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Managing flow assurance uncertainty through stochastic methods and life of field multiphase simulation
A. E. Johnson1, T. Bellion
1, T. Lim
1, M. Montini
2, A I. Humphrey
3
1FEESA Ltd, Farnborough, Hampshire, GU14 7LP, United Kingdom
2ENI Divisione E&P, Via Emilia, 1 - 20097 San Donato Milanese, Italy
3 BP Exploration, Sunbury-on-Thames, Middlesex, TW16 7LN, United Kingdom
ABSTRACT
Multiphase simulators are used widely by flow assurance engineers but the inputs to the
simulator are often thought of as apparent certainty whereas, more accurately, they
represent unquantified uncertainty. This paper shows how stochastic methods combined
with life of field multiphase simulation can be applied to the design and operation of
surface facilities, leading to more appropriate and economic systems. In particular, case
studies of three marginal projects are presented, namely: handling reservoir uncertainty
for a multiple oil well production system, Mono Ethylene Glycol optimisation of a large
wet gas network and hydrate management of a new oil well tieback to an existing
facility.
1 INTRODUCTION
Stochastic methods have become standard for oil and gas reservoir engineers and more
widely for economists, to help them understand how input uncertainties affect predictions
of quantities such as reserves, production rates or net present value (NPV) of projects.
However, stochastic methods are not often used by other engineering disciplines that are
also affected by input uncertainties (from reservoir, but also measurement, operation,
etc.). For example, facilities engineers typically develop an arbitrary design case (i.e. a
snap-shot in time), which is some combination of the worst possible scenarios of each of
the key inputs, such as reservoir temperatures and well deliverability, each of these inputs
having uncertainty associated with them.
As many modern production system designs are for deeper water and longer step-outs,
making them economically marginal, assuming the arbitrary worst design case no longer
seems appropriate and understanding the effect of uncertainty on the design becomes
increasingly important.
Applying a life of field (LoF) approach to the modelling of production systems, results in
more rigour by removing the arbitrary choices and combinations of the worst of the worst
approach. This avoids over design of systems by consideration and acceptance of
quantified risk.
A multiphase thermal hydraulic network simulator (Maximus) was used to carry out
conceptual studies for the 3 cases presented in this paper. Maximus is a LoF, steady-state,
fully compositional, thermal-hydraulic, network solver primarily for the upstream oil and
gas industry, although it can be used for any steady state pipeline simulation (1).
Maximus has a built-in link to the PVT package Multiflash (2), through which it is easy
to calculate the phase behaviour of the fluids, including hydrates.
Combining the LoF approach with stochastic methods, uncertainty in design can be
further reduced, as demonstrated in the following case studies.
2 CASE STUDY 1 – HANDLING RESERVOIR UNCERTAINTIES FOR A DAISY
CHAINED MULTIPLE OIL WELL TIEBACK
2.1 Introduction
During conceptual design of a production network, handling the uncertainties is key to a
robust and appropriate design, for the operator to plan for the most likely behaviour of
the field as a whole, rather than the worst case scenario of every well at the same time.
This case looks at predicting the minimum cool down time (CDT), for a 40 km daisy
chained deep-water production system with 7 production wells spread across 3 fields
(Phi, Beta and Kappa) as shown in figure 1.
Figure 1: Schematic of the daisy chained production network
The main sources of uncertainties have been identified as the reservoir temperatures
(Tres) and liquid productivity index (PI). For each reservoir, data are provided about the
uncertainties of these input quantities to indicate the most likely, downside and upside
values. With 3 possibilities for each of the variables and each of the fields, assessing all
possible combinations would require 36 (729) LoF simulations to fully handle these
uncertainties.
Using experimental design techniques these 729 LoF cases can be reduced whilst still
ensuring statistically representative results. The cases were reduced from 729 to 27 by
applying the Taguchi method (3). This statistical approach, using (quality) loss functions,
is a common technique in chemical and manufacturing industries, where it is used on
process improvement and quality control.
