In a positive displacement screw pump, theoretical displacement (Q_theor) is determined purely by screw geometry and shaft rotational speed: Q_theor = V_rev * N. However, because manufacturing clearances must exist between intermeshing screw threads and the housing bore (typically 0.002 to 0.006 inches), high discharge pressure drives fluid backward through these clearances toward the suction port. This backward leakage is internal slip flow (Q_slip), governed by the relation Q_slip = C_slip * (Delta_P / nu^a), where Delta_P is differential pressure, nu is kinematic viscosity, and a is an empirical exponent (typically 0.33 to 0.50). On high-viscosity fluids (> 500 cSt), internal slip is virtually zero, yielding volumetric efficiencies above 95%. Conversely, on light hydrocarbons (such as diesel, naphtha, or condensate with nu < 2 cSt) operating at high differential pressure (> 15 bar), slip flow surges, cutting volumetric efficiency to below 60%.

Twin-screw pumps utilize two parallel intermeshing rotors driven by external timing gears and supported by external bearings isolated from the pumped fluid by mechanical seals. Because the screws never touch each other or the liner wall, twin-screw pumps can handle multi-phase fluids, high gas volume fractions (GVF up to 95%+), abrasive entrained solids, and non-lubricating liquids. In contrast, three-screw pumps feature one central power rotor that drives two flanking idler rotors purely through hydrodynamic fluid film contact. Three-screw pumps have no external timing gears, making them more compact and exceptionally quiet (< 68 dBA), but they strictly require clean, lubricating liquids (viscosity >= 2 cSt, zero abrasive particulates) to avoid rotor galling and seizure.

Pump shaft power consists of three components: hydraulic work (W_hyd = Q * Delta_P / 1714), mechanical bearing/seal friction (BHP_mech), and viscous shear friction (BHP_visc). Viscous shear power represents the energy dissipated shearing fluid in the tight annular clearances between the rapidly spinning screws and the stationary bore: BHP_visc is directly proportional to dynamic viscosity (mu) and the square of speed (N^2). When cold starting a pump on heavy fuel oil (HFO) or bitumen at ambient temperature (e.g. 5,000 cSt vs 50 cSt operating), the viscous drag power can be 4 to 8 times higher than normal running power, demanding an oversized driver motor or a soft-start variable frequency drive (VFD).

Unlike centrifugal pumps that ingest fluid continuously, screw pumps ingest fluid in discrete rotating pockets. As viscosity rises, high fluid internal shear prevents viscous oil from accelerating quickly through the suction port into the opening screw cavities. Per Hydraulic Institute (ANSI/HI 3.1-3.5) standards, Net Positive Suction Head Required (NPSHr) increases sharply with viscosity. If operating speed is not reduced, localized pressure inside the screw inlet drops below vapor pressure, causing cavitation, acoustic knocking, incomplete chamber filling, and severe mechanical vibration. For viscosities above 1,000 cSt, pump rotational speed must typically be derated from standard 1,750 RPM down to 880 RPM, 580 RPM, or lower.

Rotary screw pumps are rigid positive displacement machines: every revolution transfers an exact volume of fluid regardless of discharge pressure. Unlike a centrifugal pump that hits a maximum deadhead shutoff head if a discharge valve is closed, a screw pump will continue building pressure until the driving motor stalls, the pump casing fractures, or the drive shaft shears in two. API 676 Section 6.13 strictly mandates that every rotary pump must be protected by a full-flow pressure relief valve (PRV) sized to bypass 100% of maximum rated pump flow without allowing system pressure to exceed 110% of maximum allowable working pressure (MAWP).