Estimated Volumes for Discharge of Whole Drilling Mud

8/12/2019 Estimated Volumes for Discharge of Whole Drilling Mud

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2 SPE 8669

Discharge Volumes. An estimate of the cuttings volume is

made using the well plan (drill bit diameters and interval

lengths) and an estimated amount of washout, i.e., the increase

in hole volume over that predicted by bit diameter and holelength. Estimates of washout can be obtained from experi-

enced drilling personnel based on the type of formation drilled

and the type of drilling fluid used.

Estimated volumes for discharge of whole drilling mud

solids (only WBM discharged) can be made using the mudplan. The mud plan is developed prior to drilling and should

include estimates of the quantity of drilling fluid that will beused drilling the well.

Bathymetry and Model Grid Size. The OOC Model requires

the water depth at the discharge site. For most cases, bathym-

etry data within 1 km of the well site are sufficient. Detailedbathymetry data are not necessary unless there are significant

bathymetry changes near the well. A flat or tilted plane may

describe many sites. The OOC Model can accept detailed

bathymetry data if available.The OOC Model tracks the deposition of solids on the

seabed only within a grid array that is specified by the user.The grid size is limited to 12,100 cells, which allows a squaregrid of 110 x 110 cells. Grid cells must be the same size,

however, there are no limits on the size of the grid cell.

Specifying a large grid cell to allow large grid array

coverage will limit the resolution of predicted loadings becausethe model provides the total seabed solids loading within a grid

cell (lbs/grid cell). No information about loading variation

within a grid cell is provided.

For most single-well discharges, a grid array that covers 4km2 or less is adequate. A 4-km2square grid allows a 110 x

110 array and approximately 18 m x 18 m grid cells. The grid

array coverage can be increased or decreased in size to match

specific discharge conditions. The predominant current speedsand directions combined with particle fall velocities allows the

user to estimate an acceptable grid array size that will maxi-

mize capture of solids within the grid array while maintaining

acceptable resolution.

Ambient Conditions. The OOC Model requires historic time-

series ambient current profiles throughout the water column for

stochastic modeling. Typically, this data is obtained fromAcoustic Doppler Current Profile (ADCP) instruments placed

near the project area.

The accuracy of model predictions depends on howclosely input current data represents the actual current condi-

tions that occur while drilling. In many situations, only limited

data are available. For discharges into deeper water, it is

important to have current data covering the entire water column

because extrapolating surface currents several hundred meterslikely will result in significant inaccuracies.

In addition, the OOC Model requires either temperature

and salinity profiles or a density profile. These data can beobtained from direct measurements or knowledgeable esti-

mates. The OOC Model will accept time-varying data. In

most cases, however, a single data set is adequate becausechanges in these parameters over time will not significantly

alter seabed-loading predictions.

Discharge rate. The OOC Model requires an estimate of th

discharge rate. The model accepts only a single rate within

run. To simulate changes in the discharge rate, two or mor

model runs are developed with different rates. The predictionfrom the multiple runs are summed to give the overall predic

tion. For most modeling, however, detailed information on th

discharge rate is not available. An average rate based on a

estimate of the volume of discharged solids and an estimate o

the time required to drill the well can be used.

Discharge pipe radius, depth, and orientation. The OOModel requires the discharge pipe radius, the depth of th

discharge pipe opening, the vertical orientation of the discharg

pipee.g., pointing straight down, and the azimuth orientatio

of the discharge pipe.

Discharge duration. The OOC Model requires an estimate o

the discharge duration. An exploration well might require 3

days to drill, however, discharges dont occur over this entir

period. Discharges likely correspond with periods when thdrill bit is advancingperhaps 1/3 of the total drilling time.

Discharge bulk density. The bulk density required by thOOC Model is the density of the material released at th

discharge point. For cuttings discharges, the discharge

usually a combination of the cuttings, associated drilling mu

and the seawater used to avoid plugging the discharge chuteThe discharge bulk density for these discharges can b

estimated by assuming an amount of seawater that will b

discharged with the cuttings. For whole mud discharges,

hole-averaged density can be determined using data in the muplan.