Typically an oil production network requires a CDT greater than 10hours, which will
incorporate a significant no touch time before hydrate management procedures are
implemented. Due to operational requirements, this network required a minimum CDT
through LoF greater than 18hours, as schematically demonstrated in figure 2.
Figure 2: Simple schematic plot of CDT over LoF
2.2 Methodology
To reduce the potential 729 LoF simulations down to 27 statistically meaningful cases,
the relative dependence of the minimum CDT on variation of the individual variables
was found by running approximately 40 cases and ranking the significance of each
variable. This allowed for cases to be sorted as the orthogonal array shown in Table 1
(pre-defined in (3)), where the upside, most likely and downside of each variable for each
field were input as +1, 0 and -1 respectively. The upside and downside values were +/-
75% in the PIs and +/- 2 ºC in reservoir temperatures.
Table 1: Orthogonal variable array of 27 pre-defined cases
Table 1 shows the variables, sorted by CDT dependence, along with the minimum CDT
from each Maximus LoF network simulation. The variable that has greatest impact on the
Maximus Result
Case No. Phi PI Phi T Beta T Kappa T Beta PI Kappa PI Phi PI Phi T Beta T Kappa T Beta PI Kappa PI Min LoF CDT
1 0 0 0 0 0 0 0 0 0 0 0 0 31.0
2 0 0 -1 -1 0 1 0 0 1 1 0 1 28.9
3 0 0 1 1 0 -1 0 0 1 1 0 1 32.3
4 0 -1 0 -1 1 -1 0 1 0 1 1 1 28.7
5 0 -1 -1 1 1 0 0 1 1 1 1 0 27.7
6 0 -1 1 0 1 1 0 1 1 0 1 1 29.6
7 0 1 0 1 -1 1 0 1 0 1 1 1 33.3
8 0 1 -1 0 -1 -1 0 1 1 0 1 1 32.7
9 0 1 1 -1 -1 0 0 1 1 1 1 0 32.6
10 -1 0 0 -1 -1 -1 1 0 0 1 1 1 17.9
11 -1 0 -1 1 -1 0 1 0 1 1 1 0 21.7
12 -1 0 1 0 -1 1 1 0 1 0 1 1 22.2
13 -1 -1 0 1 0 1 1 1 0 1 0 1 17.2
14 -1 -1 -1 0 0 -1 1 1 1 0 0 1 16.6
15 -1 -1 1 -1 0 0 1 1 1 1 0 0 17.1
16 -1 1 0 0 1 0 1 1 0 0 1 0 23.9
17 -1 1 -1 -1 1 1 1 1 1 1 1 1 21.1
18 -1 1 1 1 1 -1 1 1 1 1 1 1 22.3
19 1 0 0 1 1 1 1 0 0 1 1 1 33.6
20 1 0 -1 0 1 -1 1 0 1 0 1 1 32.1
21 1 0 1 -1 1 0 1 0 1 1 1 0 34.1
22 1 -1 0 0 -1 0 1 1 0 0 1 0 31.3
23 1 -1 -1 -1 -1 1 1 1 1 1 1 1 30.0
24 1 -1 1 1 -1 -1 1 1 1 1 1 1 31.8
25 1 1 0 -1 0 -1 1 1 0 1 0 1 35.1
26 1 1 -1 1 0 0 1 1 1 1 0 0 34.0
27 1 1 1 0 0 1 1 1 1 0 0 1 35.5
Field Variables Field Variables2
CDT, Phi PI, is on the left hand side of the table through to the one with the least impact,
Kappa PI, on the right hand side. The CDT was calculated from equation 1, derived from
Newton’s law of cooling. The CDT was calculated for every pipeline in the system to
find the minimum CDT time.
(
) 1
Where:
Tinit = Initial temperature,
Tfin = Final temperature,
TAmbient temperature,
B = Fitting coefficient, calculated from transient pipeline cooldown simulation
Regression analysis on the 27 cases displayed in Table 1 was then performed (in this case
using the Excel Solver), to obtain the polynomial coefficients in the functional form of
correlation 2. This resulted in a correlation that describes the CDT with variations of the
input uncertainties.
