Arild 2017
Arild 2017
Arild 2017
Øystein Arild, Hans Petter Lohne, Mohammad Mansouri Majoumerd, and Eric P. Ford, IRIS; Fatemeh Moeinikia,
UiS
This paper was prepared for presentation at the Offshore Technology Conference held in Houston, Texas, USA, 1–4 May 2017.
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Abstract
A large number of offshore oil and gas wells need to be plugged and abandoned on the Norwegian
Continental Shelf in the coming decades, implying significant costs to the industry. To develop a
methodology for evaluation of the quality of the barrier system of permanently plugged and abandoned
wells from a risk perspective, the research project "Leakage risk assessment for plugged and abandoned oil
and gas wells" has been initiated. The chosen quality measure to quantify containment risk in this context
is the "leakage risk" expressed in terms of probability of barrier failure and potential future leakage rates.
Reviewed papers consist of fragmented contributions to a complete framework for leakage risk
assessment of plugged and abandoned wells. However, they do not provide a complete risk assessment
framework with a corresponding detailed analysis. Without such a framework, regulations will be limited
to prescriptive approaches.
As an alternative to the currently prescriptive approach to plug and abandonment operation, this
article presents how a risk-based approach can be used in practice by incorporating assessments of
probability of leakage and the consequence (leakage rate), as well as uncertainty quantification. A
comprehensive methodology and workflow, encompassing required steps for risk-based evaluation of
containment performance, is established and presented in the paper. It is shown that this approach can
provide a quality measure for a given plug and abandonment design and subsurface conditions.
Introduction
In Norway, the first discovery was made on Ekofisk in 1969. Subsequently, other discoveries such as
Statfjord, Gullfaks, Oseberg, Troll and Åsgard were made. Several of these fields are at the end of
their lifetime, and many wells will need to be abandoned. Plug and abandonment (P&A) operations are
technically challenging, time consuming and costly. There are more than 2500 wells required to be plugged
and abandoned on the Norwegian Continental Shelf (NCS) at some time in the future [1]. Using fifteen
rigs full-time, it is estimated that it will take around 40 years to abandon these and future drilled wells on
the NCS [2]. All these wells will present a huge cost related to P&A operations, encouraging development
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and acceptance of new technologies and methods for abandonment. Regulations also have a significant
influence on abandonment time. In Norway, the average abandonment time increased from 16 days to about
35 days [3] following the introduction of a new version of NORSOK Standard D-010 in 2004.
Well abandonment regulations have been developed in several countries, see [4] for an overview. On the
Norwegian side of the North Sea, design solutions for P&A are based on requirements and guidelines in
NORSOK Standard D-010 [5]. Following these requirements for P&A is a prescriptive "one-size-fits-all"
approach, which disregards the fact that the wells are different with respect to e.g. flow potential. In order to
reflect this variety, a risk-based approach can be used as a "fit-for-purpose" alternative, which evaluates any
P&A solution in terms of the probability that the permanent barrier system will fail in a given time period,
and the corresponding consequence in terms of leakage to the environment. This paper aims to demonstrate
how such an approach can be realized.
The paper is structured as follows; the first two sections give a brief description of P&A regulations and
the risk assessment process and implications for decision-making. The core content of the paper is then
described by presenting a general workflow, succeeded by detailed explanations on how to assess probability
of failure and consequences in terms of leakage rate. This is followed by the application of the methodology
on an example case. Finally, the paper is summarized and a conclusion is provided.
Regulations
On the Norwegian and British sides of the North Sea, NORSOK Standard D-010 [5] and Oil and
Gas UK Guidelines for the Abandonment of Wells [6] govern abandonment activities, respectively.
Some requirements, such as plug length and barrier verification methods, are different between these
two guidelines. The Oil and Gas UK guidelines for the Abandonment of Wells is more detailed and
comprehensive than the P&A section in NORSOK Standard D-010.
Concerning general P&A requirements, according to NORSOK Standard D-010 [5] there shall be at
least one barrier between surface and potential sources of inflow. For hydrocarbon bearing formations or
pressured formations with flow potential, a minimum of two barriers are required.
