Report

New Comprehensive Equation to Predict Liquid Loading Shu Luo The University of Tulsa Foam Flow Meeting, Jul.9th, 2013 1 Outline • Introduction • Background and Approach • Model Formulation • Model Validation • Program Demonstration • Summary Foam Flow Meeting, Jul.9th, 2013 2 What is liquid loading? • Minimum pressure drop in the tubing is reached • The liquid drops cannot be entrained by the gas phase (Turner et al.) • The liquid film cannot be entrained by the gas phase (Zhang et al., Barnea) The answers from different definitions are not the same • Foam Flow Meeting, Jul.9th, 2013 3 Traditional Definition IPR Stable OPR Unstable Transition Point Liquid Loading Foam Flow Meeting, Jul.9th, 2013 4 Traditional Definition • As gas flow rate increases (∆ ) ( ) and (∆ ) ( ) • At low velocities increase in (∆ ) (∆ ) ( ) decreases faster than ( ) • When two gradients are equal, minimum occurs Foam Flow Meeting, Jul.9th, 2013 5 Definition based on Mechanisms • Two potential mechanisms of transition from annular to slug flow Droplet reversal Film Reversal • Models are either based on droplet reversal (Turner) or film reversal (Barnea) Foam Flow Meeting, Jul.9th, 2013 6 Air-Water Flow • Anton Skopich conducted experiments in 2” and 4” pipes • The results observed are different based on film reversal and minimum pressure drop Foam Flow Meeting, Jul.9th, 2013 7 Calculation Procedure • • • • Total pressure drop is measured and gradient is calculated Holdup is measured and gravitational gradient is calculated Subtracting gravitational pressure gradient from total pressure gradient to get frictional pressure gradient By dividing the incremental pressure gradient by incremental gas velocity, changes in gravitational and frictional gradients with respect to gas velocity are calculated. Foam Flow Meeting, Jul.9th, 2013 8 Magnitude of Gravitational vs. Frictional Gradient with respect to Gas Velocity Foam Flow Meeting, Jul.9th, 2013 9 dPG vs. dPF Air-Water, 2 inch, vsl=0.01 m/s Minimum Foam Flow Meeting, Jul.9th, 2013 10 Total dp/dz Air-Water, 2 inch, vsl=0.01 m/s Film Reversal Foam Flow Meeting, Jul.9th, 2013 11 dP/dz)G vs. dP/dz)F Air-Water, 2 inch, vsl=0.01 m/s dp/dz)F is zero Foam Flow Meeting, Jul.9th, 2013 12 dP/dz)G vs. dP/dz)F Data from Netherlands (2 inch) dp/dz)F is zero Foam Flow Meeting, Jul.9th, 2013 13 dP/dz)G vs. dP/dz)F TUFFP (3 inch, vsl=0.01 m/s) dp/dz)F is zero Foam Flow Meeting, Jul.9th, 2013 14 dP/dz)G vs. dP/dz)F TUFFP (3 inch, vsl=0.1 m/s) dp/dz)F is zero Foam Flow Meeting, Jul.9th, 2013 15 dPG vs. dPF Air-Water, 4 inch, vsl=0.01 m/s Minimum Foam Flow Meeting, Jul.9th, 2013 16 Total dp/dz Air-Water, 4 inch, vsl=0.01 m/s Film Reversal Foam Flow Meeting, Jul.9th, 2013 17 dP/dz)G vs. dP/dz)F Air-Water, 4 inch, vsl=0.01 m/s dp/dz)F is zero Film reversal Foam Flow Meeting, Jul.9th, 2013 18 Liquid Loading Definition • Liquid loading starts when liquid film reversal • • occurs We adopt the model of film reversal to predict inception of liquid loading The reason for this adoption, as we will show later, is because we are able to better predict liquid loading for field data using this methodology. Foam Flow Meeting, Jul.9th, 2013 19 Outline • Introduction • Background and Approach • Model Formulation • Model Validation • Program Demonstration • Summary Foam Flow Meeting, Jul.9th, 2013 20 Background Turner’s Equation • • The inception of liquid loading is related to the minimum gas velocity to lift the largest liquid droplet in the gas stream. Turner et al.’s Equation: , • − = 6.558 2 0.25 This equation is adjusted upward by approximately 20 percent from his original equation in order to match his data. Foam Flow Meeting, Jul.9th, 2013 21 Background Drawbacks with Turner’s equation • Turner’s equation is not applicable to all field data. Coleman et al. proposed equation (without 20% adjustment ) , • • • − = 5.465 2 0.25 Veeken found out that Turner’s