( ) (
) 2
Where:
C0 = Constant,
a, b, c, etc. = Coefficients,
Xn = Outcome of variable n, (+1 or 0 or -1),
R = Residual term (assumed negligible)
Figure 3: CDT comparison with Maximus results and polynomial predictions
Figure 3 presents the comparison of the results for minimum CDT – i.e. output from the
polynomial correlation 2 and the values calculated from Maximus for the 27 cases. The
comparison shows an average difference of 2.3%, which is well within the error bands of
multiphase and thermal prediction so was deemed acceptable.
A Monte Carlo simulation was then run using correlation 2, with the Excel statistical
add-in, Crystal Ball. The upside, most likely and downside values (-1, 0, +1) were
entered as the P10, P50, P90 respectively, to define triangular probability distributions
with the limits -1 and +1. The simulation was run for up to 200,000 samples to produce
the probability distributions for minimum CDT.
2.3 Results and discussion
The result of the Monte Carlo simulation is shown in Figure 4 (20,000 samples were
found to be sufficient in this case):
Figure 4: Crystal Ball output (top panel is probability density function, bottom
panel is cumulative probability distribution).
The Monte Carlo simulation results from Crystal Ball demonstrated that there was a 90%
chance of the minimum LoF CDT being greater than, or equal to, the target time of
18hrs.
This approach of LoF multiphase simulation combined with stochastic analysis
techniques has the following benefits for this conceptual design:
1. Reduced the number of simulations required
2. Presented a procedural approach to the assessment of CDT
3. Gave the project assurance on minimum CDT
4. Resulted in a robust but not overly conservative design
A much wider range of uncertainties could be investigated in this way and the use of
stochastic techniques in handling other input uncertainties in design is examined in case
study 2.
3 CASE STUDY 2 - MEG OPTIMISATION OF A LARGE WET GAS NETWORK
3.1 Introduction
Case 2 examines the Mono Ethylene Glycol (MEG) injection optimisation in the BP
West Nile Delta (WND) wet gas development in Egypt. A schematic of the full Maximus
model of the WND system is shown in Figure 5:
Figure 5: Schematic of WND network
As in case 1, careful assessment of the uncertainties, based on accurate predictions, is
required for cost effective design and operation. The prevention of hydrates through
using chemical inhibitors (MEG in this case) is a widely used practice in oil and gas
production. Accurate assessment of chemical inhibitor requirements is crucial to avoid
over or under dosing and, as initially in this case, to avoid the development appearing
unfeasible due to the size of the MEG facilities required.
WND comprises three production fields: Raven, a pre-Pliocene reservoir, Giza Fayoum
and Taurus Libra, both Pliocene reservoirs. The Pliocene reservoirs are low pressure
(<350bara) and low temperature (<65ºC) reservoirs, with a low CGR (<7.5stb/mmscf)
and low water production. The pre-Pliocene reservoirs are high pressure (~750bara) and
high temperature (~135ºC), with a high CGR (~23.5stb/mmscf) and high water
production (4).
In the WND gas development the issue of the formation of hydrates, is to be handled
with the injection of MEG downstream of the chokes in the Pliocene fields and at the
three manifolds for the pre-Pliocene field. The development comprises 34 wells and
approximately 380km of pipelines. Initial work to size the MEG injection system found
that the approach of taking the worst of the worst (i.e. water rate, temperature, pressure)
would lead to an extremely large, and unfeasible, MEG injection system. Therefore, a
more appropriate method was sought. FEESA were approached to perform the work and
used a multiphase, LoF simulation combined with stochastic methods to better calculate
the MEG requirements.
3.2 Methodology
In order to obtain the required MEG flowrate necessary to avoid the formation of
hydrates in the network of pipelines, first a set of hydrate dissociation curves needed to
be calculated. This was done via a simple Maximus model with three sources with
different compositions, pure water, MEG and dry gas, connected to a sink via a pipe.
