OilAuthority.com

Annular Space: Wellbore Geometry, Cementing Volumes, and Pressure Loss

The annular space is the ring-shaped (toroidal) geometric void that exists between the outer surface of one cylindrical object and the inner surface of a larger concentric cylinder surrounding it. In oil and gas well construction, annular space describes the open or fluid-filled gap between the outer wall of any tubular string and either the borehole wall in open-hole sections or the inner diameter of a surrounding larger-diameter casing string in cased wellbores. Also called the annulus, the annular space is simultaneously the most geometrically simple and the most operationally complex region of a wellbore: it is geometrically described by two concentric circles, but it serves as the pathway for drilling fluid to return cuttings to surface, the volume to be displaced with cement during casing cementing operations, the conduit through which formation gas migrates during a well integrity failure, the sealed pressure-monitoring space between casing strings in a completed well, and the flow pathway for either produced gas or injection fluid in specialized completions. Calculating the annular space geometry accurately is fundamental to every aspect of well construction engineering. The cross-sectional area of the annular space at any given depth is A = pi/4 x (DH2 minus DP2), where DH is the borehole or casing inner diameter and DP is the tubular outer diameter, both in the same units. The annular volume per unit length is V = A x L = pi/4 x (DH2 minus DP2) x L, used to calculate cement slurry volumes, kill fluid volumes, and displacement volumes in all cementing and well control operations. In Canadian oil and gas practice, annular space dimensions are commonly expressed in both metric (centimetres, litres per metre) and imperial (inches, barrels per linear foot) units, with conversion factors of 1 barrel = 158.99 litres and 1 foot = 0.3048 metres required for fluid volume calculations that mix the two unit systems.

Key Takeaways

  • Annular space geometry and volume calculations: The annular volume per metre of borehole depth (annular capacity) is the most frequently used annular space parameter in cementing engineering and drilling fluid management. In metric units, annular capacity (litres per metre) = pi/4 x (DH2 minus DP2) x 1000, where diameters are in metres. For a typical 215.9-millimetre (8-1/2 inch) open hole around a 127-millimetre (5-inch) drill pipe, annular capacity = pi/4 x (0.21592 minus 0.1272) x 1000 = pi/4 x (0.04661 minus 0.01613) x 1000 = 23.9 litres per metre. The total annular volume for a 2,200-metre cement job in this geometry is 23.9 x 2,200 = 52,580 litres or 330.8 barrels of cement slurry required to fill the annular space (before adding for washout and excess cement factors). In imperial units, the same calculation gives annular capacity = 0.0009714 x (Dh2 minus Dp2) barrels per linear foot where diameters are in inches, yielding 0.0009714 x (8.52 minus 52) = 0.0009714 x 47.25 = 0.04590 barrels per foot, and total volume = 0.04590 x 7,218 feet = 331.3 barrels, confirming metric and imperial calculations to within 0.15 percent.
  • Annular space in cementing operations: Primary cementing fills the annular space between a newly run casing string and the borehole wall (open-hole cement job) or between a new casing string and a previously set larger casing string (liner cementing) with cement slurry pumped down the casing bore and up through the annular space to the designed top-of-cement (TOC) elevation. The annular volume calculation determines how many sacks of dry cement and how many litres of mix water are required to fill the annular space from the casing shoe to the TOC, plus an excess volume (typically 20 to 50 percent of the calculated annular volume) to compensate for borehole washouts and lost circulation into the formation that can consume cement without filling the annular space. In the WCSB, annular space dimensions are complicated by borehole enlargement (washout) in soft shale sections where bit gauge is lost and the actual borehole diameter exceeds the nominal bit size by 10 to 60 percent, requiring calliper log data from a recent open-hole logging run to accurately calculate the washed-out annular volume and avoid over-estimating TOC by 100 to 400 metres due to unplanned washout cement consumption.
  • Pressure loss in the annular space during drilling: Drilling fluid flowing upward through the annular space from the bit to the surface generates a frictional pressure loss that adds to the hydrostatic pressure of the mud column to produce the equivalent circulating density (ECD) at the drill bit. Annular pressure loss depends on the annular space geometry (Dh minus Dp), the fluid flow rate (pump rate), and the fluid's rheological properties (plastic viscosity, yield point, and gel strength in Bingham plastic models, or K, n, tau-y in Herschel-Bulkley models). The annular pressure loss per metre (using the Bingham plastic model in turbulent flow) is approximately: dP/dL = (f x rho x v2) / (2 x De), where De is the equivalent diameter (DH minus DP), f is the Fanning friction factor from Reynolds number, rho is mud density, and v is the annular velocity. For a Montney open-hole section with 222-millimetre (8-3/4 inch) bit and 127-millimetre (5-inch) drill pipe, 1.50 SG mud at 800 L/min circulation rate, and plastic viscosity of 25 mPa-s and yield point of 12 Pa, the annular pressure loss in turbulent flow is approximately 1.8 kPa/m, contributing an ECD of 1.50 + 1.8 x 3,500 / (0.0981 x 3,500) = 1.50 + 0.018 = 1.518 SG at 3,500 metres depth.
  • Annular space standoff and cement quality: During cementing operations, the drill string or casing string being cemented must be centered in the borehole to ensure that cement slurry flows uniformly around the entire circumference of the annular space without channeling through a portion of the annulus where the standoff (gap between casing outer wall and borehole wall) is larger, while bypassing the narrower side. Standoff is measured as the ratio of the actual gap between the casing and borehole wall at any circumferential position to the average annular space dimension, expressed as a percentage from 0 (casing touching the borehole wall, no flow possible) to 100 (perfectly centered). A standoff of 100 percent is ideal but practically unachievable; API Recommended Practice 10D requires a minimum standoff of 67 percent for a qualitatively acceptable primary cement job. In deviated wellbores, gravity causes the casing string to rest against the low side of the borehole, reducing standoff on the low side to near zero without centralizer support; the industry standard for centralizer placement in deviated sections is one centralizer per joint (9 to 14 metres spacing) to maintain minimum 67 percent standoff and prevent mud channeling through the wide-standoff portion of the annular space.
  • Annular space in open-hole completions and gravel packing: In horizontal and deviated wells completed with openhole gravel packs or sand screens, the annular space between the screen assembly and the borehole wall is filled with a gravel pack slurry of sorted sand grains (typically 20/40 or 40/70 mesh gravel, 0.4 to 0.85 mm grain diameter) pumped in carrier fluid to fill the completion interval. The gravel-packed annular space acts as a highly permeable (50,000 to 150,000 millidarcy) pre-filter layer that prevents formation sand from migrating into the screen and plugging the wire-wrap or pre-pack filter medium. Gravel pack annular space volume must be calculated precisely to determine the slurry volume required to completely pack the screen-to-formation annular space from the bottom of the screen to the gravel pack packer above, without leaving voids (alpha-wave deposition requires that slurry reaches the end of the screen before reversing direction). In a 120-metre Cardium horizontal open-hole completion with a 150-millimetre (6-inch) bit and a 75-millimetre (3-inch) screen assembly, the annular volume for gravel pack = pi/4 x (0.152 minus 0.0752) x 120 = pi/4 x (0.0225 minus 0.005625) x 120 = 1,595 litres, requiring approximately 1,750 litres of slurry (10 percent excess) at a 600-kg-per-m3 gravel concentration to fill the annular space with a compacted gravel pack of adequate pack conductivity.