Note that the bulk density primarily influences th

behavior of the plume that develops from the discharge. Fo

surface discharge of cuttings in deep water, the fast fallinparticles exit the plume quickly so that plume behavior doesn

significantly influence the ultimate fate of these particle

Therefore, predictions of cuttings accumulations on the seabe

are not sensitive to the choice of bulk density.

Solids density and volume fraction. The OOC Mode

requires an estimate of the density of the discharged solids an

the volume fraction of the solids in the bulk discharge. Unlessite-specific information is available, 2.65 g/ml (the density o

quartz), can be used for WBM cuttings density. For NAF

cutting discharges, the cuttings contain adhering NAF, whiclowers the average density. Solids density can be determine

using assumed ratios of cuttings, base fluid, and other mu

solids (e.g., barite) adhering to the mud.

The WBM drilling mud solids are either primarily barit(4.3 g/ml), bentonite (2.3 g/ml), or a combination of the two

The volume fraction solids specified should be consistent wit

the discharge flow rate and discharge time to allow complet

discharge of all the solids from the well.

Discharge solids fall velocities. The OOC Model does no

calculate fall velocities from an equation such as Stokes Lawrather it requires specification of particle fall velocities. Th

modeler can estimate fall velocities from particle-size distribu

tions and theoretical (e.g. Stokes Law) or empirical correla

tions. Correlations, however, have limitations. Theoretic


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SPE 86699 3

correlations such as Stokes law are valid over a limited

particle-size range. Users should be aware of the size range

limits and other assumptions of these correlations. Addition-

ally, discharged cuttings and associated drilling mud solids fallas interacting aggregates that can break up or combine such

that the representativeness of velocities developed from

particle-size correlations is questionable. Measured fall-

velocities obtained from column studies may provide more

representative data.Two general categories of cuttings are identified because

of inherent fall velocity differencescuttings from WBMdrilling and cuttings from NAF drilling.

Generally, cuttings generated with WBM have greater

dispersion of fines as they fall in seawater compared to NAF

cuttings. NAF cuttings and associated drilling mud solids,

because they are coated with hydrocarbons, tend to remain asaggregates.

Site-specific fall-velocity data are rarely available. In the

absence of site-specific data, the distributions shown in Table 1

for WBM cuttings and Table 2 for NAF cuttings can be used.Fall-velocity distributions for bentonite and WBM solids are

provided in Tables 3 and 4.

Table 1. Fall Velocity Distribution for WBM Cuttings*Solids

Class

Solids Density

(g/cm3)

Solids Volume

Fraction

Fall Velocity

(ft/sec)

1 2.65 0.04272 4.430x10-6

2 2.65 0.03204 5.530x10-5

3 2.65 0.03738 7.160x10-4

4 2.65 0.01602 7.638x10-3

5 2.65 0.01068 4.748x10-2

6 2.65 0.09612 1.316x10-1

7 2.65 0.08544 3.214 x10-1

8 2.65 0.0801 4.435 x10-1

9 2.65 0.1335 8.522 x10-1

*Data from drill cuttings collected at 2,500 m from a well in the Lower CookInlet, Alaska(7).

Table 2. Fall Velocity Distribution for NAF Cuttings*Solids

Class

Solids Density

(g/cm3)**

Solids Volume

Fraction

Fall Velocity

(ft/sec)

1 1.97 0.0882 1.083

2 1.97 0.0882 1.017

3 1.97 0.0882 0.951

4 1.97 0.0992 0.886

5 1.97 0.0375 0.755

6 1.97 0.0176 0.591

7 1.97 0.0055 0.394

8 1.97 0.0166 0.197*Data from column measurements on cuttings collected in Brazil Campos Basin.

**Density assumes approximately 10% NAF base fluid on cuttings by weight.

Table 3. Fall Velocity Distribution for Bentonite Particles*Solids

Class

Solids Density

(g/cm3)

Solids Volume

Fraction

Fall Velocity

(ft/sec)

1 2.30 0.0007 0.3040

2 2.30 0.0300 0.1720

3 2.30 0.0300 0.0746

4 2.30 0.0250 0.0035

5 2.30 0.0050 0.0007

6 2.30 0.0093 0.0002*Data from column measurements of bentonite particles used in drilling mud.

