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.

REFERENCES

(1) M. J. Watson, N. J. Hawkes, E. Luna-Ortiz, Application of advanced chemical

process design methods to integrated production modelling, 15th International

Conference on Multiphase Production Technology, Cannes, France, June 15 – 17,

2011

(2) Multiflash for Windows, Version 3.5, Infochem Computer Services Ltd, February 1

2006.

(3) S. Manivannan, Taguchi Based Linear Regression Modelling of Flat Plate Heat

Sink, J Eng & App Sci, Vol 5, Issue 1, 36-44, 2010

(4) M. Montini, A. Humphrey, M. J. Watson, A. E. Johnson, A Probabilistic Approach

To Prevent The Formation Of Hydrates In Gas Production Systems, 7th ICGH,

Edinburgh, Scotland, UK, July 17-21, 2011

(5) Hammerschmidt EG. Formation of gas hydrates in natural gas transmission lines.

Ind. Eng. Chem. 1934; 26:851-855.