Cementing Calculations
The following calculations follow the formulas used in the cementing monograph.’ Buoyant force on the casing by the fluid in the hole tries to float the casing. Hydrostatic pressure acts
against the effective area of the casing, causing the upward force. The pressure acts on the full area of the closed end casing if the float is in place and holding or on the area created by do-di if the casing is open ended. The weight of the casing string minus the upward buoyancy force gives the buoyed or true weight of the casing string in the hole.
For 13-3/8 in., 61 Ib/ft, K-55 casing in a 17 in. hole, filled with 10 Ib/gal mud:
closed end area = x (do2/4) = 141 in.2
effective area = (1/4)x (do2-di2) = 17.5 in.2
hydrostatic at 4000 ft = 4000 ft (1 0 x 0.052 psi/ft = 2080 psi
hydrostatic effect on casing = 2080 psi x 17.5 in? = 36,400 Ib
casing string weight on air = 61 Ib/ft x 4000 ft = 244,000 Ib
The buoyed weight of the casing in mud divided by the outside area of the casing gives the pressure needed to balance the string:
207,600 lb/141 in.2 = 1472 psi
Thus, a bottomhole kick or other pressure increase of over 1472 psi (additional 0.368 psilft or 7.1 Ib/gal) could start the casing moving upwards. At shallower depths, especially with large diameter casing, the additional pressure to lift the buoyed weight can be 100 psi or less. The pressure to land the top plug when displacing 16 Ib/gal cement with fresh water to 4000 ft (assuming complete annulus fill with cement) is:
cement hydrostatic in annuls = 4000 ft x 16 Ib/gal x 0.052 .@ = 3328 psi
water hydrostatic in casing = 4000 ft x 8.33 Ib/gal x 0.052 lbft = 1733 psi
pressure to land plug = 3328 - 1733 = 1595 psi lb ft psi gal
In wells where a1 the exposed formations will not support the full weight of the cement while fracturing, the cement must be lightened or the zone must be protected by only filling the annulus with a partial column of cement (staged cementing). Assume the zone at 4000 ft (bottomhole) has a fracture gradient of 0.72 psi/ft. Calculate the height of
a 16 Ib/gal cement column that will be 200 psi below fracturing pressure:
bottomhole frac pressure = 4000 ft x 0.72 psi/ft = 2880 psi
allowable bottomhole pressure = 2880 psi - 200 psi = 2680 psi
cement gradient = 16 Ib/gal x 0.052 = 0.832 psi/ft
full column pressure = 4000 ft x 0.832 psi/ft = 3328 psi
If 16 Ib/gal cement is used, the maximum column height (within the allowable pressure) is:
column height = 2680 psV0.832 psi/ft = 3221 fl
If a full cement column is needed, the maximum cement density is:
maximum density = 2680 psi/4000 ft = 0.67 psi/ft or 12.9 lblgal
Cement densities are only part of the picture, the friction pressures developed by pumping the cement past restrictions adds to the hydrostatistic pressure of the cement.
Balanced Plug Setting
Determining the height that cement will rise where it can equalize height requires use of a simple balanced plug formula.
Squeeze Cementing
Squeeze cementing forces a cement slurry behind the pipe to repair leaks or shut of fluid loss Squeeze cementing is normally thought to be a repair step, but is also used to seal off depleted zones or unwanted fluid production. Smith2 documents eight major uses of squeeze cementing for repair and recovery control purposes:
1- To control high GORs. By squeezing the top section of the perfs, gas production can be made to pass vertically through the top part of the formation matrix, slowing the gas production by the contrast in vertical vs. horizontal permeabilities.
2- To control excessive water, squeezing lower perfs can delay water production. Only if an impenetrable barrier separates the oil and water or if vertical permeability is very low, will effective water reduction be achieved.
3- Repairing casing leaks. Cement can be squeezed through holes in casing. This is best accomplished by very small particle cement.
4- To seal thief zones or lost-circulation zones. Cement slurry may penetrate natural fractures for only a centimeter or two but may develop sufficient blockage to help control leakoff. The cement slurry bridges on the face of the matrix. Sealing off natural fractures is often difficult.
5- To stop fluid migration from a separate zone. This is usually a block squeeze or channel repair operation.
6- Isolation of zones. Selective shutoff of depleted or abnormally low or high pressure zones.