Table 4. Fall Velocity Distribution for WBM Solids*SolidsClass

Solids Density(g/cm3)**

Solids VolumeFraction

Fall Velocity(ft/sec)

1 3.377 0.00053 3.68x10-2

2 3.377 0.00211 1.40x10-2

3 3.377 0.01016 2.70x10-3

4 3.377 0.01016 2.10x10-3

5 3.377 0.00700 1.68x10-3

6 3.377 0.00700 1.43x10-3

7 3.377 0.00528 9.84x10-4

8 3.377 0.00264 4.86x10-4

9 3.377 0.00422 2.00x10-4

10 3.377 0.00370 8.99x10-5*Data from OOC Model manualBrandsma and Smith, 1999.

**Solids density is an average of bentonite and barite.

Simulation Duration. The OOC Model requires the discharg

duration and the simulation duration as inputs. The dischargduration should be shorter than the simulation duration to allow

time for particles to settle to the seabed.

The time required for slow-falling solids to reach thseabed could be tens to hundreds of hours for deepwate

discharges. Slow falling particles have wide dispersion andunder most current conditions in deep water, insignificaneffect on accumulations near the well site. For deskto

computers, memory and computing time considerations mak

extended duration simulations impractical or inconvenient.

An appropriate simulation duration can be determineusing the solids fall-velocity distributions and the water dept

to calculate the time required for various solids classes to reac

the seabed. Run times should maximize the total amount o

solids reaching the seabed considering memory and computation-time limitations. Note that particles that take tens of hour

to reach the seabed will likely be distributed over a wide are

considering the currents in most environments.

Model Output ProcessingThe OOC Model provides predictions of solids concentration

in the water column and seabed loading. The predictions o

solids concentrations in the water column can be used directl

to generate plots showing, for example, the water columconcentrations versus distance from the discharge point.

Seabed loading as provided by the model (lbs/grid cell)

a parameter that is difficult to interpret. The first step i

processing seabed loading predictions is to convert fromlbs/grid cell to lbs (or kilograms)/unit area using the specifie

grid-cell size. Seabed loading predictions can be further pos

processed to provide more easily understood parameters, sucas seabed accumulation thickness and seabed-sedimen

hydrocarbon concentration. The following discussion presentassumptions and equations to make these conversions.

Drilling Solid Accumulation Thickness. Converting mode

predicted loading to drilling solids thickness improve

comprehension of the magnitude of the accumulations. Severassumptions are required to convert seabed loading to accumu

lation thickness. The primary assumption is that the drillin

solids remain on top of ambient sediments. In reality, th

drilling solids would intermix with ambient sediments.Other important parameters that require assumptions ar

as follows:

The weight percent water in the drilling solids on th

seabed


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4 SPE 8669

The salinity of the drilling solids pore water

The density of the drilling solids pore water

The density of the discharged drilling solids.In the absence of site-specific information, the following

values can be used:

The weight percent water (Ww) in the drilling solids is

30%. The 30% by weight water is based on measure-

ments made on cuttings piles in the North Sea. The salinity of the drilling solids pore water is equiva-

lent to seawater (ppt=35.03 parts per thousand).

The density of the drilling solids pore water is equivalent

to seawater density (seawater=1.02 g/ml).

The density of the discharged drilling solids (solid) is

2.65 g/ml for WBM cuttings. A somewhat lower density

may be needed for NAF-coated cuttings to account forthe adhering drilling fluid.

For a sample area A (see Figure 1), the thickness of drilling

solids over A is

))100(

1(

wseawater

w

solid

solidW

WMT

+= in meters. (1)

where Msolidis the OOC Model-predicted seabed loading,)1000(1 pptppt +=

For a complete derivation of equation (1) see Appendix

A.

T

AmbientSediment

Deposited

Cuttings

Area of surface

A

Figure 1. Schematic diagram used for drilling solids deposition

thickness estimate.

Hydrocarbon Concentration in Seabed Sediments. Thefollowing assumptions simplify conversion of model-predicted

seabed loading to sediment hydrocarbon concentration:

The WBM solids contain no hydrocarbons.

The NAF drilling solids accumulated on the seabed re-

main on top of all drilling discharges.

The ambient sediments contain no hydrocarbons.

The NAF base fluids remain adhered to the NAF cut-

tings.

The deposited hydrocarbons do not degrade over time.