According to NORSOK Standard D-010, a permanent well barrier shall be set across an impermeable
formation where the maximum potential pressure below the barrier is less than the formation fracture
strength at the base of the barrier. The plug length shall be minimum 100 m MD with minimum 50 m MD
above any potential source of inflow or leakage point. A plug in the transition from open hole to cased
hole shall extend at least 50 m MD above and below the casing shoe. If a plug is set inside a casing with
a mechanical plug/cement as a foundation, the plug length shall be at least 50 m MD. For casing cement
to be qualified as a part of the well barrier, the required length shall be 50 m MD. If verified by logging,
a minimum of 30 m MD with acceptable bonding is acceptable. For a cement plug in open hole, the plug
shall be verified by tagging. A cased hole cement plug shall be verified by tagging and pressure testing.
In some countries, such requirements are also explicitly stated in the regulations. In the Norwegian
legislation, there are primarily two sections dealing with abandoned wells. The Facilities Regulations’
Section 48 Well barriers [7] states "When a well is temporarily or permanently abandoned, the barriers
shall be designed such that they take into account well integrity for the longest period of time the well
is expected to be abandoned". The Activities Regulations’ Section 88 Securing wells [8] says "All wells
shall be secured before they are abandoned so that well integrity is safeguarded during the time they are
abandoned". Although NORSOK Standard D-010 is recommended in the guideline to Section 88 [9], it
is not an absolute requirement. Thus, in some countries like Norway, the legislation is open to alternative
approaches already today, if a sufficiently convincing case can be made. The main issue is the added effort
by the government and the operator in accepting non-standard solutions.
OTC-27711-MS 3
Many of the requirements for the abandonment of wells, such as those in NORSOK Standard D-010,
are described in terms of required number and properties of barriers. If the well has been abandoned per
requirements, the abandonment plan is considered acceptable. Even with a prescriptive legislation of P&A
abandonment requirements, a risk assessment is still useful to assess if the ALARP principle is followed
and to promote the acceptance of alternative solutions and technologies through a comparison.
The workflow described in the steps above are well known from a variety of integrity studies in the oil
& gas industry, some examples being [16–19]. For many of these cases, there is an abundance of historical
data on failure mode frequencies and consequences, thus making it relatively straightforward to quantify
the probabilities (pi) and the consequences (ci) by means of reliability mathematics [20].
However, for permanently plugged and abandoned offshore wells, such data are scarce and fragmented;
data may only be partly available, such as the "FactPages" on abandoned fields provided by the Norwegian
Petroleum Directorate (NPD) [21], analogues from onshore fields [22] and experimental data on barrier
elements [4]. All relevant information should be taken into consideration when assessing the probabilities
and the consequences, i.e. when performing Step 4 and 5 of the workflow above. As a result, a modelling
framework for the quantification of probabilities (pi) and consequences (ci) is needed. Such a framework
should be able to integrate various pieces of information and to deal with uncertainty. We have selected
the general model from [23], which is illustrated in Figure 3. In this framework, it is assumed that the
input parameters can be categorized in three main groups; uncertain inputs, typically described by means
of probability distributions, known inputs, such as well geometry and other well design variables, and other
variables of relevance. The input parameters are fed into a model G, which in general can be regarded as
a numerical function linking inputs to outputs; examples being deterministic functions for fluid flow or
material degradation. The results are variables or parameters of interest to the stakeholders. Uncertainty is
propagated by means of Monte Carlo simulation [24], and sensitivity analysis provides information about
the importance of the input parameters, which subsequently can be used to prioritize risk reducing measures.
Figure 3—Overall methodology for assessing the variables of main interest for long-term containment
performance, such as failure probabilities, lifetime distributions and consequences (leakage rates)
Figure 4—Exemplification of the main results from a barrier risk assessment for permanent P&A barriers
(Note: Uncertainty is dealt with by means of probability distributions and explicit use of these.)
