The engineering calculations run on models built on open publications. The models were validated against both laboratory and field data. Below: the model behind each calculation, the published work it rests on, the data it was compared with, and where the two disagree. On the charts, a line is the calculation and points are the measurement.
Loads on the string are computed with the soft-string model (Johancsik, Friesen & Dawson, SPE 11380). The string is treated as a flexible cable lying along the wellbore axis; hookload and torque come from the string’s weight and its friction against the wall.
Buckling is checked with the He & Kyllingstad model (SPE 25370), which accounts for the wellbore’s curvature and gives the sinusoidal and helical buckling limits. The calculation covers the drill string and casing being run, while running in, pulling out, drilling with rotation and sliding.
The model was compared with field data from a horizontal well: hookload while pulling out, slacking off and rotating, and torque, over about 1,520–3,450 m MD.
HookloadPulling out, slacking off and rotating: calculated and measured in the field.
Pulling out
Slacking off
Rotating
TorqueRotating: calculated and measured in the field.
Calculated
Measured
Buckling calculation exampleAxial load along the string while sliding, with the buckling limits (compression is negative).
The drilling fluid is described by the Herschel–Bulkley model, a power law with a yield stress. It captures the fluid’s non-linear behaviour, including at the low shear rates that pressure losses and cuttings transport depend on. The calculation draws on a series of SPE publications.
The module computes:
pressure losses in the pipe and the annulus while drilling and circulating (standpipe pressure, ECD);
surge and swab while running in and pulling out;
the highest allowable tripping speed, with the same surge and swab model.
Standpipe pressure and ECD were compared with field data from a horizontal well, the ECD with a PWD sensor’s readings. Pressure losses in the pipe and the annulus, and surge and swab, were compared with data from the well in SPE 35057, recorded by PWD sensors.
Standpipe pressureAlong the well, 1,500–3,500 m MD: calculated and measured.
Calculated
Measured
ECDThe same well. The calculated ECD is the PWD’s static density plus the calculated annular pressure loss.
Calculated
Measured
Annular pressure lossAgainst flow rate: calculated and measured, the same well.
Calculated
Measured
Pipe pressure lossAgainst flow rate: calculated and measured, the same well.
Calculated
Measured
Surge and swabAnnular pressure change against string velocity (negative: pulling out, swab; positive: running in, surge), calculated and measured by PWD; the well from SPE 35057.
Cuttings transport is computed with a steady-state method based on the work of Larsen, Pilehvari & Azar (SPE 25872); string rotation and eccentricity follow Peden, Ford & Oyeneyin (SPE 20925). For steady drilling the method finds the critical annular velocity at which cuttings are carried out without settling and, where the flow is slower, the equilibrium cuttings bed.
The method was compared with the laboratory tests of SPE 25872 and SPE 20925 across different muds and conditions.
Minimum transport velocityAgainst inclination: large and medium cuttings, mud No. 1, ROP 54 ft/h; laboratory data, SPE 25872.
Large cuttings
Medium cuttings
Cuttings bedAgainst inclination: large cuttings, muds No. 1 and No. 3, flow rate 150 gal/min; the same tests.
The ROP of PDC bits is computed with a physics-based model developed from the approach of Hareland & Rampersad (SPE 26957): the rate of penetration is built up from how each cutter cuts into the rock.
It takes only known parameters:
the bit: cutter count and diameter, and their rake angles;
the rock: unconfined compressive strength and abrasiveness;
the drilling: weight on bit, rotary speed and the pressure at the bit.
It needs none of the calibration coefficients that vary by orders of magnitude in empirical models. It models cutter wear and its effect on ROP. The forecast is accurate to within tens of percent.
The model was compared with field data: an 8¾″ PDC bit (MDi613) over 2,025–2,290 m MD. The calculation stepped along the interval, carrying the cutter wear from step to step.
ROPAlong the interval: calculated with bit wear, and the actual ROP.