The NAF cuttings includes the cuttings, the base fluidadhering to the cuttings, and the barite in the NAF.

In addition, assumptions must be made regarding the

following:

The thickness of a hypothetical control volume (see Fig-ure 2)a common thickness used for field sampling is

the top 2 cm

The wet-weight percent hydrocarbons adhering to thedeposited NAF drilling solidsan average value for

base fluid retained on cuttings for wells drilled wit

similar cuttings cleaning equipment can be used.

The composition of the NAFthe composition shoul

be based on project-specific mud or, if not available, us

the EPA generic mud from EPA(8)(47% base fluid, 33%

solids as barite, and 20% brine by weight).

The density of benthic sedimentsin the absence o

site-specific data, assume the density is the same as tha

of the WBM drilling solids.

The porosity of the ambient sediments and non-NA

drilling depositsin the absence of site-specific information, a porosity of 0.4 can be used.

The calculation of hydrocarbon concentration in sedimen

is developed using a control volume consisting of an area ACand total thickness TCV. This volume is intended to represen

the sediment material sampled for analysis during a hypothet

cal field sampling operation. The equation to calculat

hydrocarbon concentration in sediments containing NA

cuttings is as follows:For the control volume shown in Figure 2, the hydroca

bon concentration can be calculated using the followin

equation:

lCV MT

xMppmHC

l

)1()(

)101()(

6

+++= (2)

where Ml=the OOC Model-predicted NAF-cuttings anassociated drilling fluid loading

)( SWoilBFoilBF FFFFF =

))100((1 wseawaterwsolid WW +=

)1( pamb =

pSalseawater =

)100( www WWW =

FBF=fraction base fluid in NAF

Foil=fraction base fluid adhering to cuttings

Fseawater=fraction of saltwater in NAFp=porosity of ambient sediments or WBM deposits

Sal=is seawater salinity (kg salt/kg seawater)

SalSal)1( =

For a complete derivation of equation (2) see Appendix A.

T cv

Ambient

Sediment/

WBM

Deposits

Deposited

Cuttings

Area of surface

Acv

TNAF

Figure 2. Conceptual control volume needed for convertin

model-predicted seabed loading to seabed-sediment hydrocarbon concentration. Acv should correspond to the area of

model grid cell as specified in the model input.

Contour Plot Examples. The figures below provide exampleof the type of visuals that can be generated from mode

predictions. The plots were generated from modeling th

surface and seabed discharges of a single exploration well i


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SPE 86699 5

625 m of water. The bathymetry was simulated as a flat plane.

The concentration of base fluid on the cuttings at the seabed

was assumed to be 10%.

-500 -400 -300 -200 -100 0 100 200 300 400 500

Distance East-West (m)

-500

-400

-300

-200

-100

0

100

200

300

400

500

DistanceNorth-South(m)

Figure 3. Thickness contours for the discharge of all drillingsolids in 625 m water. The cross marks the discharge point.

Thickness contours are in centimeters and the maximum

thickness is 57 cm.

-500 -400 -300 -200 -100 0 100 200 300 400 500

Distance East-West (m)

-500

-400

-300

-200

-100

0

100

200

300

400

500

DistanceNorth-South(m)

Figure 4. NAF base fluid concentration (ppm) contours for the

discharge of all drilling solids in 625 m water. The cross marks

the discharge point. Hydrocarbon concentration contours are inparts per million and maximum concentration is 100,000 ppm.

References1. Policastro, A.: Evaluation of Selected Models. In:An Evaluation

of Effluent Dispersion and Fate Models for OCS Platforms. Vol-

ume I, Summary and Recommendations. U.S. Dept. of Interior,Minerals Management Service. Workshop Proceedings. 7-10

February. Santa Barbara, California (1983) 33.2. Brandsma, M.G., Smith, J.P., O'Reilly, J.E., Ayers, R.C.,Jr.,

Holmquist, A.L.: Modeling Offshore Discharges of ProducedWater. In: Produced Water. J.P. Ray and F.R. Engelhart, Eds.

Plenum Press. New York (1992) 59.3. Nedwed, T. J., Smith, J. P., Brandsma, M. G.: Verification of the

OOC Mud and Produced Water Discharge Model Using Lab-ScalePlume Behavior Experiments.J. of Marine Science,in press.

