developing synthetic reservoir type curve model for use in
TRANSCRIPT
Accepted Manuscript
Developing synthetic reservoir type curve model for use in evaluating surface facilityand gathering pipe network designs
Michael Dennis
PII: S1875-5100(17)30270-6
DOI: 10.1016/j.jngse.2017.06.025
Reference: JNGSE 2223
To appear in: Journal of Natural Gas Science and Engineering
Received Date: 6 July 2016
Revised Date: 26 June 2017
Accepted Date: 26 June 2017
Please cite this article as: Dennis, M., Developing synthetic reservoir type curve model for use inevaluating surface facility and gathering pipe network designs, Journal of Natural Gas Science &Engineering (2017), doi: 10.1016/j.jngse.2017.06.025.
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Developing synthetic reservoir type curve model for use in
evaluating surface facility and gathering pipe network designs
Michael Dennis
School of Chemical Engineering
The University of Queensland, St Lucia, 4072, Queensland, Australia
Email: [email protected]
Abstract
Surface facilities and unconventional gas gathering networks are typically designed to collect
gas from a large number of wells to a central location. The unit operations that make up the
surface network need to be installed before the wells are producing and thus need to be sized
on predicted performance rather than actual performance which is not known until production
data is available. This means each reservoir’s production profile which is based on uncertain
input parameters and imperfect reservoir models forms the sizing basis for the surface
facilities.
In this study a method is developed to generate synthetic reservoir flow type curves based on
a set of input parameters that is independent of reservoir parameters. The main qualitative
characteristics of an unconventional gas reservoir type curve are described such as gas ramp
to peak, peak gas flow and production decline, along with the discontinuities and variations
from expected performance seen in operating trends. The synthetic type curve proposed in
this work can be parameterised to mimic these characteristics, along with a well deliverability
mechanism and subsurface communication between wells.
The method of being able to describe a type curve by means of input parameterisation allows
an unconventional gas surface facility of gathering pipe network and in-field booster
compressors to be designed against many sets of synthetic type curves rapidly generated by
randomisation of those input parameters.
Key words: Type curve; CBM; CSG; Shale; Modelling; surface network;
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1 Introduction
Surface network facilities for a field development of many gas producing wells dispersed
over a geographic area includes a gas gathering pipe network and gas treatment operations,
such as compression and dehydration to meet export specifications. In this work, a surface
network is treated as a process as defined by Couper et al. 2012 and the input boundaries are
chosen to be each individual wellhead.
The process system in a coal bed methane (CBM) and Shale surface network is typically
made up of a network of pipes, compressors and gas treatment operations (Flores, 2014;
Garlick, et al., 2014; Guarnone, et al., 2012) to transform the inputs (gas received at the
wellhead) into a desired output state, such as gas with set pressure, water dew point and
concentration limits of undesirable gas constituents (Flores, 2014; Garlick, et al., 2014).
For designing a gas gathering surface facility, each wellhead input boundary can be
individually defined as a ‘type curve’ that describe gas flow rate over time for the
corresponding gas well. Type curves provide a powerful method for analysing pressure
drawdown (flow) and build-up tests (Lake & Fanchi, 2006). Fundamentally, type curves are
pre-plotted solutions to the [reservoir] flow equations, such as the diffusivity equation, for
selected types of formations and selected initial and boundary conditions (Lake & Fanchi,
2006).
Type curves, showing either flow rate over time or cumulative production over time is a
common tool used to describe the performance of a reservoir in unconventional gas well
(Nobakht, et al., 2013; Mingqiang, et al., 2016; Sugiarto, et al., 2015; Burgoyne & Clements,
2014; Aminian, et al., 2004; Baihly, et al., 2010; Karacan, 2013; Mavor, et al., 2003).
Although attempts have been made to generate type curves from reservoir properties of
unconventional resource (Nobakht, et al., 2013; Clarkson & Bustin, 2010), it is a large
subject on its own and no attempt is made in this work to solve those challenges. This work is
the first part in a larger investigation into surface facility designs against input boundary
uncertainty, and proposes a synthetic type curve as a means to describe the input boundary.
