Two-Pass Method

The two-pass method in drilling fluid hydraulics is a calculation procedure for optimizing drill bit nozzle sizing and surface pump pressure allocation between two flow objectives — maximum hydraulic horsepower at the bit (HHPb) or maximum jet impact force (JIF) — by first calculating the optimum surface circulating pressure at the bit for each objective and then selecting nozzle sizes that achieve those pressures, enabling drillers and engineers to systematically maximize bit cleaning and bottom-hole cutting removal efficiency for a given pump and drill string configuration.

Key Takeaways

In the two-pass method, Pass 1 calculates the total system pressure losses (in the surface lines, drill pipe, drill collars, and annulus) at the design flow rate, leaving the remaining surface pressure budget to be allocated to the bit nozzles; Pass 2 uses this bit pressure drop budget to calculate the optimal nozzle total flow area (TFA) that achieves either maximum hydraulic horsepower or maximum impact force at the bit.
Maximum hydraulic horsepower at the bit (HHPb) is achieved when the bit pressure drop (Pb) equals two-thirds of the total available surface circulating pressure (Ps): Pb = 2/3 × Ps — this optimization criterion assumes that increasing bit pressure drop beyond this fraction reduces jet velocity faster than the increased pressure compensates, resulting in lower total power at the bit.
Maximum jet impact force (JIF) at the bit is achieved when the bit pressure drop equals one-half of the total available surface pressure: Pb = 1/2 × Ps — this criterion is preferred for soft formations where the momentum of the jet impinging on the formation (force = mass flow rate × velocity) is more important for cleaning the bit face and removing cuttings than total power delivery.
The choice between optimizing for maximum HHPb versus maximum JIF depends on formation hardness: hard formations benefit from maximum HHPb (high hydraulic power to break and remove rock), while soft or gummy formations benefit from maximum JIF (high jet velocity and momentum to prevent bit balling and clean the bit face).
Practical application of the two-pass method requires accurate measurement of the actual circulating pressure losses in the drill string (typically determined by a pressure step-down test at multiple flow rates before drilling ahead) to establish the frictional pressure profile, since pressure losses scale approximately with flow rate squared and inaccurate loss estimates produce incorrect nozzle sizing recommendations.

Fast Facts

The two-pass method for bit hydraulics optimization was developed in the 1960s and 1970s as part of the systematic approach to drilling hydraulics that recognized bit cleaning as a primary determinant of penetration rate in many formations. Research by Arthur Lubinski and colleagues at the API established the theoretical basis for the 1/2 Ps and 2/3 Ps optimum pressure allocations. Modern drilling optimization software performs the two-pass calculation automatically, but the manual two-pass method remains an important conceptual framework for understanding how pump pressure should be allocated between the circulating system and the bit nozzles to maximize drilling performance. In a typical 12-inch hole section at 3,000 metres depth with a 1,500 HP pump, the system pressure loss (drillstring friction) may consume 60 to 70 percent of available pump pressure, leaving only 30 to 40 percent for the bit nozzles — making nozzle sizing critical to bit hydraulics performance.

What Is the Two-Pass Method?

Drilling fluid circulates from the surface pump, down through the drill pipe and drill collars, through the bit nozzles, and back to surface through the annulus. Everywhere the fluid travels, it loses pressure due to friction in the pipes and fittings. The pump provides the total driving pressure (circulating pressure), and this pressure must be distributed among all the resistances in the circuit — with the bit nozzles receiving whatever pressure remains after the pipe and annulus frictional losses are satisfied.

The bit nozzles are the component the engineer can most easily design to control: by choosing different nozzle sizes (measured in 32nds of an inch for tricone bits, or specific millimetre diameters for PDC bit nozzles), the engineer controls the pressure drop across the bit and therefore the jet velocity and hydraulic power delivered at the cutting face. Too-large nozzles result in insufficient bit pressure drop and poor bit cleaning; too-small nozzles result in excessive bit pressure drop that starves the annulus of required flow velocity for cuttings transport.

The two-pass method provides a systematic procedure for finding the optimum nozzle size that maximizes either hydraulic horsepower or jet impact force at the bit, given the pump capacity and the frictional losses in the drill string. It is called "two-pass" because the calculation is done in two steps: the first pass accounts for all system losses, and the second pass allocates the remaining pressure to the bit nozzles according to the chosen optimization criterion.

Two-Pass Method Calculation Procedure

Pass 1 — System Loss Calculation: At the design flow rate, calculate the pressure loss in each component of the circulating system using the appropriate hydraulic model (Bingham plastic, Power Law, or Herschel-Bulkley). Sum the losses in surface lines, drill pipe, heavy weight drill pipe, drill collars, and the annulus (return flow path). Subtract the total system loss from the available pump pressure (maximum pump pressure at the design flow rate) to find the pressure budget available for the bit nozzles. This is the bit pressure drop: Pb = Ps − ΣPi, where ΣPi is the sum of all system frictional losses.