In the following two sections, we will describe in detail how to quantify the probability with scarce data
and how to calculate the consequences (leakage rates), respectively. Note that for simplicity the probability
and consequence are assessed independently in this paper.
Assessment of probability
The assessment of barrier failure fits well within the domain of reliability engineering. Reliability is defined
in ISO 9001 [25] as "the probability of a device performing its purpose adequately for the period of time
intended under the operating condition encountered," which in a P&A setting means that the barrier system
contains the hydrocarbons from the reservoir(s) inside the well for "the period of time intended". Although
the definition does not impose any specific method for how to calculate or assess the reliability, a common
and feasible approach is to use the concept of survivability or lifetime, i.e. how long the containment barrier
system will contain hydrocarbons before it starts to leak, or before a certain leakage rate reaches the surface.
The key quantity of interest in survival analysis is the lifetime distribution. This is a probability distribution
representing the possible range of lifetimes for a component or system as well as the corresponding
probability of how likely the values in this range are. An example of a commonly used model for lifetime
is the Weibull distribution shown in Figure 5. Once a lifetime distribution is available, various variables of
interest such as the expected lifetime (mean time to failure) and the "probability of failure before x years"
can easily be calculated by means of numerical integration techniques.
Many industries have records of failure data for components and systems over long time spans. With
such historical data, statistical methods such as maximum likelihood estimation (MLE) [26] can be used
to estimate the corresponding lifetime distribution and the corresponding failure probability, either for a
component and specific failure modes, or at the system level. Such an approach will say something about the
system performance based on historical data, but will not be very applicable when taking new information
about a system into account, for example a design change.
For the assessment of lifetime distributions and the subsequent calculation of failure probabilities of
permanently plugged and abandoned wells, there are some historical data from North America [22] and
fragmented experimental data [4] available. However, these are currently not considered applicable for the
study of permanently plugged and abandoned wells on the NCS. The only information that we have available
from the NCS on abandoned fields are publicly available data from the NPD [21]. By manually processing
these data, we identified 334 wells in the NPD database [21] that are assumed plugged after finished drilling
(for exploration wells not used further) or when the field was closed down (for production wells), see Figure
6. As a result of this approach, there are many wells abandoned in a single year, although in reality they
would have been spread over multiple years. As none of these wells has been reported to leak, they can be
regarded as censored data, i.e. data where we know for how long the well barrier system has survived, but
not when it failed, with failure time being defined as the point in time where the well will leak at a rate
that would have been detected.
Figure 6—Histogram presentation of the time since abandonment of permanently P&A-ed wells on the NCS
(Note: The histogram shows only censored data, i.e. how long the wells have been
permanently plugged and abandoned without leaking, with no recorded failure times.)
The MLE method mentioned above cannot be used with censored data only. However, a Bayesian
approach is feasible for the assessment of a lifetime distribution when only censored data are available. The
Bayesian approach also allows for expert input, physical considerations and phenomenology through the
establishment of a prior distribution. Figure 7 illustrates the main steps in a Bayesian approach for assessing
lifetime distributions using a prior distribution and censored data only. Further explanation and supporting
mathematical details are provided below.
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Figure 7—Steps to achieve the predictive distribution when using a Bayesian approach to lifetime prediction
The starting point for a Bayesian approach is the application of Bayes formula [26]:
(1)
To obtain the main result, i.e. the posterior predictive distribution for the barrier lifetime, the following
steps should be taken:
Step 1
Establish the likelihood distribution. Essentially, this can be any valid probability distribution, and the shape
of it must be selected by the analyst. Commonly used likelihood models are parametric distributions such
as the Weibull, lognormal, Gamma and exponential distributions. In Figure 7, the illustrated parametric
distribution is a Weibull distribution.
Step 2
A parametric likelihood distribution model has one or several parameters that defines its shape. Since these
parameters are unknown, they can be expressed by means of a so-called prior distribution. The choice of the
prior distribution should be based on all relevant available information, such as expert input, empirical data
or models. In theory, the prior distribution can be any shape, but common engineering choices are normal,
uniform or triangular distribution. In Figure 7, the prior distribution illustrated is a uniform distribution. It
should be noted that a so-called prior predictive distribution could be generated at this stage by using the
same procedure as described in Step 4.