Annular Space Volume Calculations for WCSB Cementing Operations

Accurate annular space volume calculation is the foundation of every primary cement job design in the WCSB, because under-calculating the annular volume leads to a short cement job with the top of cement below the required regulatory height (AER Directive 009 requires surface casing to be cemented to within 30 metres of surface), while over-calculating can waste cement and push excess slurry into the formation, causing lost circulation and channeling in the freshly placed cement column. The design workflow begins with the open-hole calliper log: a standard 4-arm calliper run on the formation evaluation logging string measures the borehole diameter at each depth and identifies enlarged sections (washouts) where the annular volume exceeds the nominal bit-diameter calculation. The calliper data is integrated over the cemented interval to produce a depth-corrected annular volume profile that accurately accounts for washout zones.

In the Cardium play of west-central Alberta, where Cretaceous Colorado Group shale sections above the Cardium are prone to significant borehole enlargement (calliper readings of 130 to 200 millimetres in an 8-3/4 inch bit section are common in the first 200 to 400 metres below the intermediate casing shoe), neglecting calliper data in cement volume calculations can under-design the annular fill by 15 to 35 percent, producing a TOC 200 to 500 metres below the required regulatory height and necessitating a remedial cement top job at additional cost. A TOC top job in a Cardium intermediate casing string requires a coiled tubing unit to run a perforating gun above the existing TOC, perforate the casing, and pump cement through the perforations to fill the uncemented annular space above the first cement placement, at a remedial cost of CAD 35,000 to CAD 65,000 including coiled tubing rig, perforating charges, cement materials, and pressure testing to verify the remedial cement placement.

The standard cement volume design calculation for a 244-millimetre (9-5/8 inch) intermediate casing string set at 1,800 metres in a 311-millimetre (12-1/4 inch) open hole in the Cardium play proceeds as follows: nominal annular capacity without washout = pi/4 x (0.31102 minus 0.24402) x 1,000 = pi/4 x (0.09672 minus 0.05954) x 1,000 = 29.2 litres/metre; nominal annular volume from shoe to surface (1,800 metres) = 29.2 x 1,800 = 52,560 litres (331 barrels); calliper-corrected annular volume accounting for an average 15 percent borehole enlargement in the 600-metre Colorado shale section = 29.2 x 1,200 (competent formation) + 29.2 x 1.15 x 600 (enlarged section) = 35,040 + 20,148 = 55,188 litres; plus 25 percent excess cement = 55,188 x 1.25 = 68,985 litres total slurry required. At a 1.90 SG slurry yield of 1.55 litres per kilogram of dry cement, this requires 68,985 / 1.55 = 44,506 kg of Class G cement (945 sacks of 47-kg sacks) for the intermediate casing job.

In directional and horizontal Duvernay wells, annular space geometry changes significantly along the wellbore trajectory: the annular space in the vertical section from surface to kickoff point (approximately 300 to 600 metres) is the largest in cross-section (311-millimetre hole with 244-millimetre casing gives only 33.5-millimetre average annular gap), the intermediate-to-horizontal transition (311-millimetre hole with 244-millimetre casing in the build section) has variable standoff driven by gravity, and the lateral section (222-millimetre hole with 139.7-millimetre production casing) has the smallest annular space with average gap of 41.2 millimetres. Cementing the production casing in the 3,200-metre horizontal lateral of a Duvernay well requires a minimum cement velocity in the annular space of 0.6 to 1.0 m/s to achieve turbulent flow displacement of the drilling mud, which at the 222-millimetre to 139.7-millimetre annular geometry requires a pump rate of minimum 1,100 L/min, close to the maximum sustainable rate for the available cementing pumps on most Duvernay cement jobs. Achieving turbulent flow displacement in the horizontal annular space is critical for removing the drilling mud filter cake from the formation face before cement contacts it, because filter cake removal is the prerequisite for an adequate cement-formation bond that provides hydraulic isolation between the perforated production zones in the 40-stage completion.

Browse the Oil and Gas Glossary