cálculos de cementación primaria

CEMENTING ENGINEERING MANUALSection 8.E.1 Primary Cement-Job Calculations (Revised Sept. 1999)

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This manual section is a confidential document which must not be copied in whole or in any partor discussed with anyone outside the Schlumberger organization.

Primary Cement-Job Calculations

INTRODUCTION .............................................................................................................2

SLURRY AND PREFLUSH VOLUMES................................................................................2

CEMENT-SYSTEM QUANTITY..........................................................................................6

DISPLACEMENT VOLUME ...............................................................................................7

CASING CAPACITIES ............................................................................................................ 7

WATER REQUIREMENTS ................................................................................................8

MAXIMUM LIFTING FORCE ............................................................................................8

EXAMPLE WELL INFORMATION.............................................................................................. 10

CEMENT CALCULATIONS ..................................................................................................... 12

DISPLACEMENT VOLUME ..................................................................................................... 12

WATER REQUIREMENTS...................................................................................................... 12

MAXIMUM LIFTING FORCE................................................................................................... 13


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IntroductionThe following must be known before a primary cement job can be successfully completed:

• slurry and preflush volumes

• cement-system quantity

• displacement volume

• water requirements

• maximum lifting force (casing buoyancy)

The manual calculation of these values is presented in this manual section.

SLURRY AND PREFLUSH VOLUMESCasing/openhole annular volumes are calculated to determine

• the amount of slurry required for a desired fill-up

• the preflush volumes to provide a desired annular-height coverage.

During the initial cement-job design, drilling is normally still in progress and the caliper log hasnot been run. The slurry and preflush volumes are estimated based on the bit size plus an excessvolume (e.g., 30%) determined from field experience or based on government regulations.

Vslurry = Cannulus x Lslurry

where

Vslurry = slurry volume (ft3)

Lslurry = length of slurry column (ft)

Cannulus = annular capacity (ft3/ft; from the Dowell Field Data Handbook).

The job design is later finalized based on annular volumes determined from the caliper log. Thetype of caliper can affect the calculated amount of cement, and the resulting fill-up by thecement. Two- or three-arm calipers, with arms that operate together, may underestimate (oroverestimate in the case of the two-arm caliper) the size of the hole. This is especially true fordeviated wells which tend to have oval boreholes. For these situations, four-arm Hole calipers orsix-arm calipers (with independently operating arms) are preferred.


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Figure 1: Hole Calipers


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For calculating the annular volume using a basic caliper log, the interval of interest is divided intoincrements, and the average hole diameters are estimated for each increment.

Annular-Volume Calculations from Caliper Measurements

Hole Diameter(in.)

Annular Capacity for 7-in. Casing(ft3/ft)

Annular Length(ft)

Annular Volume(ft3)

10.0 0.2782 30 8.346

10.5 0.3341 40 13.364

11.0 0.3927 10 3.927

13.5 0.7267 10 7.267

15.5 1.0431 10 10.431

TOTAL 43.335

Once the slurry volume has been calculated, an excess is added (normally 10 to 20%), based onfield experience or government regulations, and then the cement (or blend) requirements aredetermined. Assuming a 43.335-ft3 total slurry volume (from Table 98), a 10% excess, and aslurry yield of 1.18 ft3/sk, the required cement is calculated as follows.

Slurry Volume = 43.335 ft3 x 1.10 (10% excess) = 47.669 ft3

Most logging companies offer computerized annular-volume calculations which are presented onthe basic caliper log (see figure below).


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Figure 2: Borehole Geometry Log


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The tick marks on the depth track represent the total hole volume (left) and the annular volumebetween the casing and openhole (right) in 10-ft3 increments. The long tick marks represent 100-ft3 increments and therefore replace each tenth small tick mark. For metric logs, the small andlong tick marks indicate the total volume in 1-m3 and 10-m3 increments, respectively. The totalhole volume (VHOL) and cemented annulus (VCEM) are also shown in the header.

Slurry excess is only calculated for the openhole portion to be cemented. This excess is toaccount for the inaccuracy of the caliper measurement, cement which may be lost into theformation, hole enlargement, or fluid loss from the cement into permeable zones. When slurryreturns to the surface are desired or required, excess volumes may be used to ensure that theyare achieved.

The amount of excess must be carefully selected. If the well has a weak formation which is closeto being fractured, then excess cement (which will raise the cement top) may cause theformation to be fractured because of the increased hydrostatic and friction pressures.

The final slurry-volume calculation is the amount that will remain in the shoe joints (between thefloat collar and the shoe). This is simply the casing volume between those two points. Thisvolume is added to the annular slurry volume and the slurry excess to equal the total slurryvolume for the job.

CEMENT-SYSTEM QUANTITYBesides the class of cement and additive details, a cement-system description always includes

• slurry density (lbm/gal)

• slurry yield (ft3/sk)

• mix-water requirement (gal/sk).

