. To keep formation fluid from entering the wellbore, the mud column must exert at least 4,600 psi in the other direction -- from the well to the formation. Our required mud weight is therefore:

Balanced drilling with an unweighted mud system is a viable option in areas or depth intervals having well-established pressure trends and little blowout risk. In low-permeability, high-strength formations, operators may even drill underbalanced (P0) to protect against sudden fluid level drops, unintentional mud weight reductions or other circumstances that might decrease wellbore pressure.

In addition, we need a safeguard against abnormal formation pressures. In many areas (e.g., south Louisiana, south Texas, the North Sea, parts of the Middle East), it is not uncommon to see P values on the order of several thousand psi.

Example 4: Differential pressure

Determine the differential wellbore pressure at 15,400 ft TVD on a U.S. Gulf Coast well, where the mud weight is 14.0 lbm/gal and the formation pressure is 7,600 psi.

Solution:

Disadvantages of overbalanced drilling are lower penetration rates and higher mud costs, along with increased potential for formation damage and stuck pipe. Up to a point, this is a fair trade-off, since weighted muds allow us to better control formation pressure and maintain hole integrity. We need to keep in mind, however, that our drilling objectives also include optimizing penetration rates and reducing expenses. We should not compromise these objectives unnecessarily by using heavier muds than safety requires.

Formation fracture gradients define our upper wellbore pressure limit. Exceeding this limit can cause lost circulation, resulting in formation damage and induced fractures. Severe fracturing can cause the wellbore fluid level to drop, thereby creating a blowout risk.

Fracture pressure is related to overburden stress, which is equal to the rock matrix pressure plus the pore pressure:

(7)

where S = overburden stress

= matrix stress at depth of interest

Ppore = pore pressure at depth of interest

Over the years, a number of researchers have developed theoretical methods for determining fracture gradients. Matthews and Kelly (1967), building on the landmark work of Hubbert and Willis (1957), developed the following relationship for sedimentary rocks:

(8)

where frac = fracture gradient, psi/ft [kPa/m]

D = depth, ft [m]

Ki = matrix stress coefficient for the depth at which the value of s would be the normal matrix stress (dimensionless)

Matthews and Kelly based this equation on the assumption that the cohesiveness of a rock matrix is generally related to matrix stress, and thus varies only with the degree of compaction. Their procedure for determining the fracture gradient is as follows:

1. Determine the pore pressure (based on seismic measurements, well log anlaysis or drilling data correlations).

2. Assume a gradient of 1.0 psi/ft [22.62 kPa/m] for the overburden, and calculate the matrix stress s.

3. Determine the depth (Di) at which s would have a normal value, assuming that S=1.0 psi/ft [22.62 kPa/m] and the normal stress gradient equals 0.535 psi/ft [12.10 kPa/m]. Therefore,

(9)

When depth is expressed in meters and s is expressed in kPa, 0.535 becomes 12.10.

4. Using Figure 5 (Matrix stress coefficients of Matthews and Kelly, basd on data from U.S.

Figure 5

Gulf Coast Sands), determine Ki and calculate frac from Equation 8 (note that Figure 5 is empirically generated from field data).

Example 5: Determining fracture gradient

Using the Matthews and Kelly procedure, determine the fracture gradient just below the casing seat for the following Louisiana Gulf Coast well.

Casing set at 6,650 ft TVD

Formation pressure = 3,300 psi

Solution:

In the field, we can estimate the minimum fracture gradient at each new casing point by performing a leak-off test as follows:

1. Close the blowout preventer and apply pressure down the drill pipe in small increments, using a low-volume pump.

2. Continue pumping small volumes of mud until the formation begins to take fluid, or until the pressure reaches a pre-set test limit.

3. Plot pressure versus the pumped volume to determine the initial fracture pressure.

Example 6: Leak-off test-- calculating fracture gradient (after Adams, 1985):

Determine the fracture gradient at a well's casing point (6,750 ft. TVD), given the information in Table 1., below (mud weight = 12.5 lbm/gal).

Solution:

Figure 6 (Results of leak-off test from Example 6) indicates that the formation begins to fracture at an applied pressure of about 820 psi.

Figure 6

The fracture pressure is equal to this applied pressure plus the hydrostatic wellbore pressure:

Volume pumped, bblPressure, psi

00

14

1.5100

2.0190

2.5280

3.0370

3.5460

4.0550

4.5640

5.0730

5.5820

6.0850

6.5880

Table 1: Results of leak-off test.

Buoyancy

An object immersed in fluid is subject to an upward-acting buoyant force, which equals the weight of the fluid the object displaces (i.e., the product of the fluid volume and density). The net effect of buoyant force is that an object submerged in liquid weighs less than it would in air.

In practical terms, this means that a string of pipe in a mud-filled wellbore weighs less than it would if suspended in air, by an amount that corresponds to the weight of the displaced mud. It is important to account for buoyancy effects when calculating hook loads, bit weights, drill collar requirements, casing specifications, rig capacity and other weight-related parameters.