A synthetic type curve is generated by way of a set of input parameters, most of which are
qualitative parameters and some that are based on readily available and reliable reservoir
parameters. It is entirely ignorant of the underlying knowledge domain of geologists and
reservoir engineers used to generate them and makes no attempt to reconcile a synthetic type
curve against a description of reservoir properties. The interest lies in being able to describe
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an input boundary for surface gathering network design and apply bounded randomisation of
those parameters to simulate the inherent uncertainty of that system boundary for evaluation
of the robustness and flexibility of surface network design against that uncertainty, seeking
both upside opportunities and downside risk (de Neufville, 2004).
This work focusses on unconventional gas resources including shale gas and coal bed
methane (CBM), as there are many similarities between them particularly in the surface-
subsurface interface uncertainty.
1.1 Unconventional gas reservoir uncertainty
The uncertainty in CBM wells is partly due to a complex production mechanism involving
desorption of gas from the coal matrix and diffusion through the fractures and cleats under
two-phase flow conditions (Aminian, et al., 2004). The mechanism of methane desorbing
from the coal matrix through the cleats and fractures of the coal seam provides a challenge to
correctly predict the time to peak, the magnitude of the peak as well as decline rate for both
the gas and water phase accurately throughout the lifecycle of the field (Sharma, et al., 2013).
There are many physical factors that are related to coal permeability but are difficult to
quantify (Gentzis, et al., 2008). Even in a laboratory setting, it is not easy to measure the
relative permeability of coal mainly because of the difficulty in reproducing results (Ham &
Kantzas, 2013). While laboratory measurements provide some insight into the coal seam
properties potential behaviour, there could be significant differences with the behaviour in the
reservoir due to issues of scale and heterogeneity (Connel, et al., 2010).
Historical challenges to predicting CBM-well performance and long-term production have
included accurate estimation of gas in place (including quantification of in-situ sorbed gas
storage); estimation of initial fluid saturations (in saturated reservoirs) and mobile water in
place; estimation of the degree of under-saturation (under-saturated coals produce mainly
water above desorption pressure); estimation of initial absolute permeability (system);
estimation of absolute-permeability changes as a function of depletion; and accurate
prediction of cavity or hydraulic-fracture properties (Clarkson & Bustin, 2010).
It has been seen that variability in production from early CBM wells in Queensland began to
suggest that lateral continuity of the coals, either as individual seams or as packages, was
much more complex and less predictable than original expectations (Towler, et al., 2016).
Fisk et al. (2010) report that in the Bowen Basin of Queensland, it is not unusual for
production to changes as much as 50-75 % between neighbouring wells within a few
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kilometres. Likewise for the Surat Basin of Queensland, where reservoir productivity changes
quickly over small distances (Bottomley, et al., 2015).
This heterogeneity of physical properties of coal has been reported to affect the performance
of individual reservoirs in many ways. Cumulative production performance after 40 months
of operation between 23 wells in a field in the Black Warrior basin, USA, with similar coal
thicknesses and original gas contents, and which were drilled and completed identically at
equal well spacings was shown to vary by two orders of magnitude (Anderson, et al., 2003).
Sharma et al. (2013) reported that not only can time to peak vary greatly for CBM wells, but
also peak flow wells can deviate as much as six times the average. This is also supported by
work shown by Burgoyne & Clements (2014) in the variance of peak flow from CBM wells
with similar key geological properties. On actual rate of gas production, Towler et al. (2016)
report that CBM wells in Queensland have mean gas production rates between 1 and
2 MMSCFD, with some wells exceeding 20 MMSCFD.
The post peak flow decline curves of CBM wells, as classified by Arps (1944) into
exponential, hyperbolic or harmonic, have been seen to be primarily described as exponential
(Sugiarto et al. 2013 found 85 %, Mavor et al. 2003 found 99 %), with some following
hyperbolic or harmonic (11 % and 3 % respectively in the analysis by Sugiarto et al. 2013).
The work by Clarkson & Bustin (2010) showed that there is difficulty in estimating original
gas in place. This is partially due to the variability in coal seam thickness (Baker, et al., 2012;
Kabir, et al., 2011) which is a key input to calculating the initial gas in place (Seidle, 2011).