Figure 6: Maximus model for the calculation of hydrate dissociation curves
A sensitivity analysis of various gas, water and MEG flowrates resulted in the hydrate
dissociation curves displayed in Figure 7.
Figure 7: Hydrate dissociation curves for various MEG concentrations (%)
Then, by using the hydrate dissociation curves in Figure 7, the fitting parameters k1 to k4
were solved for the modified Hammerschmidt equation 3. This provided a relationship to
rapidly calculate the MEG concentration for any specific pressure and temperature
(within the study range). The modified Hammerschmidt equation is given below:
3
4
( ) 5
( ) 6
Where:
= Mass fraction of glycol to avoid hydrate formation,
= Hydrate dissociation temperature,
= Actual flowing temperature,
= Difference between and ,
= Hammerschmidt coefficient,
k1 to k4 = Composition specific fitting parameters
The modification to the Hammerschmidt equation is to make the term H, which is a
constant in the original equation 3, a function of the pressure for a better fit to the data.
By introducing equation 3 into the user defined production logic of the Maximus model,
it was determined where in the LoF there was a risk of hydrate formation at any point in
the system. The model then automatically calculated the required MEG flowrate to dose
each pipeline section out of the hydrate region (for each timestep of the simulation
through LoF). After the Maximus LoF multiphase simulation results were obtained,
further analysis of the uncertainty was carried out stochastically using an Excel model set
up to perform Monte Carlo simulations.
In calculating the MEG requirement, it is known that there would be a measurement
uncertainty on each of the inputs required in the calculation (i.e. the pressure,
temperature, water flowrate and MEG flowrate). Thus, when determining the necessary
MEG flowrate, various methodologies were considered for the calculation, as shown
below:
Exact calculation of MEG required to exit the hydrate region
A 3ºC margin on the associated hydrate dissociation temperature
A 2.5% error added as measurement uncertainties
A 10% error added as measurement uncertainties
An absolute measurement error for each of the 4 measured quantities (Table 2).
Table 2: Absolute measurement errors
The four measurements with uncertainty, shown in table 2, were input as probability
distributions assuming that the uncertainties are of a random nature and therefore
considered to be normally distributed.
Measured quantity Unit Error
Pressure bara ±2 Temperature K ±0.2
Water flowrate kg/s ±0.1 MEG flowrate kg/s ±0.05
3.3 Results and discussion
An example of the MEG flowrate results, from the LoF simulation, for each of the above
methodologies are plotted in Figure 8 for the Raven trunkline:
Figure 8: Comparison between MEG flowrates with different errors for the Raven
trunkline
Figure 8 shows, as expected, the higher the error applied, the more MEG is required.
However, the case at the end of life for the Raven trunkline shows an interesting
difference between the methodologies considered. The trends in late life indicate that for
cases with a small uncertainty band applied, MEG injection is not required, but for the
other cases it is. To better assess such spread in the results statistical analysis was
applied.
Figure 9 shows an example of the results from the Monte Carlo analysis applied to the
Raven trunkline at a point towards the end of LoF.
Figure 9: Results of statistical analysis
From the Maximus simulation described above, the MEG flowrate necessary to remain
outside the hydrate curve is -1.3kg/s (i.e. a negative value, so no MEG is required).
However, once all the measurement uncertainties are taken into account, the resulting
probability density function (PDF) shows that there is a certain risk of hydrate formation
and in order to be 99% confident of flowing outside the hydrate region, an amount of
MEG equivalent to 1.4kg/s would be required (4).
The above methods were successfully used to:
1. Show that many of the worst cases can’t happen simultaneously
2. Reduce the MEG design rates by a factor of approximately 3, making the
project feasible and moving it into the next design phase
3. Avoid hydrates with 99% certainty
The above demonstrates the combined use of multiphase simulation and stochastic
methods applied to input uncertainties, can greatly impact the feasibility of a project.
Case 3 uses similar stochastic techniques applied to input uncertainties in the assessment
of hydrate prevention strategies, in a multiphase tie-back of an infill well to an existing
system.