results underestimate critical gas velocity by an average 40% for large well bores. Droplet size assumed in Turner’s equation is unrealistic based on the observations from lab experiments. Turner’s equation is independent of inclination angle which is found to have great impact on liquid loading. Foam Flow Meeting, Jul.9th, 2013 22 Approach Film Model • Two film models are investigated to predict liquid loading: Zhang et al.’s model(2003) is developed based on slug dynamics. Barnea’s model(1986) predicts the transition from annular to slug flow by analyzing interfacial shear stress change in the liquid film. Foam Flow Meeting, Jul.9th, 2013 23 Approach Zhang et al.’s Model Foam Flow Meeting, Jul.9th, 2013 24 Approach Zhang et al.’s Model • • Momentum equation for annular flow: With other equations and closure relationships, we can solve this momentum equation and calculate critical gas velocity Foam Flow Meeting, Jul.9th, 2013 25 Approach Barnea’s Model • • • Constructing force balance for annular flow and predict the transition from annular to slug flow by analyzing interfacial shear stress changes. The combined momentum equation: 1 1 + − − − sin = 0 Interfacial shear stress from Wallis correlation: 2 1 = 2 (1 − 2)4 Foam Flow Meeting, Jul.9th, 2013 Schematic of Annular Flow 26 Approach Barnea’s Model • • • • Solid curves represent Interfacial shear stress from combined momentum equation Broken curves represent Interfacial shear stress from Wallis correlation Intersection of solid and broken curves yields a steady state solution of film thickness and gas velocity at transition boundary Another transition mechanism is liquid blocking of the gas core. Foam Flow Meeting, Jul.9th, 2013 Transition 27 Outline • Introduction • Background and Approach • Model Formulation • Model Validation • Program Demonstration • Summary Foam Flow Meeting, Jul.9th, 2013 28 Three Main Modifications • Accounted for variable liquid film thickness • Changed the equation for liquid film friction • factor Accounted for presence of liquid in the form of droplet Foam Flow Meeting, Jul.9th, 2013 29 Model Formulation • In inclined wells, the film thickness is expected to vary with radial angle Vertical Well Foam Flow Meeting, Jul.9th, 2013 Inclined Well 30 Original Barnea’s Model at Different Inclination Angles Foam Flow Meeting, Jul.9th, 2013 31 Non-uniform Film Thickness Model Foam Flow Meeting, Jul.9th, 2013 32 Non-uniform Film Thickness Model • • Let A1=A2, we can find this relationship. 1 = [ 0, + , ] 2 If film thickness reaches maximum at 30 degree inclination angle Foam Flow Meeting, Jul.9th, 2013 33 Non-uniform Film Thickness Model • We will use the following film thickness equation in the new model: ≤ ≤ , = − + > , = − + Foam Flow Meeting, Jul.9th, 2013 34 Non-uniform Film Thickness Model • • Only maximum film thickness will be used in the model because thickest film will be the first to fall back if liquid loading starts. Find critical film thickness δT by differentiating momentum equation. δT equals to maximum film thickness δ(π,30). 1 1 = [0 + , 30 ] = 2 2 Foam Flow Meeting, Jul.9th, 2013 35 Non-uniform Film Thickness Model Foam Flow Meeting, Jul.9th, 2013 36 Interfacial Friction Factor • • Critical gas velocity calculated by Barnea’s model is conservative compared to other methods. Fore et al. showed that Wallis correlation is reasonable for small values of film thickness and is not suitable for larger film thickness liquid film. A new correlation is used in the new model : = 0.005 1 + 300 Foam Flow Meeting, Jul.9th, 2013 1+ 17500 ℎ − 0.0015 37 Outline • Introduction • Background and Approach • Model Formulation • Model Validation • Program Demonstration • Summary Foam Flow Meeting, Jul.9th, 2013 38 Turner’s Data • • • 106 gas wells are reported in his paper, all of the gas wells are vertical wells. 37 wells are loaded up and 53 wells are unloaded. 