CBM wells are also prone to unplanned shutdowns (Gilbert, et al., 2013) resulting in
discontinuities in the production profile.
In this section, the demonstration of uncertainty on unconventional reservoirs has focussed on
CBM. However, common challenges prevail in shale gas. All shale gas reservoirs are not the
same and there are no typical tight gas reservoirs (Kennedy, et al., 2012). Multi-fractured
wells completed in shale gas reservoirs are difficult to analyse quantitatively due to a
combination of unique reservoir properties (eg, non-static porosity and permeability,
desorption, non-Darcy flow) and potentially complex induced hydraulic fracture geometries
(Nobakht, et al., 2013). Conventional reservoir simulators cannot provide, without alteration,
a reasonable production analysis for shale gas reservoirs (Xie, et al., 2013).
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The difficulty in measurement of fractures and shale gas reservoir properties needed for the
reservoir model, as there exists large uncertainty in the key parameters, lead to large
uncertainty on well production predictions (Xie, et al., 2013). Guarnone et al. (2012)
acknowledge that there is a high degree of uncertainty and unknowns in predicting both
Initial Production (IP) and Estimated Ultimate Recovery (EUR) for a shale gas well, with a
risk of over-estimating production performances.
The consequence of this uncertainty means that it is difficult to predict with accuracy a well’s
performance until it is online and producing (Acuna, et al., 2015; Gentzis, et al., 2008;
Howell, et al., 2014; Karacan, 2013; Xie, et al., 2013). However, a pipe network to gather the
gas needs to be in place before the wells begin producing, and as the performance of the wells
are not accurately known until they are producing, this presents a design challenge.
Developing the synthetic type curves method aims to address this in part by evaluating a
surface network’s design against many sets of type curves for low computation cost
compared to a detailed reservoir model.
2 Description of a gas well flow type curve
The aim of a developing a synthetic type curve is not to understand the underlying physics
and geological properties of an unconventional reservoir; however, it is to be able to generate
type curves that exhibit the same characteristics of actual production data and complex
reservoir model outputs for use as input boundaries into a surface network model.
A qualitative analysis of the reservoir type curves of flow-rate to time show common
characteristics: a steep ramp to peak flow; a time period producing at peak flow rate; and
declining gas rate for the remainder of reservoir production life (Sharma et al, 2013), (Mavor
et al, 2003), (Burgoyne & Clements, 2014) (Clarkson & Qanbari, 2016), (Lewis & Hughes,
2008). Some examples of flow type curves presented in literature show a sharp peak flow that
exist for a single point in time and other examples with a smooth plateau. This difference in
appearance is likely due to the time scale used. Peak flow appears to exist for a relatively
short time in an unconventional gas well, if the time scale is on years this presents as a sharp
peak (Mavor et. al, 2003), (Burgoyne & Clements, 2014) whereas on a shorter scale of days it
appears as a smooth plateau (Clarkson & Qanbari, 2016). The CBM production type curves
have a longer ramp time to peak flow than the shale gas examples which appear to be almost
instantaneous (Mavor et al 2003), (Burgoyne & Clements, 2014), (Clarkson & Qanbari,
2016), (Bazan et al, 2010), (Lewis & Hughes, 2008). Post peak flow, the reservoir production
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decreases at a decreasing rate for the remaining life of the reservoir, tending towards zero
flow. The key to the synthetic type curve parameterisation will be to facilitate flexibility to
accommodate all the qualitative variations that can present in a CBM type curve.
3 Parameters to create synthetic type curves
The following sections define the parameters and equations used to generate synthetic type
curves.
3.1 Phase 1: Initial flow
Initial flow is the gas flow for the first time interval is defined in equation (1).
��0� = �� �1� Where:
- q0 is flow rate at t = 0 (typically 0)
The time period for the reservoir is relative to the reservoir’s production where t = 0 is when
gas production begins, and is independent on the actual time in the life of the field
development. Thus, comparing t = 0 for each reservoir will be a function of the drilling and
commissioning schedule.