7- Repair of primary cement job. Filling voids or channels, and repair of liner tops are common.
8- Abandonment squeezes. Shutting off depleted reservoirs or protecting fresh water sands.
Squeeze cementing is separated into high pressure squeezing and low pressure ~ q u e e z i n g . ~ ’ ~ ~ ~
High pressure squeezing involves fracturing the formation with cement until a required surface pressure is reached. The importance of high pressures at the end of the job, although popular with many companies, is actually of little importance and should be well below 1 psi/ft.32333 The high pressure squeeze uses “neat” cement (no additives) with very high fluid loss. The best use of the technique is usually to shutoff depleted zones and to seal perforation^.^^ The low pressure squeeze technique is probably more efficient in placing a controlled amount of cement in a problem area of the well. With this technique, formation fracturing is completely avoided. The pressure is achieved by pressuring-up on the cement and allowing the cement to filter out on the formation creating a block in the annulus. Once the cement slurry has hardened or dehydrated to a sufficient extent, no more fluid will be displaced. The excess cement that is still the drill pipe or the annulus can be displaced from the well by opening the casing valve and flushing with a displacement fluid. The advantages of the low pressure squeeze are less pressure exposure to tubing and casing and special cementing tools, and a smaller quantity of cement. For either of the squeeze cementing process, a relatively low water loss, strong cement is part of the design. Most operations use nonretarded API Class A, G or H, which are suitable for squeeze conditions
to 6,000 ft without additives. For deeper wells, Class G or H can be retarded to gain necessary pumping time. In hotter wells (above 230°F), additives should be considered at high temperature to increase strength.
Although squeeze cementing is often used to help repair primary cement failures to protect the pipe, it is possible to collapse the casing during squeeze cementing. If a packer is set immediately above the zone to be squeezed and an open channel exists that links the backside of the casing above the packer to the interval being squeezed Figure 3.14, then the outside of the casing above the packer may be exposed to the full pressure of the cement squeeze. If the inside of the casing is not be loaded or pressurized, casing failure can occur if the Ap is above pipe strength.
The thickening time and set time of cement used in squeeze operations are calculated in the same manner as those used in primary cementing. Squeeze pressure does effect the dehydration of the slurry, particularly across zones which are very permeable. Fluid loss additives may be included if the slurry is designed to move any significant distance across a permeable formation. Normal dehydration of a cement on a permeable section is severe enough to seal off the flow channel before complete displacement is accomplished.
Cement Squeeze Tools
are normally used below 3000 ft where the weight of the string is adequate to completely engage the slips. Drillable cement tools are more restricted in setting and application than retrievables but offer more control on the set cement. The drillable models are preferred where continued pressure must be maintained after squeezing. When squeezing formations that are naturally fractured, it is more important to fill the fractures rather than buildup a filter cake.’ Smith’ cites a two slurry system as successful in fractures: a highly accelerated slurry and a moderate- fluid-loss slurry. Accelerated slurries are pumped into the zones of least resistance and allowed to take an initial set. After the first slurry has gelled, the moderate fluid loss slurry is forced into the narrower fractures. The first slurry used for this type of squeeze should take an initial set 10 to 15 minutes after placement.
Liner Cementing
Cementing liners, especially deep liners at high pressures, is complicated since the liner is often isolated from the rest of the string by packers and close clearances. The result is that pressures are often trapped behind the pipe. Pipe collapse and deformation are ~ o m m o n .L~in~er, c~em~e nting technology is little different from full string technology except that pipe movement (including rotation) is done on drill pipe40r43 and use of plugs requires two part plugs. Liner tie back operations may require special circulating guidelines because of the narrow clearance^.^^ Liner hanger clearances near the top will be critical in minimizing backpressure if the cement is circulated around the top of the liner in a complete circulation job. Close clearances created by a large liner hanger can raise the backpressure and the equivalent circulation density. In some cases, this increase in equivalent density is enough to fracture the well. In a puddle job, the cement slurry is spotted by the drill pipe over the section in which the liner is to be run. The volume calculation for the puddle of cement must consider hole volume and liner volume. Undetected washouts in the hole can lead to lack of cement around the liner top. Although the procedure is much simpler than the circulation/squeeze technique, it is also often less effective in providing a seal. The technique is used for short liner sections.
Frictional Pressure Dropin Pipe
The pressure drop of general slurries in pipe is given by:
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