Step 3
By using Bayes formula as above, a posterior distribution for the parameters in Step 2 can be calculated.
Irrespectively of the likelihood and prior probability distributions used, the posterior distribution can always
be generated using modern statistical methods such as rejection sampling or Markov Chain Monte Carlo
methods [26]. In Figure 7, an example of a posterior distribution generated by means of rejection sampling
is shown below the box named "Posterior".
Step 4
The main variable of interest is the lifetime distribution, and not the parameters in the likelihood distribution.
A lifetime distribution can be generated by computing the posterior predictive distribution, which can be
calculated as follows:
1. Sample the distribution parameters from the posterior distribution
2. Use the sampled parameters to sample failure times from the likelihood distribution
OTC-27711-MS 9
3. Repeat until the population of sampled failure times is a statistically significant representation of the
posterior predictive distribution
In Figure 7, an example of a posterior predictive distribution using the three-step method above is shown
below the box named "Posterior predictive".
With the posterior predictive distribution in place, the probability of failure within a given time period can
easily be calculated. A specific numerical example of the steps above is shown in the example case section.
Assessment of consequences
Leakage can occur in presence of a leak source (e.g. hydrocarbon-bearing formation), a driving force
(e.g. buoyance) and a leakage pathway [22]. A leakage pathway represents a space in which flow of
reservoir fluids escapes from its originally confined space, implying a breach or failure of one or more
barriers. Leakage pathways may be of various natures, including geological pathways due to e.g. fractures
in caprocks, and manmade pathways due to e.g. wells and boreholes. There can be various leakage pathways
in a P&A-ed well including (but not limited to) leakage between the casing and the cement, through the
cement plug and through cracks/fractures in the cement. Note that any of these leakage pathways (failure
modes) can have several root causes, including deterioration of chemical or physical bonds between the
barrier material/casing/formation, external/internal stresses exceeding strength limits, chemical degradation
or corrosion, shrinkage and expansion, poor quality of placement etc. [27].
Leakage due to the abovementioned pathways have been incorporated into a leakage calculator [28] that
aims to estimate the consequences (i.e. leakage rates) through a failed permanent barrier system (see the
consequence assessment part in Figure 2 and Figure 4). The structure of the leakage calculator is illustrated
in Figure 8.
This calculator requires two sets of inputs, namely known (e.g. design variables) and uncertain inputs
(represented by probability distributions). For each barrier element, which in this context is limited to cement
plugs and annulus cement, calculations of leakage rates are performed using the models described in Table
1, resulting in an overall distribution of the leakage rate to the seabed. In the leakage calculator, a well can
be described in terms of architecture (casing and hole dimensions), mud (density) and trajectory, and the
reservoir in terms of pressure, fluid density and viscosity. The barrier elements of the wellbore are then
placed into the well. Both cement plugs and annular cement are described in terms of depths and lengths.
10 OTC-27711-MS
Parameters such as cement permeability, gap size of micro-annuli as well as fracture aperture, orientation
and width represent the main uncertainty.
Table 1—The models used to estimate leakage rates of different leakage pathways included in the leakage calculator
Leakage through cracks h: Fracture aperture [m] Fracture aperture, orientation and
Q= W [30]
α: Fracture orientation [°] width are treated as uncertain
W: Fracture width [m] Rest as above parameters in the leakage calculator.
Leakage through micro-annuli Rc: Casing diameter [m] Micro-annulus gap is treated as an
Q= δR3 [31]
δ: Micro-annulus gap [m] uncertain parameter in the leakage
Rest as above calculator.
The models implemented for leakage rate estimation are run inside a Monte Carlo simulation framework,
and thus the system uncertainty is propagated onto the resulting leakage rate to seabed, which essentially
becomes an aggregate distribution representing the sum of leakage rates across all barrier elements of the
well. Further details can be found in a separate publication by the authors [28].