3.2 Phase 2: Ramp to peak flow
Linear ramp to peak flow is defined in
����� = � ∙ � + �� �2�
Where:
- m is the slope in equation (2) and defined in equation (3)
- t is time
� = ������������� �3� Where:
- qpeak is peak flow rate
- tpeak is time when peak flow rate qpeak is attained
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As seen in the example type curves, there are some instances where the ramp up to peak flow
is not linear, but contains initial increase at increasing rate before a decrease at increasing rate
as it approaches peak flow. This fits with the qualitative description of sine function.
Sine function to peak flow is defined in equation (4).
������ = ������ ∙ sin � ����� ∙ � −
�" + ������ �4� Equation (4) has not been factorised to facilitate explanation to its genesis: the first qpeak / 2
term sets the amplitude of the sine function and the final qpeak / 2 shifts the sine function
positively to get a minimum of 0 MMSCFD and maximum of qpeak. The π / tpeak alters the
frequency of the function that is equal to tpeak / 2. The π / 2 term shifts the function so its
minimum coincides with t = 0 and maximum (qpeak) with t = tpeak.
The stiffness parameter k is a linear weighted average between the two ramping functions, as
described in equation (5).
����$%&' = ( ∙ ������ + �1 − (� ∙ ����� �5�
3.3 Phase 3: Peak flow plateau
The gas flow during plateau flow is given in equation (6)
����'%� = �'*%+ �6�Where:
- tplat is duration of plateau flow
3.4 Phase 4: Decline flow
Post peak flow, the flow rate declines for the remainder of its production life. Rate-time
decline curve extrapolation is one of the oldest and most often used tools of the petroleum
engineer (Fetkovich, 1980). The equations described by Arps (1944) are used as the basis,
along with the terminology of exponential, hyperbolic and harmonic decline. Where b > 0,
equation (7) is used for harmonic (b = 1) and hyperbolic (0 < b < 1) flow decline.
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����-*.�* = �����/012∙%3����������4�56789
�7�
Exponential decline flow is used when b = 0, as shown in equation (8).
����-*.�* = �'*%+ ∙ ;<�%∙=�−�>;?(−�>@?�AB �8�3.5 The synthetic type curve equation
The synthetic type curve equation case selection determining which q(t) function to select
given the current time period is given in equation (9).
����D =EFGFH ��, � = 0����$%&', 0 < � ≤ �'*%+����'%� , �'*%+ < � ≤ �'*%+ + �'%�����-*.�* , � > �'*%+ + �'%�
�9�
3.6 Synthetic type curve testing
The synthetic type curve equations proposed has been tested to recreate the examples of type
curves presented in this section to demonstrate that the input parameters and approach gives
sufficient flexibility as a model to proceed with. Type curves found in literature that were
given as plots were converted into discrete data points by way of plot digitisation. Table 3-1
shows the input parameters for the synthetic type curve generation with Figure 1 showing the
resulting type curves against the data points.
In Case 03 and 04, the maximum b value of 1 is reached, though relaxing this limit allowing a
higher b value could lead to a better fit.
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Table 3-1: Input parameters for synthetic type curve generation against data
Case q0
MMSCFD
qpeak
MMSCFD
tpeak
month
tplat
months
a b k
01 0 0.164 32 0 0.086 0.184 0.419
02 0 0.362 14 0 0.156 0.216 0.703
03 0 0.39 1.1 1.2 0.193 1.0 0.0
04 0 7.51 0.15 0 0.500 1.0 1.0
05 0 7.2 2 45 0.0075 0 0
06 0 8.5 1.1 0.05 0.075 0.9 1
07 0 4.76 24 2 0.028 0 0
08 0 1.25 10 14 0.025 0 0
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Figure 1: Comparison of synthetic type curve parameterised to match unconventional gas type curve data points found in literature. From top right, clockwise Case 01: Example of slow ramp to sharp peak, data taken from Mavor et al.(2003); Case 02: Example of quick ramp to sharp peak, data taken from Mavor et al. (2003); Case 03: Example of a ramp to peak flow plateau, data taken from Clarkson & Qanbari (2016); Case 04: Example of immediate ramp to sharp peak, data taken from Basan et al. (2010); Case 05 production data from Fairway Fruitland Coal taken from Clarkson et al. (2007); Case 06 production data from Horseshoe Canyon taken from Okuszko et al. (2008); Case 07 taken from Salmachi & Yarmohammadtooski (2015) for CBM production data in San Juan basin; and Case 08 taken from Mazumder et al. (2003) from Surat Basin CBM production data. Referenced data points have been digitised from raster images and is reproduced as faithfully to the original sources as possible.