4 CASE STUDY 3 - HYDRATE MANAGEMENT OF AN NEW OIL WELL
TIEBACK TO AN EXISTING FACILITY
4.1 Introduction
Stochastic techniques were applied to investigate feasible hydrate management strategies,
for a new infill well to be tied back to an existing deep-water (approximately 1400m)
production system, via a 1 km flexible pipeline with an internal diameter of 12cm. Figure
10 shows a schematic of the system with the new well highlighted:
Figure 10: A schematic of the production system with the new well indicated
The relatively high U value for the flexible of 4.8W/m2/K gives a short cooldown time.
This combined with the volume of the flexible, presented economic and operational
issues with the use of conventional methanol (MeOH) displacement (i.e. large volumes
would be needed frequently). Therefore, it was deemed necessary to investigate whether
there was a better approach for the operation of the flexible and well, that would improve
the operability and the economics of the new well. Therefore, alternative strategies were
studied, alongside MeOH displacement, using thermodynamic modelling of the system in
Maximus combined with stochastic techniques.
The following hydrate management strategies were investigated:
MeOH displacement
Hydrate remediation through depressurisation from each end of the flexible
MeOH displacement or hydrate remediation (combined risk based approach)
MeOH dosing (continuous)
Anti-agglomerate / LDHI dosing (continuous)
No hydrate prevention with abandonment upon blockage
4.2 Methodology
LoF modelling was used to assess the thermal behaviour and performance of the new
infill well incorporated into the existing network, to allow calculation of blockage risk
and revenue throughout operation of the well.
As is common with production wells, the watercut and water flowrate were shown to
increase rapidly over the first 2 years, approaching an asymptote over the remaining life.
Over the same time the oil flowrate decreased.
4.2.1 Heat transfer and hydrate weight calculation
To model the amount of hydrate formed in the 1 km tieback during a restart from an
unplanned shutdown, Multiflash was used in a simple Maximus model to characterise the
composition for a GOR of 620scf/stb at an isobaric pressure, P, of 120 bara. Watercuts
from 1% to 95% and temperatures from 4°C to 20°C, using water salinity of 3.5wt%,
were modelled.
For modelling flowing conditions, both relationships of hydrate weight with temperature
and enthalpy change with temperature are required. The approach taken to develop these
relationships is described in the following sections.
4.2.1.1 Assumptions
Pipe is considered to be isobaric, as the variation of mixture enthalpy with pressure
doesn’t change significantly at pressures above 100 bara
All the hydrates formed accumulate into one cylindrical plug during restart
(conservative)
Hydrates have no insulation effect (conservative)
A >1m plug can block a pipeline (input into the model as a normal distribution).
The fluids and wall are at thermodynamic equilibrium
No hydrate kinetics are considered
Figure 11: Hydrate weight (%) against watercut (%) at varied temperatures (°C)
4.2.1.2 Hydrate weight with temperature
Using Multiflash in a Maximus model, the hydrate weight (%), , was calculated for
a range of temperatures and a fit was produced, using equation 7, for each of the
watercuts.
7
Where:
T = Temperature,
n, & are fitting parameters
4.2.1.3 Temperature of fluid with time & position
Also using Multiflash, results for specific enthalpy change from 4°C, allowed a
relationship to be fitted for each of the watercuts using equation 8.
8
Where:
= Specific enthalpy,
= fitting parameter
The relationship given by equation 8 was then used to model the temperature of the fluid
with time and position, using equation 9.
(
) ( ) 9
Where:
t = Time step,
i = Position,
T = Temperature, = Mass of a 50m long wall section,
= Specific Heat capacity of wall,
= Mass of a 50m long fluid section,
= Coefficient (from Equation 8)
The above hydrate mass formed and pseudo-transient heat transfer calculations were
incorporated into a spreadsheet model, along with the economic and statistical inputs
described below.