16 wells are reported questionable in the paper. Current flow rate and liquid loading status of gas well are reported. Foam Flow Meeting, Jul.9th, 2013 39 Turner’s Model Results Turner’s Data Vg < Vg,c Foam Flow Meeting, Jul.9th, 2013 Vg > Vg,c 40 Zhang et al.’s Model Results Turner’s Data Foam Flow Meeting, Jul.9th, 2013 41 Barnea’s Model Results Turner’s Data Foam Flow Meeting, Jul.9th, 2013 42 New Model Results Turner’s Data Foam Flow Meeting, Jul.9th, 2013 43 Coleman’s Data • • • 56 gas wells are reported, all of the wells are also vertical wells. These wells produce at low reservoir pressure and at well head pressures below 500 psi. Coleman reported gas velocity after they observed liquid loading in gas wells. Foam Flow Meeting, Jul.9th, 2013 44 Turner’s Model Results Coleman’s Data Foam Flow Meeting, Jul.9th, 2013 45 Zhang et al.’s Model Results Coleman’s Data Foam Flow Meeting, Jul.9th, 2013 46 Barnea’s Model Results Coleman’s Data Foam Flow Meeting, Jul.9th, 2013 47 New Model Results Coleman’s Data Foam Flow Meeting, Jul.9th, 2013 48 Veeken’s Data • • • • Veeken reported offshore wells with larger tubing size. 67 wells, which include both vertical and inclined wells, are presented. Similar to Coleman’s data, critical gas rate was reported. Liquid rate were not reported in the paper. We assumed a water rate of 5 STB/MMSCF. Foam Flow Meeting, Jul.9th, 2013 49 Turner’s Model Results Veeken’s Data Foam Flow Meeting, Jul.9th, 2013 50 Zhang et al.’s Model Results Veeken’s Data Foam Flow Meeting, Jul.9th, 2013 51 Barnea’s Model Results Veeken’s Data Foam Flow Meeting, Jul.9th, 2013 52 New Model Results Veeken’s Data Foam Flow Meeting, Jul.9th, 2013 53 Chevron Data • Production data: Monthly gas production rate Monthly water and oil production rate • 82 wells have enough information to analyze • • liquid loading Two tubing sizes: 1.995 and 2.441 inch Get average gas and liquid production rate when cap string is installed from service history. Assume liquid loading occurred at this point. Foam Flow Meeting, Jul.9th, 2013 54 Production Data Foam Flow Meeting, Jul.9th, 2013 55 Turner’s Model Results Chevron Data Foam Flow Meeting, Jul.9th, 2013 56 Zhang et al.’s Model Results Chevron Data Foam Flow Meeting, Jul.9th, 2013 57 New Model Results Chevron Data Foam Flow Meeting, Jul.9th, 2013 58 ConocoPhillips Data • Daily production data and casing and tubing • • • pressure data are available Select 62 wells including 7 off-shore wells Two tubing size: 1.995 and 2.441 inch Determine liquid loading by casing and tubing pressure divergence. Foam Flow Meeting, Jul.9th, 2013 59 ConocoPhillips Field Data liquid loading starts Pc and Pt diverge Liquid Loading starts at 400 MCFD Foam Flow Meeting, Jul.9th, 2013 60 Turner’s Model Results ConocoPhillips Data Foam Flow Meeting, Jul.9th, 2013 61 Zhang et al.’s Model Results ConocoPhillips Data Foam Flow Meeting, Jul.9th, 2013 62 New Model Results ConocoPhillips Data Foam Flow Meeting, Jul.9th, 2013 63 Outline • Introduction • Background and Approach • Model Formulation • Model Validation • Program Demonstration • Summary Foam Flow Meeting, Jul.9th, 2013 64 Program • This program is developed in .net framework • using c sharp. It consists two pages: single well calculation and multiple well calculation. Foam Flow Meeting, Jul.9th, 2013 65 Summary • • • • • We analyzed various definitions of liquid loading and concluded that definition based on liquid film reversal is most appropriate. A new model for liquid loading is developed for gas well using liquid film reversal method. The new model is applicable for both vertical and inclined wells. The new model is able to better predict the inception of liquid loading compared to most often used Turner et al.’s equation. Liquid loading prediction program is developed to determine onset of liquid loading. Foam Flow Meeting, Jul.9th, 2013 66 Thank You! Questions… Foam Flow Meeting, Jul.9th, 2013 67