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4 Adding irregularities to synthetic type curves
Unconventional gas wells do not follow a smooth type curve partly due to being subject to
planned and unplanned shut-ins (Gilbert et al. 2013). During an interview conducted on 16
June 2016 with David Hazle, Engineering Manager for Arrow Energy which operates coal
seam gas wells in the Bowen Basin and Surat Basin in Queensland, much of what is viewed
as noise or irregular flow deviations from a smooth production curve is likely not actual gas
production from the well, but rather external influences on the measurement such as flow
meter failure or maintenance work interrupting either production or control system
functionality. The causes for the noise in data can be anything, and likely to be external and
not representative of a reservoir’s actual performance. Unplanned well shut-ins, however, do
occur and should be accounted for.
To mimic this in the synthetic type curve additional parameters are introduced.
4.1 Gas Rate Noise
Gas flow rate noise is defined as the deviation of the actual gas flow rate from the defined
type curve, where it is just a likely to exceed and be less than the given type curve.
N����O�* = P Q�1, R0�1 + R� ∙ sin�2S ∙ RT ∙ �� (10)
Where:
- x(t)noise is a multiplier to the flow rate at t with noise applied to it
- Φ is a function to sample from a probability distribution with mean 1
- c1 is the variance being defined as a constant fraction (c1) of the current flow rate q(t).
- c2 is a fixed amplitude when selecting a periodic noise function
- c3 is the frequency for the periodic noise function, constant throughout the life of well
4.2 Gas Rate Disturbance
Gas rate disturbance is defined as a random occurrence that results in a significant deviation
of gas flow rate less than the given type curve. The production data presented in Figure 1
shows a large number of spikes of flow deviations to less than the prevailing type curve
shape.
N���-�� = PQ�RU, RV�, W�0,1� ≤ >-��1, W�0,1� > >-�� (11)
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Where:
- x(t)dist is a factor multiplied by q(t) to get the resulting flow rate
- pdist is the probability a disturbance will happen at each time increment in units per
time increment (eg month-1)
- U(0,1) is a random sample from a uniform distribution between 0 and 1
- c4 is the average flow rate value for a disturbance, typically 0 < c4 < 1
- c5 is the variance as a fraction, typically 0 < c5 < c4
4.3 Unplanned well shut-in
An unplanned well shut-in is defined as a period of no flow for a set amount of time. Being
unplanned in nature, the occurrence is random, and the duration is also a random as the
actions required to re-start a well cannot be easily defined.
N����XY� = P�P0, Q�0,1� ≤ >�XY�1, Q�0,1� > >�XY� �12�Where:
- x(t)shut is a factor multiplied by q(t) to get the resulting flow rate (in this case, either 1
or 0)
- pshut is the probability a disturbance will happen at each time increment in units per
time increment (eg month-1).
Shut-ins that last for less than a time increment (month) resulting in an average flow
greater than 0, can be considered to be handled by the gas rate disturbance equation (12).
4.4 Synthetic type curve equation with noise, disturbance and shut-ins
The resulting synthetic type curve equation with noise, disturbance and shut-ins is given in
equation (13).
����[ =����D ∙ N����O�* ∙ N���-�� ∙ N����XY� �13�Where:
- q(t)B is the synthetic type curve with irregularities incorporated.
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4.5 Synthetic type curve variance examples
A comparison on how a synthetic type curve is affected by the variance parameters is
presented. Table 4-1 shows the parameters used to generate the synthetic type curves shown
in Figure 2, with blank parameters indicating the particular variance being disabled. It is seen
that x(t)noise, whether a Gaussian based probability distribution of frequency dependent, has
negligible impact on the cumulative gas. This is to be expected as the noise, with an average
multiplier of 1, is just as likely to be an increase as a decrease. A sine wave frequency based
noise with a multiplying factor cantered at 1 gives the same outcome. Probability distribution
functions, where the chance to sample greater than or less than the mean is not equal, may
result in changes to the cumulative gas.
