## An Experimental Investigation and Process Modeling of Multiphase Flow Through Multiple Restrictions

##### Doctoral thesis

##### Permanent lenke

http://hdl.handle.net/11250/2373704##### Utgivelsesdato

2015##### Metadata

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##### Sammendrag

A methodology for simultaneous estimation of multiphase flow rate and stream
composition has been developed to be applied in a multiple restriction assembly composed of
two orifice meters and a cage trim valve. These differential pressure elements are typical
instrument installed in the wellhead of production wells in Urucu field (Petrobras/Brazil). To
deliver composition and rates four steps were done: 1) a multi-rate well test - an experimental
procedure carried out in real operation conditions. 2) modeling of multiphase flow expansion
process through cage trim valves. 3) performance and validation of multiphase flow through
orifice plate meters by the use of homogeneous and slip models. 4) tuning and metering
procedures for coupling the valve and orifice plate models. The last investigation developed a
full field production optimization procedure honouring pressure and routing constraints to be
applied in multiple wells.
Essentially, the research performed in this thesis is an experimental work followed by
numerical modeling. Model errors and performance validation were calculated on the basis of
measured data from a multi-rate well test. This field scale experiment consisted in a
sequential step response test followed by a transient and a steady state period “a priori” to
each next step. Three wells named Well 1, Well 2 and Well 3 were single routed to a test
separator. Two types of well performance were investigated: 1) production with stream
composition variation caused by gas/water coning. 2) production with steady state
composition. Eight wellhead variables were monitored: two orifice plate differential
pressures, the differential pressure and temperature through the cage valve, the downstream
choke pressure, the wellhead pressure and temperature and the gathering system temperature.
The field scale experiments generated a database composed by 1781 test points, averaged in
30 minutes interval.
Multiphase flow expansion process through cage trim valve is discussed in chapter 2. It
represents an enabler investigation to the thesis main objective. A systematic error in the
downstream temperature was calculated up to 8% for isenthalpic flash (PS) and up to 14% for
isentropic flash (PH) through the cage trim valve. The maximum error corresponded to the
maximum pressure drop in the valve. Deviation from ideal process in cage trim valve was
quantified with an adiabatic efficiency term. This adiabatic efficiency correction works as a
tuning parameter updated periodically to be used in the metering model. The flash input
parameters influence in the adiabatic efficiency calculation was studied through a parametric
analysis. The parameters investigated were: the gas/oil ratio, the valve pressure drop, the
wellhead pressure and the water cut were. Among the conclusions, it has been found that
increase the gas/oil ratio and decrease the differential pressure in the valve influenced the
expansion process in opposite directions. The observation explains the difference in adiabatic
efficiency behavior for wells with composition variation compared with the ones with
constant composition.
The performance and validation of orifice plate meter to estimate oil, gas and water
flow rates is discussed in chapter 3. It represents an enabler investigation to the thesis main
objective developed in chapter 4. It has been concluded the model which honors the slip
between liquid and gas phase is more accurate to predict multiphase flow rate through orifice
plates. It was found a coefficient of variation for the root mean square error fewer than 4% for
the slip model and fewer than 10% for the homogenous model. So, it was decided to use an
equation that incorporates the slip between gas and liquid to calculate the discharge coefficient in the tuning model and to calculate the orifice plate differential pressure in
metering model.
The simultaneous rate and composition estimation strategy was designed with a periodic
tuning and metering procedures in chapter 4. Periodic tuning runs after every well test
performed in the field. The procedure calculates three calibration parameters: two orifice plate
discharge coefficients and the adiabatic efficiency related to fluid expansion process through
the cage trim valve. Multiphase flow rate and stream composition were calculated with a
mathematic optimization formulation which minimized the residual sum of squares error
between the calculated and the measured orifice plate differential pressure and the
downstream choke temperature. The objective function was solved with a mixed method
strategy composed by the box method and the sequential quadratic programming solvers.
Tuning and metering steps were implemented in a compositional process simulation
(Aspentech Hysys) with input data from the multi-rate experiment. Gas/liquid ratio (GLR)
calculation was privileged compared to the gas/oil ratio estimation running the metering
strategy for three unknowns (gas/water fractions and oil flow rate). When two unknowns were
defined (gas fraction and oil flow rate) the procedure estimated the gas/oil ratio more
accurately. One of optimization decision variables is the volumetric oil flow rate at standard
condition. Therefore, the global solution that minimizes the problem also delivers the phase
flow rates. Furthermore, once the composition is found, the flow rates can be calculated with
a single orifice plate as demonstrated in the results of chapter 3.