The weight of pipe in a well is equal to its weight in air multiplied by a buoyancy factor (BF):

(1)

The buoyancy factor is a function of the fluid density, and for steel pipe is equal to

(2)

where MW is the mud weight and steel is the density of steel, which equals 65.5 lbm/gal [7860 kg/m3]. Table 2.2 lists buoyancy factors for mud weights ranging from 8.33 to 16.0 pps.

Example 1: Buoyancy effects

Determine the maximum weight-on-bit provided by 450 ft of 7 3/4-inch o.d., 144 lb/ft drill collars for both of the following mud weights. (Assume that all of the drill string compression is in the drill collars.)

9.5 lbm/gal

16.0 lbm/gal

Solution:

MW, lbm/gal[kg/m3]Buoyancy Factor

8.33[1000]0.873

9.0[1078]0.862

9.5[1138]0.855

10.0[1198]0.847

10.5[1258]0.840

11.0[1318]0.832

11.5[1378]0.824

12.0[1438]0.817

12.5[1498]0.809

13.0[1558]0.801

13.5[1618]0.794

14.0[1678]0.786

14.5[1738]0.778

15.0[1798]0.771

15.5[1858]0.763

16.0[1918]0.756

Table 1. Buoyancy Factors for Various Mud Weights (Based on Steel Density of 65.5 lbm/gal [7860 kg/m3])

Rheological Models

Rheology, a term often used in drilling engineering, is the study of the flow or deformation of matter. We generally describe flow or deformation in terms of shear stress and shear rate.

We may best understand these concepts by considering a fluid located between two parallel plates separated by a distance d ( Figure 1 ).

Figure 1

If we apply a force to the upper plate while holding the lower plate stationary, the upper plate attains a constant velocity (v), which depends on the applied force (F), the distance between the plates, the surface area (A) and the fluid viscosity ():

(1)

Shear stress () is equal to the force per unit area,

(2)

while shear rate () is equal to the fluid velocity divided by the distance between the plates:

(3)

These parameters define the flow relationships used to characterize drilling mud behavior: the Newtonian, Bingham Plastic and Power Law models. (A fourth relationship, the Three Parameter model, combines elements of the Bingham Plastic and Power Law models.)

Newtonian fluids exhibit direct proportionality between shear stress and shear rate ( Figure 2 ):

Figure 2

(4)

The proportionality constant () is the fluid viscosity. Although this model has often been used to describe drilling fluid behavior, it is an oversimplification; most drilling fluids do not exhibit this straight-line relationship.

A common method for describing the shear stress/shear rate relationship is the Bingham-Plastic model ( Figure 3 ):

Figure 3

(5)

where

p = plastic viscosity (PV), cp

y = yield stress or yield point (YP), lbf /100 ft 2 (1.0 cp = 0.001 Pa-s; 1 lbf /100 ft 2 = 0.4788 Pa)

Note that a certain initial pressure is required to initiate fluid movement, and that the mud's circulating pressure depends on the initial yield point and the plastic viscosity. We can determine these quantities using a rotational viscometer and the following equations:

(6)

(7)

where 600and 300 = the viscometer readings at rates of 600 and 300 RPM, respectively, and PV is given in cp.

The Bingham Plastic model thus depends on a linear relationship (the difference between the two viscometer readings) to describe drilling fluid flow. Although widely used, its application to turbulent flow conditions, where fluid behavior deviates from linear relationships, is limited.

The Power Law model is a non-linear relationship, which is more descriptive of real drilling fluid behavior ( Figure 4 ):

Figure 4

(8)

where (9)

n = flow behavior index = 3.32 x log( 600/300) (10)

While it is more realistic than the Bingham Plastic model, the Power Law model is also more complex.

Flow Regimes

The flow regimes most commonly encountered in drilling are laminar, turbulent and transitional.

In laminar flow, fluid behaves as a series of parallel layers moving at uniform or near-uniform velocities. There is no large-scale movement of fluid particles between layers. The fluid layers nearest the center of the pipe or annulus generally move faster than the layers adjacent to the hole wall ( Figure 1 , Laminar flow profile in drill pipe/hole annulus).

Figure 1

Turbulent flow is characterized by velocity fluctuations among the fluid stream particles, both parallel and axial to the mean flow stream. These fluctuations break down the boundaries between the fluid layers, resulting in a chaotic flow pattern ( Figure 2 , Turbulent flow in drill pipe and at bit face).

Figure 2

Transitional flow exhibits characteristics of both laminar and turbulent regimes. It describes the often hard-to-define region where flow is neither wholly laminar or wholly turbulent.

(An additional term, plug flow, describes the low-velocity, sub-laminar condition of a fluid moving as a homogeneous, relatively undisturbed body.)

We usually prefer to see laminar flow in the annulus to move cuttings up the hole and prevent erosion. Turbulent flow, on the other hand, is more desirable at the bottom of the hole, because it promotes cleaning and cuttings removal.