4. O'Reilly, J.E., Sauer, T.C., Ayers, R.C. Jr., Brandsma, M.G., Meek,

R.: Field Verification of the OOC Mud Discharge Model. In:

Drilling Fluids. F.R. Engelhart, J.P. Ray, A.H. Gillam, Eds

Elsevier Applied Science. New York (1989) 647.5. Smith, J.P., Mairs, H.L., Brandsma, M.G., Meek, R.P., Ayers, R.C

Jr. 1994. Field Validation of the Offshore Operators Committe(OOC) Produced Water Discharge Model. Proceedings of SP

Annual Technical Conference. SPE28350. New Orleans. (25-2September 1994).

6. Smith J. P., Brandsma, M. G., Nedwed, T. J.: Field Validation othe Offshore Operators Committee (OOC) Mud and Produce

Water Discharge ModelJ. of Marine Science,in press7. Brandsma, M.G. and Smith, J.P.: Offshore Operators Committe

Mud and Produced Water Discharge Model -- Report and UseGuide. Offshore Operators CommitteeP.O. Box 50751New

Orleans, LA 70150-0751 www.offshoreoperators.com(1999).8. EPA: "Development Document for Proposed Effluent Limitation

Guidelines and Standards for Synthetic Based Drilling Fluids another Non-Aqeuous Drilling Fluids in the Oil and Gas Extractio

Point Source Category" EPA-821-B-98-021 (19990) VII-6.

Appendix ADerivation of Drilling Solid Accumulation Thicknes

Equation. Using the assumptions and parameters described i

the main body of the report and with reference to Figure 1, th

volume of drilling solids over A with thickness T is))(( seawatersaltwatersolidsolid MMMAATV ++== (1)

Therefore

seawatersaltwatersolidsolid MMMT )( ++= (2)

where M represents the loading (kg/m2) of the individua

components making up the drill solid accumulations; eithecuttings solid (solid), pure water (water), or salt in pore wate

(salt). Msolidis the OOC Model-predicted seabed loading.

The Msaltcan be determined using the assumed pore watesalinity (35.03 g/kg) and the assumed weight percent water.

)1000( pptMpptM watersalt = (3)

Express Mwater in terms of Ww (weight percent water) an

Msolids.)(100 saltwatersolidwaterw MMMMW ++= (4)

Substituting Msalt into (4) gives

)1000

1(

100

ppt

pptMM

MW

watersolid

water

w

++

=

(5)

Let

)1000(1 pptppt += (6)

then

)100( wsolidwwater WMWM = (7)

Substituting Mwaterand Msaltinto thickness equation gives

))100(

1

(

wseawater

w

solidsolid W

W

MT +=in m. (8)

0363.1= for kggppt 03.35=

The following values can be used as an equation check

If Msolid=1000 kg/m2, Ww=30%, ppt = 35.03 g/kg, solid=265

kg/m3, and seawater=1020 kg/m3then T=0.8197 m.

Derivation of Hydrocarbon Concentration in Seabe

Sediments Equation. Using the assumptions and parameterdescribed in the main body of the report and with reference t

Figure 2, the equation to calculate hydrocarbon concentratio

in sediments containing NAF cuttings is derived as follows:


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6 SPE 8669

saltsedsaltambambBaBFC

BF

MMMMMM

xMppmHC

+++++=

)101()(

6

(9)

where MBFis the loading of base fluid in the control volume,

MCis the loading of cuttings in the control volume,MBais the loading of barite in the control volume,

Mamb is the loading of ambient sediment in the control

volume,

Msaltamb is the loading of salt in the control volumeambient sediment or WBM solids pore water,

Msaltsed is loading of salt in the NAF sediment in the

control volume.

Transform (9) into a function of the model predicted NAFcuttings loading (Ml) starting with an expression for Foil, the

wet-weight fraction of NAF base fluid retained on the cuttings.

)( SWBaBFcBFoil MMMMMF +++= (10)

where Foil is fraction oil in discharged NAF cuttings (oil oncuttings by retort test), and

MSW is mass of the aqueous phase in the NAF that is

discharged with the cuttings.

