Pressure Drop in Pipe SystemsOIL AND GAS TRANSPORTATIONLesson Outcomes At the end of lecture, students should beable to:Explain the basic principles to determinepressure drops in pipingDescribe flow equations for liquid flow andcompressible flowApply flow equations to calculate pressuredrop in various types of pipeLecture Outline Introduction Basic principles applied for pressure drop determination Fluid flow equationsLiquid flowGas flow ExamplesIntroduction Piping design in production facilities involvesselection of pipe diameter and wall thickness. The pipe size selected must be sufficient to transportfluid from one point to the other (e.g. one processequipment to another). The concepts of pressure drop are applied for alltypes of pipe.Basic Principles In pressure drop calculation, the basic principles of fluid mechanics are applied. It includes:1. Reynolds Number2. Flow Regimes3. Bernoullis Theorem4. Darcy-Weisbach Equation5. Moody friction factor Invented by Osborne Reynolds in the 1880s A dimensionless parameter that relates the ratio of inertial forces to viscous forces Expressed by general equation: For liquid: For gases:Basic Principles Reynolds Number|DV+ Re| d Q G Sl) . (1 . 92 Re +| d S Qg20100 Re + Describe nature of fluid flow Two basic flow regimes for single-phase fluid: Laminar A stable well-ordered state of fluid flow in which all pairs ofadjacent fluid particles move alongside one another forminglaminates Characterized by smooth streamline and highly ordered motion Re4000Basic Principles Flow Regimes Energy contained in fluids is expressed in terms ofthe potential energy contained in an equivalentheight or head of a column of the fluid. Bernoullis theorem breaks down the total energy ata point in terms of1. The head due to its elevation above datum of zero potentialenergy2. A pressure head due to the potential energy contained in thepressure in the fluid at that point3. A velocity head due to the kinetic energy contained in thefluidBasic Principles Bernoullis Theorem Assume :1. No energy added to the fluid by pump or compressor2. Fluid is not performing workBasic Principles Bernoullis TheoremLHgV PZgV PZ O O O + O O214421442222221111 States that friction head loss between two points in a completely filled, circular cross section is proportional to velocity head and the length of pipe and inversely proportional to the pipe diameterBasic Principles Darcy-Weisbach Equationg DfLVHL22+ The Darcy-Weisbach equation forms the basis fornumerous other equations to determine pressureloss in specific applications The friction factor fudge factor already takesinto account the viscosity, density and internalpipe roughness How to find friction factor? Moody Diagram Fanning friction factorBasic Principles Darcy-Weisbach Equation Determined from Moody resistance diagram Friction factor is a function of the Reynolds numberand the relative roughness of the pipe For Laminar flow, For turbulent flow,is a function of both pipe roughness and Reynolds numberBasic Principles Moody Friction FactorDRe64+ ffBasic Principles Moody DiagramBasic Principles Moody Friction Factor Laminar Flow (Re4000) Friction factor, f depends on Reynolds number and the relative roughness of the pipe, /D f=0.042/Re0.194 (large pipe >8) f=0.042/Re0.172 (small pipe 8)Basic Principles Fanning Friction factor2000668 . 0dLVPf|+ @xd gfLVPcf@ ((+ @ 22 Few flow problems can be solved with an acceptable degree of accuracy when using equations designed to fit idealized application. Flow regimes and associated pressure drop discontinuities are complex phenomena and require complex equations to predict their relationships. For engineering design purposes, several empirical formulae have been developed to fit particular circumstances in predicting flow capacity and pressure dropFluid Flow EquationsFluid Flow Equations For liquid flow:Darcy-Weisbach EquationGeneral EquationHazen Williams Equation For gas flow:General EquationWeymouth EquationPanhandle EquationSpitzglass Equation For two-phase flow Darcy-Weisbach Equation General Equation Hazen-Williams formulaFluid Flow Equations - Liquid FlowdLV fP20013 . 0+ @526.) . () 10 5 . 11 (dG S fLQPl( + @85 . 1 87 . 485 . 11015 . 0C dL QHL+Fluid Flow Equations - Liquid Flow General Equation Panhandle A Equation Panhandle B EquationFluid Flow Equations - Gas Flow= =21122215199 . 0'_Z'[(+fLS ZTP P dQg= =62 . 2058 . 0853 . 012221020 . 0 dS L ZTP PE Qmg '_Z'[(+= =53 . 251 . 0961 . 012221028 . 0 dS L ZTP PE Qmg '_Z'[(+ Weymouth Equation Spitzglass EquationFluid Flow Equations - Gas Flow= =211222167 . 211 . 1'_Z'[(+LS ZT P Pd Qg21503 . 06 . 3109 . 0'_ZZZZ'[--m,O O@+ddLSd hQwg Recommended guidelines for the usage ofgas flow equationsFluid Flow Equations - Gas FlowGAS FLOW EQUATION USAGEGENERAL EQUATION Most general usageWEYMOUTH EQUATIONFor small diameter, shot-run pipesWithin production facilities where Reynolds Number are expected to be highPANHANDLE EQUATIONFor large diameter, long-run pipesSPITZGLASS EQUATIONLow pressure vent-line, less than 12 diameter5 minutes Q & A