While they are conceptually easy to visualize, flow regimes may be difficult to identify. Not only does fluid behavior vary within the circulating system, but we often find that more than one flow regime exists at the same point in the system. For example, while the main flow stream in an annulus may exhibit laminar behavior, the adjacent fluid at the pipe boundary may be in turbulent flow.

The most common method for determining a fluid's flow regime is to calculate its Reynolds number. In its simplest form (i.e., for the case of a Newtonian, non-elastic liquid inside pipe) we may define the Reynolds number as

(1)

where = fluid density, kg/m3

(2)

= inside diameter of pipe, m

= fluid viscosity, Pa-s

For annular flow, the Reynolds number becomes

(3)

where d2 = hole or casing diameter, m

d1 = outside diameter of pipe, m

(4)

The term 0.816(d2-d1) in Equation 3 is the equivalent circular diameter of a slot representation of the annulus (Bourgoyne et al, 1986).

In field units (where is given in lbm/gal, v in ft/s, q in gal/min, d, d1 and d2 in inches and in cp), Equations 1 through 4 become:

(Pipe flow):

(5)

(6)

(Annular flow):

(7)

(8)

As a general guideline, Reynolds numbers of less than 2,100 indicate laminar flow, while Reynolds numbers greater than 4,000 indicate turbulent flow. Between these values, flow is considered transitional.

In field applications, we identify flow regimes by determining the critical Reynolds number or critical velocity (vc) at which flow changes from laminar to turbulent. For example, we may calculate vc and compare it to the actual fluid velocity (v). If vc < v, flow is laminar, while if vc >v, it is turbulent. Because the transition between laminar and turbulent flow may not be clear-cut, it often becomes necessary to calculate a range of critical velocities to determine the flow regime.

Example 1: Flow regimes

A 10.5 lbm/gal drilling mud with a viscosity of 30 cp is circulating at 250 gallons per minute in an 8 3/4 inch diameter wellbore. Determine the flow regime inside 4.5 inch o.d., 16.60 lb/ft drill pipe (3.826 inch inside diameter), and in the drill pipe/hole annulus. For this example, assume that the mud behaves as a Newtonian fluid.

Solution:

Drill pipe:

NRe > 4,000 Turbulent flow

Annulus:

NRe < 2,100 Laminar flow

Unfortunately, determining flow regimes is seldom this straightforward. Laminar flow has been observed under controlled conditions for Reynolds numbers as low as 1200 and as high as 40,000 (Bourgoyne et al., 1986), although we do not usually encounter such extremes in drilling operations.

Bingham Plastic Fluids

We can modify Equations 5 and 7 for Bingham-Plastic fluids by defining an apparent viscosity to account for the yield point and plastic viscosity:

(Pipe flow) (9)

(Annular flow) (10)

where a = apparent viscosity, cp

PV = plastic viscosity, cp

YP = yield point, lbf /100 ft2

d = inside pipe diameter, inches

d2 = hole or casing diameter, inches

d1 = outside pipe diameter, inches

v = average velocity, ft/s

When Equations 9 and 10 are expressed in SI units, 6.66 becomes 0.1669, and 5 becomes 0.1253.

Thus, for Bingham-Plastic behavior,

(Pipe flow) (11)

(Annular flow) (12)

Using these equations, the criterion for turbulence is the same as for Newtonian fluids, with laminar flow occurring below a Reynolds number of 2100.

Power Law Fluids

For power law fluids, we may use correlations developed by Dodge and Metzner (1959):

(Pipe flow): (13)

(Annular flow): (14)

where n = flow behavior index (dimensionless)

K = consistency index (dimensionless)

r = fluid density, lbm/gal (U.S.)

v = fluid velocity, ft/s

d2 and d1 are expressed in inches

When expressed in SI units, Equations 13 and 14 become

(13 SI)

(14 SI)

The turbulence criterion for power law fluids is based on a critical Reynolds number ( Nrec ), which depends on the value of the flow behavior index. A simple equation for estimating the critical Reynolds number at the upper limit of laminar flow is

(15)

For the region between transitional and turbulent flow, the critical Reynolds number is

(16)

System Pressure Loss

For mud to flow through the circulating system, it must overcome frictional forces between the fluid layers, solid particles and pipe or borehole walls. The mud pump or standpipe pressure corresponds to the sum of these forces:

(1)

where Ppump = mud pump pressure

Psurf = pressure loss through surface equipment

Pds = pressure loss through drill string

Pbit = pressure loss through bit

Pann = pressure loss in annulus

Pressure losses are functions of circulation rate, mud weight, viscosity, pipe diameter and hole diameter. The maximum amount of friction loss that we can overcome is limited to the working pressure of our mud pumps.

The general procedure for calculating system pressure losses is as follows:

1. Determine the fluid velocity (or Reynolds number) at the point of interest.

2. Calculate the critical velocity (or Reynolds number) to determine whether the fluid is in laminar or turbulent flow.

3. Choose the appropriate pressure loss equation. (The choice depends on which rheological model and flow regime apply to the point of interest).

Note: In the field, determine both the critical and the actual flow velocities. If vc