The slurry yield is the volume occupied by one unit of cement or cement blend (e.g., sack,equivalent sack, tonne) plus additives and mix water. For cement measured in sacks, the yield isexpressed in cubic feet per sack (ft3/sk) or cubic feet per equivalent sack (ft3/eq sk); for cementmeasured in tonnes, the yield is expressed in liters per tonne (liter/t) or cubic meters per tonne(m3/t). The term equivalent sack is used when the cementitious material is a blend of fly ash andcement. The amounts of fly ash and cement to equal an equivalent sack can be obtained fromyour laboratory. Once the total slurry volume has been determined, the total cement in sacks,equivalent sacks, or tonnes is calculated using the following equation:

Total Cement = Total Slurry Volume / Slurry Yield


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DISPLACEMENT VOLUMEThe displacement volume to land the plug equals the length of the pipe to the float collar timesthe pipe capacity.

Vdisplacement = Lfloat collar x Cpipe

where

Vdisplacement = displacement volume (bbl/ft)

Lfloat collar = float-collar depth (ft)

Cpipe = casing capacity (bbl/ft; from the Dowell Field Data Handbook).

During the displacement, the actual volume pumped may be greater than the calculated volumedue to air entrainment in the slurry and pump inefficiency. Overdisplacement of the slurry pastthe shoe must be avoided. Therefore, the decision to pump a volume in excess of the calculatedvolume must be well thought out.

Casing CapacitiesThe casing dimensions and weights used by CemCADE and presented in the Dowell Field DataHandbook are nominal values as defined in API Specification 5CT. Tolerances are associated withthese nominal values. A 9-5/8-in., 36-lbm/ft casing with a nominal ID of 8.921 in. is used in thisdiscussion to illustrate the possible effect of these tolerances. The casing OD tolerances are+1.0% with an absolute maximum of 0.125 in. and -0.5%. Therefore, the casing OD can varyfrom 9.577 to 9.721 in.

The casing weight tolerances are +6.5% and -3.5%. Therefore, the casing weight can vary from34.74 to 38.34 lbm/ft.API Specification 5CT does not define a tolerance on the casing ID, butderives it from the tolerances on the casing OD and weight.

The maximum possible casing ID corresponds to the maximum casing OD and the minimumcasing weight. The minimum possible casing ID corresponds to the minimum casing OD and themaximum casing weight. Assuming a steel density of 505 lbm/ft3 (value calculated from thenominal OD, ID and weight), the minimum and maximum ID for a 9-5/8-in., 36-lbm/ft casing are8.820 and 9.049 in., respectively.

The casing capacities for the different inside diameters are

• minimum ID: 0.07557 bbl/ft

• nominal ID: 0.07731 bbl/ft

• maximum ID: 0.07954 bbl/ft.

For a displacement length of 10,000 ft, the absolute errors on the displacement volume (from thenominal value) are +22 bbl and -17 bbl.

All of the casing joints in a 10,000-ft well do not have their ID at the upper or lower limit.Statistical ID data from the casing manufacturers are required to calculate more reasonable errorfigures. However, this calculation exercise does show that the displacement volume for a givencasing size and depth is not fixed but may vary significantly as a result of the tolerances in thecasing OD and weight.


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WATER REQUIREMENTSThe water requirements for a primary cement-job operation equals the sum of

• water required to fill the mixing/pumping units and the treating lines

• water to pressure test the treating lines

• mix water for the washes and spacers

• mix water for the cement

• displacement volume (if displacing the slurry with water)

• water required for flushing the treating lines before the displacement

• water needed for washing up the cementing equipment

• tank bottoms (the tank volume from the tank bottom to about six inches above thesuction valves).

The mix water for the cement is calculated as follows:

Vmix water = REQmix water x AMTcement

where

Vmix water = volume of mix water (gal)

REQmix water = mix-water requirement (gal/sk)

AMTcement = amount of cement (sk).

The mix-water volumes for the spacer and washes are calculated by following the instructions intheir respective sections in the Cementing Materials Manual. The instructions for determining thedisplacement volume are discussed in Subsection 4 of this manual section. The volume for thetank bottoms can be calculated. The remaining water volumes must be estimated.

Once the total water requirements have been determined, a safety factor (excess) should beincluded (e.g., an additional 50 bbl).

MAXIMUM LIFTING FORCEDuring some cementing treatments, there is a danger that the casing may be " pumped " out ofthe well. The conditions which favor such an occurrence are

1. lightweight pipe

2. short pipe length

3. large-diameter pipe

4. high-density cement slurries

5. low-density displacement fluids

6. high annular friction pressures

7. bridging in the annulus

8. backpressure.


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Conditions 2 through 5 are all met when cementing surface or conductor casings.

The Fill Sequence module of the CemCADE program automatically calculates the maximum liftingforce (MLF) based on the static conditions at the end of the job. The CemCADE calculation of theMLF is not performed for liner cement jobs.

The MLF is manually calculated as follows:

MLF = 0.785 x (Phyd(ann) Phyd(cas)) x Dcas2

where

Phyd(ann) = annular hydrostatic pressure at end of job (psi)

Phyd(cas) = casing hydrostatic pressure at end of job (psi)

Dcas2 = casing outside diameter (in.).

If the MLF value exceeds the total weight of the casing, then the casing can be pumped out ofthe hole and must therefore be chained down.