BaBFCl MMMM ++= (11)

Substituting (11) into (10) gives

)( SWlBFoil MMMF += (12)

also

NAFBaBaNAFBFBFNAFSWSW MFMandMFMMFM === ,, (13)

where FSWis fraction seawater in the NAF,

MNAF is the loading of whole NAF in the discharged

NAF cuttings (MNAF=MBF+MBa+MSW), (14)FBF and FBaare the fractions of base fluid and barite in

the NAF.

Combining equations in (13) and rearranging gives

BFBFSWSW FMFM = (15)

Substituting (15) into (12) gives

)( BFBF

SW

lBFoil MF

FMMF += (16)

Solve (16) for MBFto give

lSWoilBFloilBFBF MFFFMFFM == )( (17)

Now determine Mambas a function of Ml.

))(1( NAFCVambamb TTpM = (18)

for TCV>TNAF, zero otherwise

where ambis density of ambient sediments,

p is porosity of ambient sediments or WBM drilling

deposits,

TCVis the thickness of the control volume,TNAFis the thickness of NAF drilling deposits as defined

in (8).lwseawaterwsolidlNAF MWWMT =+= )))100((1( (19)

where , Ww, and seawaterare defined in the previous thickness

derivation. The value of solid is determined based on thecomposition of the NAF solids, i.e., the relative loadings of Mc,

MBF, and MBain Ml determined by (12) and (13). The determi-

nation of solidis as follows:

Ba

Ba

BF

BF

c

C

BaBFC

BaBFC

BaBFC

solid MMM

MMM

VVV

MMM

++

++=

++

++=

(20)

where c, BF, and Ba are the densities of dry cuttings, basefluid and barite, respectively, and VC, VBF, and VBarep-

resent the volume of dry cuttings, base fluid, and barit

respectively, in the discharged drilling solids.

From (10) and (13)

)()( NAFcoilSWBaBFcoilNAFBFBF MMFMMMMFMFM +=+++==(21)

Rearranging gives

)( oilBFcoilNAF FFMFM = (22)

Since solid is constant if we assume the ratio of cuttings

base fluid, and barite is constant, we can let Mc= 1 lb/grid ceto simplify (20) and (22).

Then

)( oilBFoilNAF FFFM = (23)

Substituting into (20) gives

Ba

NAFBa

BF

NAFBF

c

NAFBaNAFBF

solid MFMF

MFMF

++

++=

1

1 (24)

Now, substituting (19) into (18) gives

))(1( lCVambamb MTpM = (25)

for TCV>Ml, zero otherwise

Next determine Msaltambas a function of Ml.

SalMMamb

SWsaltamb= (26)

where MSWambis mass seawater in ambient sediment or WBM

drilling deposits,

Sal is salinity of seawater (kg salt/kg seawater).

)()( lCVseawaterNAFCVseawaterSW MTpTTpM amb == (27)

Substituing (27) into (26) gives

SalMTpM lCVseawatersaltamb )( = (28)

for TCV>Ml, zero otherwise

Finally determine Msaltsedas a function of Ml.

saltsedwl

w

saltsedwBaBFc

ww

MMM

M

MMMMM

MW

++=

++++=

100100 (29)

)1( SalSalMMwsaltsed

= (30)

rearrange (30) to give

SalMSalM saltsedw )1( = (31)

Substitute (31) into (29) and solve for Msaltsed.

Sal

Salwhere

WW

MWM

ww

lw

saltsed

=

=

1

100

(32)

Now substitute (32), (28), (25), (17), & (11) into (9).

lCV MT

eMppmHC

l

)1()(

)61()(

+++= (33)

where )1( pamb = , pSalseawater = , and

)100( www WWW =

The following values can be used to check equation (33):

Foil 0.100 amb 2650 kg/m3FBF 0.47 c 2650 kg/m

3

FBa 0.33 solid(eqtn. 23 & 24) 2166 kg/m3

Fsw 0.20 p 0.400

sw 1020 kg/m3 Sal 0.03503 kgsalt/kgseawater

BF 780 kg/m3 Ww 30%

Ba 4200 kg/m3 Tcv 0.02 m

Ml HC (ppm) from eqtn (33)

20 89,275

15 61,269

10 37,648

1 3,300

Estimated Volumes for Discharge of Whole Drilling Mud

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