The x(t)dist and x(t)shut variance factors have an appreciable impact on the cumulative gas
production. This is to be expected as they are both variances that result in reduction in gas
flow.
Table 4-1: Parameters for variance on synthetic type curve
Case x(t)noise
Gauss.
x(t)noise
Frequency
x(t)dist
x(t)shut
Cum.
Gas
MMSCF
c1 c2 c3 c4 c5 pdist pshut
A 17.20
B 0.05 17.22
C 0.05 0.55 17.20
D 0.5 0.1 1/12 16.49
E 1/24 16.48
F 0.05 0.5 0.1 1/12 1/24 15.79
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Figure 2: Results of synthetic type curves with variance added. Case A shows a clean synthetic type curve with no variance. Case B introduces Gaussian distribution of noise. Case C introduces a frequency based noise. Case D shows the impact of large disturbances. Case E demonstrates the impact of shut-ins. Case F is the synthetic type curve in Case A with the disturbances of Cases B, D and E incorporated.
5 Well deliverability at wellhead conditions
A type curve is a flow rate for a reference pressure during the declining flow period
(Clarkson & Qanbari, 2016). In using the synthetic type curve as an input boundary to test
surface network equipment, reward and penalty must be accounted for deviation in pressure
through lower and higher flow rates respectively. This requires the introduction of further
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parameters that are designed to mimic an inflow performance relationship that can
approximate either a single-phase or two-phase inflow performance relationship, as discussed
in Sugiarto et al. (2015). The approach here is a simplification and the intention is to develop
a flexible model based on high level theory with parameterisation that can be utilised to
generate sets of randomised synthetic type curves, and not to provide a detailed model of
actual reservoir performance.
With the methane being adsorbed in the coal matrix (Sugiarto, et al., 2013) and shale pores
(Alexander, et al., 2011), the isotherm models can be used to model how reservoir pressure
can decline over production. Sugiarto et al. (2013) reported a typical isotherm for methane
adsorbed onto coal, with a some measured data, and demonstrates the relationship of change
in reservoir pressure to gas production for a fixed mass of coal. The isotherm curve is
determined by the parameters Langmuir volume, the theoretical limit for gas adsorption at
infinite pressure, and Langmuir pressure, which is the pressure at half the Langmuir volume
(Alexander, et al., 2011).
The Langmuir isotherm equation is given in equation (14).
\�O� = ]^∙_̀ �a_^1_̀ �a �14�Where:
- Gtot is the original gas content (standard volume per unit mass);
- VL is the Langmuir volume;
- PL is the Langmuir pressure; and
- Pres is the reservoir pressure
As demonstrated by equation (14) full recovery of gas adsorbed can only be achieved by
reducing the reservoir pressure to absolute vacuum. This is of course not practical, and thus
an abandonment pressure is typically determined to calculate the recovery efficiency as a
ratio of the original hydrocarbon in place that is technically and economically feasible to
produce (Sugiarto, et al., 2015). In this work, the gas recoverability is denoted as Grec.
The Rawlins and Schellhardt equation is an empirical relationship for deliverability from a
gas well (Lake & Fanchi, 2006). Although it is not rigorous, and does not apply to high
pressure wells (greater than 13 500 kPag [2000 psia]) where gas compressibility and viscosity
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change appreciably as a function of pressure, it is still widely used (Lake & Fanchi, 2006). It
is adapted for this work to describe the shape of the well inflow performance relationship in
the synthetic type curve at each time interval and that the pressure of wells will generally be
below the high pressure threshold where gas properties deviate appreciably. The Lake &
Fanchi (2006) also present the Houepeurt theoretical deliverability equation as an alternative
to the empirical Rawlins and Schellhardt equation for estimating production rates at variable
pressures. The two coefficients in the Houepeurt theoretical equation only allow inflow
performance relationships curves that have characteristic between linear and quadratic shape,
where as demonstrated in this section, is a constraint unconventional gas wells’ inflow
performance relationships may not fit. More flexibility is needed and this is provided with the
Rawlins and Schellhardt equation (15).