The casing and annular hydrostatic pressures at the end of the job are calculated using thefollowing equation:

Phyd = 0.052 x H

where

ρ = fluid density (lbm/gal)

H = height having fluid density (ft).


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Example Well Information

Surface casing: 13-3/8 in., 54.5 lbm/ft to 1700 ft

Openhole: 12-1/4 in. to 4950 ft

Casing: 9-5/8 in., 36.0 lbm/ft

Excess required: 25% (caliper log is not available)

Shoe joint: 42 ft

Top of cement: 300 ft inside 13-3/8-in. casing

Top of tail cement: 4450 ft

50:50, fly ash (Denver):Class A + 4% D20 + Additives

density: 12.9 lbm/gal

yield: 1.54 ft3/eq sk

Lead system:

mix water: 7.80 gal/eq sk

Class H + Additives


yield: 1.05 ft3/sk

Tail system:

mix water: 4.29 gal/sk

40 bbl Chemical Wash 100 (41.5 gal/bbl water)Preflush:


Displacement fluid: 11.5 lbm/gal mud


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This well information is illustrated in the figure below. Data is taken from the Dowell Field DataHandbook.

Figure 3: Example Well For Primary Cement-Job Calculations

Casing Capacity and Annular Capacities

Casing capacity: 0.4341 ft3/ft or 0.0773 bbl/ft (9-5/8 in.)

0.3627 ft3/ft (9-5/8-in. casing/13-3/8-in. casing)Annular capacities:

0.3132 ft3/ft (9-5/8-in. casing/openhole)


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Cement CalculationsLead slurry volume between 9-5/8-in. and 13-3/8-in. casings:

V1 = 0.3627 ft3/ft x 300 ft = 108.8 ft3

Lead slurry volume between 9-5/8-in. casing and openhole:

V2 = 0.3132 ft3/ft x (4450 - 1700) ft x 1.25 (25% excess) = 1076.6 ft3

Total lead slurry volume:

VL = V1 + V2 = 1185.4 ft3

Total lead cement

SacksL = 1165.4 ft3 / 1.54 ft3 / eq sk = 770 eq sk

Tail slurry volume between 9-5/8-in. casing and openhole:

V3= 0.3132 ft3/ft x (4950 - 4450) ft x 1.25 (25% excess) = 195.8 ft3

Tail slurry volume in shoe joint:

V4= 0.4341 ft3/ft x 42 ft = 18.2 ft3

Total tail slurry volume:

VT = V3 + V4 = 214.0 ft3

Total tail cement

SacksT = 214.0 ft3 / 1.05 ft3 / sk = 204 eq sk

Displacement VolumeThe treating lines are to be flushed with water before commencing the displacement.Displacement volume:

VD = 0.0773 bbl/ft x (4950 - 42) ft = 379.4 bbl

Water RequirementsMix water for the cement:

VMIX = 7.80 gal/eq sk x 770 eq sk + 4.29 gal/sk x 204 sk = 6882 gal = 164 bbl

Mix water for the preflush

Vpreflush = 41.5 gal/bbl x 40 bbl = 1660 gal = 39.5 bbl 40 bbl

The rig and two 100-bbl water trucks will supply Dowell with fresh water. Therefore, tankbottoms are not a concern.


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Water Requirements

Purpose Water Volume (bbl)

Mix water for preflush 40

Mix water for cement 164

Fill mixing/pumping units and treating lines 5 (estimate)

Pressure test treating lines 2 (estimate)

Flush treating lines 5 (estimate)

Wash up the cementing equipment 10 (estimate)

Additional water available (safety factor) 50 (estimate)

Total Water Requirement 276

Maximum Lifting ForceTo calculate the maximum lifting force, the annular height that the 40-bbl preflush occupies mustbe determined before the casing and annular hydrostatic pressures at the end of the job arecomputed.

The annular height of the preflush:

Hwash = (40 bbl x 5.6146 ft 3 / bbl) / (0.3627) ft3 = 619 ft

Because the top of the lead cement is at 1400 ft, the height of the mud:

Hmud= 1400 ft - 619 ft = 781 ft

The hydrostatic pressure of each fluid segment is calculated using the following equation and theresults are summarized in Table 102.

Phyd = 0.052 x x H

where

ρ = fluid density (lbm/gal)

H = height having fluid density (ft).

The maximum lifting force:

MLF = 0.785 x (3207 - 2971) x 9.6252= 17,163 lbm

The casing weight:

Wcas = 36.0 lbm/ft x 4950 ft = 178,200 lbm

Since Wcas is greater than the MLF, the casing will not be pumped out of the hole and does notneed to be chained down.


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Hydrostatic Pressure of Fluid Segments

Casing Calculations Annular CalculationsFluid

Segment Interval (ft) Hydrostatic Pressure(psi)

Interval (ft) Hydrostatic Pressure(psi)

Drilling mud 0 to 4908 2935 0 to 781 467

Preflush 781 to 1400 268

Lead slurry 1400 to 4450 2046

Tail slurry 4908 to 4950 36 4908 to 4950 426

TOTAL 2971 3207

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