4.2.2 Economic Modelling
To assess the hydrate management strategies relative to each other, an economic Excel
LoF model of the system was set up with monthly time steps. Key inputs of the economic
model were:
1. Global economic inputs that affect the LoF as a whole (i.e. discount rate, $/bbl,
well cost, flexible cost, abandonment cost, kinetic hydrate inhibitor (KHI) cost,
KHI concentration, MeOH cost and MeOH concentration)
2. Specific inputs as probability distributions (i.e. critical hydrate plug length,
number of shutdowns, abandonment cost and shutdown length)
The uncertainties in the specific inputs (i.e. 2. above) were represented as PDFs fitted to
data. Weibull distributions were fitted to the historic operational shutdown data (see
Change in Enthalpy of a 50m length
of fluid from (i-1, t-1) to (i, t)
= Heat lost by a 50m length of wall
at position i from time t-1 to time t
Figure 12) and normal distributions were fitted to the other two. The resulting PDFs were
sampled in a Monte Carlo simulation to produce model input values for each Monte
Carlo case.
Figure 12: In the left panel, distribution for the frequency of unplanned shutdowns;
in the right panel, distribution for the length of unplanned shutdowns.
50,000 samples were performed in the Monte Carlo simulations, for each of the 6 hydrate
management strategies considered. The outputs of the Monte Carlo simulations were
probability distributions, discussed below, of the economic and operational risk for each
strategy.
4.3 Results and discussion
From the Monte Carlo simulation, output probability distributions for blockage risk,
abandonment date, number of blockages and overall NPVs were produced for each
strategy. Figure 13 demonstrates that MeOH displacement is economically favoured but,
given operational constraints, it might not be operationally possible.
Figure 13: NPV comparison of hydrate management strategies
Figure 14 shows an example of the output of hydrate blockage risk, with the highest
period of risk being from approximately the end of year 1 to the end of year 5. In the first
few months of operation there is no risk of hydrate blockage (no water present) and after
about year 7 the risk of blockage is minimal.
Figure 14: Hydrate blockage risk period
This investigation method provides a relative comparison of strategies. The stochastic
investigation showed that the strategy of hydrate remediation (allowing blockages to
occur then removing them via depressurisation) has a 90% probability that approximately
75% of the maximum NPV is still achieved. For this strategy, during the highest risk
period, there is only a 20% risk of hydrates forming.
Therefore, a combination of the MeOH displacement and hydrate remediation strategy
was recommended by FEESA - i.e. a conventional MeOH displacement strategy during
early to midlife, (whilst there is a higher blockage risk, as shown in Figure 14) followed
by a hydrate remediation strategy in later life (during the low risk periods) when the high
watercut could create operational difficulties using displacement. This strategy was
shown to have an NPV close to the strategy of using MeOH displacement only.
The above LoF Maximus and stochastic investigation:
1. Showed hydrate remediation is a feasible alternative to solely dosing or
displacing
2. Showed MeOH displacement is still economically favoured in this case, but
might not be operationally possible
3. Showed there is a 90% probability that circa 75% of NPV achieved with
remediation
4. Allowed the client to:
a. Better understand their hydrate risks
b. Perform detailed economic analysis of the options
c. See the benefits of improved MeOH sparing on the FPSO
5 CONCLUSIONS
Three marginal production system conceptual design case studies have been presented as
follows:
a. Handling reservoir uncertainty for a multiple oil well deep water production
system
b. MEG optimisation of a large wet gas network
c. Hydrate management of an new oil well tieback to an existing deep water
facility
The case studies demonstrate the benefits to projects and operations from combining
stochastic techniques, with multiphase LoF network simulation in such scenarios. The
stochastic methods allow uncertainty in input data of various kinds (reservoir,
measurement and operational uncertainties) to be handled. The handling of input data
uncertainty, in turn, results in quantification of the output uncertainty, moving it away
from the apparent certainty that is often implicit in oil and gas production system
conceptual design presentation. The handling of uncertainty in this way results in designs
which are not over conservative, a factor which is becoming increasingly important in
designs for economically marginal developments.
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