1-2 of 2
Keywords: closure relation
Sort by
Proceedings Papers

Publisher: BHR Group
Paper presented at the 11th North American Conference on Multiphase Production Technology, June 6–8, 2018
Paper Number: BHR-2018-005
... for slip between the phases. Field data collected during his stay at Shell Oil in the USA enabled Nico Ros to adapt his closure relations based on atmospheric laboratory data at Shell Rijswijk. This led to an important improvement of the accuracy of his model. Quite a number of the models form the core...
Proceedings Papers

Publisher: BHR Group
Paper presented at the 10th North American Conference on Multiphase Technology, June 8–10, 2016
Paper Number: BHR-2016-087
... < Ucrit , the pressure gradient decreases with increasing surfactant concentration (up to a maximum concentration). Most of the foam is transported along the wall of the pipe as wavy structures. For a gas flow near the critical velocity these foam waves seem to flow over a stagnant foam substrate. Foam seems to suppress the entrainment of liquid into the gas core. The viscosity of the foam is significantly higher than that of the base liquid constituting this foam. 3.2 Flow loop data used for modelling Nimwegen (2015, ref. (6)) has performed experiments in three flow loops having an inner diameter of 34, 50 or 80 mm. Dry air is flowing into the setup at the bottom, and is released to atmosphere at the top of the setup. Liquid is injected into the system downstream of the gas inlet through an annulus, thereby creating a liquid film at the wall. The liquid is dragged by the air flow to the top of the pipe where it is separated from the air stream in a separator. A short distance downstream of the liquid injection foam is visually present in case surfactants have been added to the liquid. Two fast closing ball valves are used to shut-in the liquid/foam flow during a holdup measurement. Directly after shut-in of the liquid/foam flow (i.e. before foam collapse), the volume of the liquid + foam is measured, which gives the value for f. After waiting for about 30 mins, all foam has collapsed (or most liquid has drained out of the foam) and the volume of the liquid below the foam is measured, which gives the value for l. Two pressure transducers are used to estimate the pressure gradient and are located in between the two fast-closing valves. In case a surfactant mixture was tested in the setup, a master solution was prepared initially in a small portable vessel. The amount of water and surfactant for this master solution was measured on a scale with an accuracy of 0.1 g. Hereafter, the master solution is poured into the large tank and mixed with an additional amount of water in order to obtain a specific surfactant concentration. The error in surfactant concentration is estimated to be less than ~0.02ppm. Two surfactants have been tested, which are reffered to as Foamer A and Foamer B, see table 1. Besides the flow loop data mentioned above, some other data from literature (air/water flows) has been used in validation of the model. Table 1 shows the data sets that are used, together with the symbols used throughout the paper and some key numbers. 90 © BHR Group 2016 Multiphase 10 Table 1: Datasets used for modelling 3.3 Modelling Based on the observations of foam flow (section 3.1), a film flow model has been selected to predict foam flow behaviour. The film flow model assumes that all liquid flows as a thin film along the wall. The film thickness, f, is constant along the pipe circumference and the interaction of waves with the gas core is only represented via an interfacial shear stress, i. Based on the observations of foam flow, liquid entrainment has been neglected. The model uses a momentum and mass balance to compute the total liquid holdup, l, and pressure gradient, zp, for a given flow condition (i.e. combination of superficial gas and liquid velocity, Usg, and Usl, and surfactant concentration, C). This film flow model follows similar arguments as Hewitt (1961, ref. (11 The shear stress in the film, , is computed via a momentum balance: where r is the radial coordinate, f is the local film quality (i.e. partial volume of free gas in the film), g and l are the gas and liquid phase density, and g is the gravitational acceleration. The term in square brackets equals the local film density, f. The shear stress profile is obtained by integration of equation (1) over f using a suitable closure relation for i. From the shear stress profile the velocity gradient in the liquid film, ruf, is calculated via: © BHR Group 2016 Multiphase 10 91 where f,tot is the local total viscosity of the film, which may include non-Newtonian behaviour as well as turbulence effects (apparent viscosity). Assuming no-slip at the wall, the velocity profile in the liquid film, uf, is obtained by integration of equation (2) over f. The onset of liquid loading is marked by a negative film velocity near the wall, which corresponds to a negative wall shear, w. An example of the film shear and velocity profile is presented in fig. 2, showing a condition with negative w (i.e. partial down flow). w is related to zp and l via: Figure 2: Example of the film shear (blue solid line) and velocity (green dashed line) in the film for f = 500 m, i = 5 Pa, and w = 1 Pa in a ID = 50 mm tube. y is the distance to the wall (y = ½D r). In this profile f,tot equals 1 mPas and does not depend on location in the film (i.e. water without turbulence effects). The superficial liquid velocity is computed from the velocity profile via: where Dc = D - 2 f is the diameter of the gas core corrected for the film thickness. Usl,model is an increasing function of the film thickness, and is computed by the model. Note that equation (4) only integrates the liquid phase inside the film, and does not consider the gas phase. Closure models for i, f, and f,tot are required to have a closed system of equations (sections 3.3.1 to 3.3.3). These closure relations are developed using the flow loop data of Nimwegen (2015) and an extension of this work using another surfactant. In these experiments the pressure gradient, zp, the total liquid holdup, l, and the total film holdup (including foam and free liquid), f, have been measured (section 3.2). The flow loop tests are vertical upward gas/liquid flows with various values for C, D, Usg and Usl. Equations (1), (2) and (4) together with the required closure relations are solved numerically to allow for f,tot and f to vary over the film thickness (note that in the current model f and f are assumed constant over the film thickness due to the absence of more detailed data on this). A solver computes Usl,model for various values of f until 92 © BHR Group 2016 Multiphase 10 Usl,model reaches the value specified by the flow conditions (i.e. Usl,model = Usl). In this way the liquid mass balance is satisfied. To compute the TPC for a well, where gas expansion is significant, the flow conditions change along the pipe length and the model needs to be solved multiple times. The TPC then follows from a straight forward integration of the pressure gradient along the pipe length. 3.3.1 Closure relation for film quality With air/foam flows, foam is formed by entrainment of gas into the liquid film, which increases the quality of the film. The mean film quality of the experimental data is calculated by: f is reasonably well correlated with f/D, see fig. 3. f/D is computed from f via: Figure 3: Mean film quality versus the normalised film thickness for a subset of the data used (C > 0 ppm). The left graph represent the data of Nimwegen (2015) using the Foamer A, and the right graph represent the data obtained in this study using the Foamer B. The solid lines represent the closure relation (eqn. (7) to (10 Table 1 presents the details of the data sets. Gas entrainment, which...

Product(s) added to cart

Close Modal