Modelling Twin Screw Multiphase Pumps a Realistic Approach to Determine the Entire Performance Behaviour

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Multiphase pump
  PAGES 104 // 105 ABSTRACT Multiphase screw pumps are used for the delivery of gas-liquid-flows even at high gas rates. In order to estimate their delivering behaviour a model is derived, which is based on mass and energy balances for single closed chambers formed by the intermeshing and counter-rotating screws. Thereby the pressure profiles inside the pumps are predicted, which determine the mechanical loads to the rotating and static components as well as the delivered volume flows. In order to verify the calculated results, the pressure profiles are measured along the inside of the cylindrical casing in dependence of several characteristic operating modes of multiphase screw pumps. NOMENCLATURE General symbols b width, m c specific heat capacity, J/kgK d diameter, m h specific enthalpy, J/kg h pitch, m M mass, kg M   mass flow, kg/s n rotational frequency, 1/s N number of rotations, - p pressure, Pa R radius, m R individual gas constant, J/kgK s height, m t time, s T temperature, K U internal energy, J V volume, m3 v velocity, m/s V   volume flow, m3/s W work, J z axial coordinate, m   gas volume fraction, -   efficiency, -   rotation angle, rad   kinematic viscosity, m2/s   density, kg/m3 Subscripts0 initial 1 status 1 2 status 2 g gas h hydraulic i chamber index in inflow l liquid loss loss n rotation Modelling Twin-Screw Multiphase Pumps - A RealisticApproach to Determine the Entire Performance Behaviour Prof. Dr.-Ing. Dr.h.c. D. Mewes, Dr.-Ing. G. Aleksieva, Dipl.-Ing. A. Scharf, Prof. Dr.-Ing. A. Luke Leibniz University of Hannover, Germany  2ND INTERNATIONAL EMBT CONFERENCE // MODELLING TWIN-SCREW MULTIPHASE PUMPS – A REALISTIC APPROACH TO DETERMINE THE ENTIRE PERFORMANCE BEHAVIOUR Prof. Dr.-Ing. Dr.h.c. D. Mewes, Dr.-Ing. G. Aleksieva, Dipl.-Ing. A. Scharf, Prof. Dr.-Ing. A. Luke out outflow p constant pressure rec recirculation rot rotational t before a time step t +  t after a time step theo theoretical vol volumetric 1 INTRODUCTION Multiphase pumping is applied in the oil and natural gas exploring and conveying industry especially in offshore applications. By means of multiphase transport cost-intensive separation units on offshore platforms can be avoided, because the gas-liquid-mixtures are conveyed directly to central separation units located onshore. The multiphase pumps are installed on or close to the wellheads. As a consequence the number of platforms is reduced, which leads to a saver and more efficient offshore oil production (1). Multiphase delivering systems have to handle volume flows with varying gas void fractions. Therefore positive displacement pumps are superior to centrifugal ones. Screw pumps operating with two intermeshing co-rotating screws turned out to be an appropriate pump type for multiphase delivering systems. They can handle gas-liquid-flows with gas volume fractions up to 0.95 and withstand even temporary dry runs. Furthermore, screw pumps are suitable for the delivery of high-viscous fluids (2) since they operate without valves. High rotational frequencies of the intermeshing screws lead to a compact design compared to other rotating displacement pumps.In Figure 1 the design of a screw pump is presented. The multiphase mixture entering the pump gets into the chambers formed by the intermeshing screws and the enclosing housing(Figure 2). Figure 1: Twin screw pump Figure 2: Position and shape of a chamber in a screw pump Due to the rotation of the screws, the chambers are closed at the suction side of the pump and move along the screw axis towards the outlet. At the discharge side, the chambers open and the gas-liquid-mixtures are released through the outlet. Since the rotation of the screws is contactless, several gaps are located between the intermeshing screws and between the screws and the housing. Three different types of gaps occur and are shown schematically in Figure 3.  PAGES 106 // 107 ModellingTwin-Screw Multiphase Pumps - A Realistic Approach to Determine the Entire Performance Behaviour Figure 3: Gap types in a screw pump The circumferential gap is located between the tip circle of a screw and the inner wall of the housing. The radial gap is placed between the tip circle of one screw and the root circle of the opposed screw. The flank gap is a lenticular gap, which is placed between the flanks of adjacent intermeshing screws. During the movement of a chamber along the axis of the intermeshing screws, the chamber pressure increases. This leads to pressure differences between adjacent chambers and thus to internal backflows of the gas-liquid-mixture through the different types of gaps. The gap flows determine the shape of the resulting pressure profiles along the screw axis. The pressure profiles are highly affecting the delivery flows as well as the mechanical loads to the pump’s components. In order to estimate