Pass 2 — Nozzle Sizing: Determine the optimization criterion (maximum HHPb or maximum JIF) and apply the corresponding condition. For maximum HHPb: set Pb_optimum = 2/3 × Ps and calculate the nozzle total flow area (TFA) that produces this pressure drop at the design flow rate. For maximum JIF: set Pb_optimum = 1/2 × Ps and calculate the TFA accordingly. The TFA calculation uses the standard orifice flow equation: Pb = ρ × Q² / (2 × Cd² × TFA²), where ρ is mud density, Q is flow rate, and Cd is the discharge coefficient (typically 0.95 for well-designed nozzles).

The calculated TFA is then matched to available nozzle combinations — commercial nozzles come in discrete sizes, so the engineer selects the combination (typically three nozzles for a tricone bit) that most closely approximates the calculated TFA without exceeding pump pressure limits. The resulting bit hydraulics are checked against minimum annular velocity requirements to confirm cuttings transport is adequate.

Two-Pass Method Across International Jurisdictions

Canada (AER / WCSB): Two-pass hydraulics calculations are a standard component of WCSB pre-drill engineering programs, performed by drilling engineers or mud engineers as part of the hydraulics design for each hole section. AER well licensing and completion reporting requirements do not specifically require two-pass calculation documentation, but industry practice in the WCSB follows API and SPE-based hydraulics optimization standards. CAOEC contractor performance reporting for WCSB wells includes penetration rate and bit performance metrics that reflect hydraulics optimization quality. For Montney and Duvernay horizontal wells with long lateral sections and complex drill string configurations, managed pressure drilling (MPD) systems provide real-time hydraulics monitoring that supplements the pre-drill two-pass calculation.

United States (API / IADC): API RP 13D (Rheology and Hydraulics of Oil-Well Drilling Fluids) provides the standard reference for drilling hydraulics calculations including two-pass bit optimization in US oilfield practice. IADC drilling engineering courses include two-pass hydraulics as a core competency for drilling engineers and supervisors. Permian Basin horizontal drilling programs use automated bit hydraulics optimization software that performs the two-pass calculation in real time as drilling parameters change, updating nozzle recommendations for the next bit run based on actual measured pressure losses in the current drill string configuration.

Norway (Sodir / NORSOK): NORSOK D-010 references appropriate hydraulics design for NCS wells, and NORSOK D-002 (Well Intervention Equipment) addresses coiled tubing hydraulics. Equinor's pre-drill engineering process for NCS wells includes hydraulics modeling with bit optimization as a standard deliverable, typically using specialized software (Landmark's WELLPLAN, Halliburton's COMPASS, or similar) that incorporates two-pass method logic in its bit hydraulics module. The high density and viscosity of oil-based muds used for HTHP NCS wells require careful two-pass optimization because system losses are higher than for water-based muds, leaving a smaller fraction of pump pressure for bit hydraulics.

Middle East (Saudi Aramco): Saudi Aramco's drilling programs specify bit hydraulics optimization requirements in the pre-drill engineering package, using two-pass methodology or equivalent software-based hydraulics calculations. Aramco's deep Khuff wells and HTHP wells require careful hydraulics design because the high-temperature conditions thin the oil-based mud and change pressure loss profiles significantly from the surface-temperature calculation baseline. Aramco's real-time drilling optimization centers monitor actual standpipe pressure against the pre-drill hydraulics model and flag deviations that indicate changes in mud properties or drill string condition requiring bit hydraulics recalculation.

The two-pass method is also called the two-step method or the hydraulics optimization method in some textbooks. Related terms include bit hydraulics, hydraulic horsepower (HHP), jet impact force (JIF), nozzle velocity, total flow area (TFA), circulating pressure, and pressure loss. The annular velocity requirement — typically specified as a minimum of 120 to 150 feet per minute (0.6 to 0.75 metres per second) in vertical wells and higher in deviated wells for cuttings transport — must be satisfied simultaneously with the bit hydraulics optimization, creating a constraint on minimum flow rate that limits the range of nozzle sizes that can be selected.

Tip: Before running the two-pass calculation on paper or in software, perform an actual circulating pressure test by pumping at multiple flow rates (typically 50%, 75%, and 100% of planned drilling flow rate) before drilling the new hole section and measuring standpipe pressure at each rate. Plot standpipe pressure versus flow rate squared — the slope gives you the actual system K-factor (the combined frictional resistance of the drill string and annulus), which is far more accurate than the theoretical calculated K-factor from mud rheology models, especially when you have OBM at downhole temperature and a complex drill string configuration. The bit pressure drop at drilling flow rate then equals: Pb = Ps − K × Q², using the measured K from your pressure test. This empirical approach eliminates the cumulative errors from multiple theoretical pressure loss calculations and gives you the correct starting point for Pass 2 nozzle selection.

FAQ

Does the two-pass method apply to PDC bits as well as tricone bits?
Yes, the two-pass method applies to any rotary drill bit with hydraulic nozzles, including PDC bits. PDC bits typically use fewer, larger nozzles than tricone bits and may have specialized nozzle geometries (angled, side-discharge) designed to direct fluid flow specifically toward the cutting elements and junk slots for optimal bit cleaning. The two-pass TFA calculation produces the same result for any bit type — it is the flow area of the nozzles that matters, not the bit type. PDC bit hydraulics design may additionally consider directed flow for cleaning specific nozzle configurations, but the fundamental two-pass optimization criterion (whether to maximize HHPb or JIF) and the corresponding Pb/Ps relationship remain the same as for tricone bits.