Example case
An example case study has been performed to illustrate the method described. The numbers used may not be
representative for a real well. The example well is an offshore well that has been abandoned in compliance
with NORSOK Standard D-010, with the measurements given in Figure 9. Both the primary and secondary
barrier uses the 9 5/8" casing with the original annular cement as barrier elements, along with separate
cement plugs set inside the casing (plugs 1 and 2). For the purpose of these calculations, the two barriers
are treated as a single barrier. In addition there is a surface barrier in the 20" casing consisting of the old
annular cement and a new cement plug inside the casing (plug 3).
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Casing shoe depth (13 3/8" casing) 1900 m MD, 1700 m TVD
Top of plug (plug 1+2) Base of plug (plug 1+2) 2900 m MD, 2200 m TVD 3100 m MD, 2270 m TVD
Top of plug (plug 3) Base of plug (plug 3) 300 m MD, 300 m TVD 400 m MD, 400 m TVD
Leakage calculation
Calculating the leakage requires some additional parameters related to the leakage pathways described in
the previous section. As these parameters are difficult to measure, they are described using probability
distributions based on literature sources [29–31]. The distributions used for the parameters are shown in
Table 2. Here, T(low, mode, high) represents a triangular distribution with low as the lowest possible value,
mode as the most likely value and high as the highest possible value.
12 OTC-27711-MS
A conservative assessment of the possible flow rates is then calculated as explained in the previous
section, which results in flow rates to seabed distributed as seen in Figure 10. See [28] for more details on
the leakage results.
Figure 10—Probability density function (blue) and cumulative distribution function (red) of simulated leakage rates
Step 1
For illustration purposes, the chosen likelihood distribution is a Weibull distribution due to its versatility,
with known shape β = 1.5 but unknown scale parameter. As the shape parameter is larger than one, it
indicates that the failure rate increases with time.
Step 2
To represent our uncertainty about the scale (and to get a visible effect from the available data), the scale
parameter is assumed to follow a uniform distribution from zero to 1000 years, i.e. the prior distribution
here is a uniform distribution from 0-1000. With these assumptions in place, a prior predictive distribution
can be calculated. The result is shown in Figure 11a.
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Figure 11—Histogram presentation of prior (a), and posterior (b) distributions of failure time in years
(Note: The data have clearly shifted the distribution to the right, giving
more confidence in longer survival times than the prior assumption.)
Step 3
The next step is to use the data from the North Sea (Figure 6), following the approach outlined in the previous
sections, to update our prior perception of the scale parameter. The posterior distribution can be calculated by
using Bayes formula with the information provided in Step 1-2. Combining the selected prior and likelihood
distributions by using Bayes formula does not result in known type of probability distributions. This was
solved by using numerical discretization to estimate the posterior distribution.
Step 4
The discretized approximation to the posterior distribution can easily be sampled with rejection sampling.
These samples of the scale parameter can then be used to sample failure times from the Weibull distribution.
These failure times then represent the posterior predictive distribution shown in Figure 11b.
It can be seen in Figure 11b that the failure times have been skewed to the right, as the censored
evidence suggest that an early failure is very unlikely. The probability the well would leak within 100 years
was originally 20%, but the data reduced the probability to 5%. Giving the prior distribution of the scale
parameter a wider span, such as from zero to 4000 years, would mean that the data would have a smaller
impact, as the data is more supportive of a less conservative prior distribution. Note that the prior distribution
was chosen to create a noticeable effect from the data, and should not be interpreted as an argument for
more restrictive plugging requirements. Further work will consider the creation of priors based on plugging
methods and failure mechanisms to include more knowledge in the prior.
Together, these results provide an overview of the probability of a detected leakage and leakage rate, as
illustrated in Figure 12.
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Acknowledgement
The authors acknowledge the Research Council of Norway, ConocoPhillips, AkerBP, Statoil and
Wintershall for financing the work through the research centre DrillWell - Drilling and Well Centre for
Improved Recovery, a research cooperation between IRIS, NTNU, SINTEF and UiS.
Nomenclature
ALARP As low as reasonably practicable
FEP Features, events and processes
OTC-27711-MS 15
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