the delivering behaviour of screw pumps the calculation of the pressure profiles are done by mass and energy balances for closed chambers. In order to verify the calculated pressure profiles the pressure build-up is measured in a multiphase screw pump for different operational conditions. The experimental results are compared with the calculated ones. There are several attempts to describe the delivering behaviour of multiphase screw pumps by the transport equations for momentum, mass and energy. Etzold (3) calculates the change of pressure in closed chambers inside the pump and the loss flows by setting up boundary conditions for estimated steadily rising pressures inside the closed chambers while moving from the inlet to the outlet. Furthermore, Etzold (3) reduces the boundary value problem to an initial value problem, which he solves iteratively. Körner (4) and Wincek (5) use similar approaches but calculate two separate cases with an integer number of stages, which are below and above the real number of stages. Weighting these two cases according to the real number of stages leads to an approximate solution. Feng, Yueyuan, Ziwen and Pengcheng (6) present a model, by which the backflow within the screw pump depending on the rotational angle is determined. There is two-phase flow in the radial and flank gaps and pure liquid flow in the circumferential gaps. The effect of acceleration pressure drop on the gap flows is neglected. Nakashima (7) chooses a different approach by deviding the multiphase pumping operation into an arrangement of fundamental processes like separation, pumping, compression and mixing. Nakashima (8) applies the process simulator HYSYS for solution. Naujoks (8) applies a chamber model to calculate the delivering behaviour of screw compressors, which considers the reduction of the chamber volume. Neumann (9) predicts the delivering behaviour of screw compressors by means of mass and energy balances, including the heat transfer across the chamber boundaries. 2 MATHEMATICAL FORMULATION The volume flow of the multiphase mixture at inlet conditions reclosstheo VVVV     (1) is determined by the difference between the theoretical displacement volume flow theo V   and the loss flow loss,gloss,lloss VVV     (2) and the recirculation flow rec V  . The theoretical displacement volume flow is a function of the shape and the rotational frequency of a twin screw pump. In order to estimate the  Prof. Dr.-Ing. Dr.h.c. D. Mewes, Dr.-Ing. G. Aleksieva, Dipl.-Ing. A. Scharf, Prof. Dr.-Ing. A. Luke performance of a pump the volumetric efficiencyVV theovol    (3) is defined as the ratio of the theoretical displacement volume flow theo V   and the actual displacement volume flow of the pump V  .Within some special designed pumps, separated liquid is recirculated from the outlet to the inlet (10). This flow is defined as recirculation flow. This design helps to enhance the sealing of the gaps inside the pump for high gas volume fractions. The loss flows are directed across the closed chambers inside the pump via different gaps back to the inlet of the pump. They are of single phase or of multiphase type and are caused by two components. One is pressure driven and the other component is a shear flow induced one and due to the rotation of the screws (11). 2.1 Mass and energy balances for closed chambers The movement of the chambers along the rotating screws is described by time intervalls. For each time intervall mass and energy balances are set up for the closed chambers, considered as open systems (Figure 4). Figure 4: Closed chamber as an open mass system The differential equation for the change of liquid mass inside a closed chamber gives    outlinll iii MMdtdM   (4) and for the mass change of gas    outgingg iii MMdtdM   (5) i has the meaning of the chamber index. Eq. 3 and Eq. 4 mean that the amount of each phase in a closed chamber is only changed by the incoming and the outgoing mass flows crossing the gaps. After each full rotation (N n    N n  + 1) the index of a closed chamber increases by the number of 1 (i   i + 1). This leads to initial conditions          N,n1tM1N,0tM i1i ll  (6)          N,n1tM1N,0tM i1i gg  (7) for the next chamber, which postulate that the masses of liquid and gas are kept constant when they are transferred to the next chamber.Since enthalpy is transferred between adjacent chambers via the gap streams, a closed chamber is considered as a transient open thermodynamic system. Figure 5: Closed chamber as an transient open thermodynamic system The energy balance for a closed chamber is     voutggll inggll i WQhMhMhMhM dtdU iiiiiiii      (8) The change of the internal energy U i  by time is determined by the sum of incoming and outgoing enthalpy flows. The heat flow Q   is crossing the chamber boundary and W v  is the 2ND INTERNATIONAL EMBT CONFERENCE // MODELLING TWIN-SCREW MULTIPHASE PUMPS – A REALISTIC APPROACH TO DETERMINE THE ENTIRE PERFORMANCE BEHAVIOUR
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