����b = c�d$*�� − d$*e� �� (15)
Where:
- q(t)C is flow rate at time t;
- λ is the performance coefficient;
- n is the exponent that determines the shape of the inflow performance relationship,
constant for the life of the well
The shape of the inflow performance relationship, determined by the value of n in equation
(15) can be different depending on the flow conditions of the well. Theoretical values of n
can range between 0.5 indicating turbulent flow to 1 indicating laminar flow (Lake & Fanchi,
2006). However, depending on single phase or two phase flow in the reservoir can lead to
different shapes of inflow performance curves (Sugiarto et al. 2015) which for the two phase
flow curve can be achieved with n > 2 in equation (15) as demonstrated in Figure 6. This is
also supported by the work of Cong et al. (2014).
Adapting this theory to the generate an inflow performance relationship for each time interval
requires a synthetic type curve generated from the steps presented so far, definition of
adsorption isotherm parameters Langmuir volume (VL) and Langmuir pressure (PL), initial
reservoir gas content (Gtot) and gas recoverability (Grec). Figure 3 shows a synthetic type
curve and its cumulative gas production, and next to it a typical isotherm for methane on coal,
generated with values VL = 550 scf/tonne and PL = 5170 kPaa (750 psia) taken from the
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reported values from Sugiarto et al. 2013. Using an initial gas content of 250 scf / tonne and
gas recoverability of 85 % (Sugiarto, et al., 2013) an initial reservoir pressure can be
determined. Performing a mass balance on the reservoir by subtracting the cumulative gas
production from the initial gas content, a reservoir pressure profile can be estimated, as
shown in Figure 4.
Figure 3: Synthetic flow type curve with cumulative gas flow built with equations presented in this paper and an adsorption isotherm curve built from equation (14) and values reported by Sugiarto et al (2013).
Figure 4: Estimated change in reservoir pressure as a function of gas production from an assumed gas isotherm and synthetic type curve
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With a profile of reservoir pressure, a specified reference pressure for the synthetic type
curve, equation (15) can be used to generate an inflow performance relationship. The
exponent n determines the shape of the curve and is assumed constant throughout time. The
performance coefficient λ is then calculated at each time interval such that the relationship
intersects the points (q(t)B, Pref) and (0, Pres(t)). This is illustrated in Figure 5, where the
inflow performance curve for different time intervals are calculated for different curve
exponents, and the maximum back pressure, associated with zero flow, aligns with the
reservoir pressure decline in Figure 4.
Figure 5: Difference in synthetic type curve inflow performance curves over time and curve exponent
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Figure 6: Difference in IPR curve exponent demonstrating the intersection of reservoir pressure at zero flow and the well type curve flow at t = 100 and its reference pressure.
This gives the synthetic type curve an inflow performance relationship, with the reservoir
pressure declining in a manner that is consistent with basic theory, and a curve shape
parameter that has the flexibility to represent different inflow performance relationship
shapes as reported in literature.
6 Subsurface communication
It has been reported in some unconventional gas wells that there is subsurface communication
between reservoirs (Young, et al., 2014; Howell, et al., 2014; Lagendijk & Ryan, 2010; Sani,
et al., 2015), where a decrease in pressure in one reservoir can be detected in a neighbouring
reservoir by a corresponding decrease in pressure. Using the reservoir pressure decline model
established in the previous section, and an equation based on Darcy’s law, a simplified
subsurface transmissibility relationship has been developed, with the following assumptions:
- The change in pressure of a reservoir is centred on the wellhead location;
- All unconventional well types, such as vertical multi-seam CBM and horizontal
hydraulically fractured shale gas wells behave the same;
- Subsurface flow is directly proportional to pressure difference and resistance, and
inversely proportional to length;
- Fluid viscosity is constant throughout the entire field; and
- Flow area is constant between all reservoirs across the field.
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These assumptions lead to equation (16).
���� = ����b, +min g∑ i∙3_̀ �a���j�_̀ �a���k6lkjmno� , Rp ∙ ����q �16� Where:
- w is the number of wells in the field;
- c6 is a factor to ensure that the subsurface flow doesn’t exceed a set fraction of the
actual wellhead flow, as the limit of w tends towards infinite will result in infinite
subsurface flow. Also a well doesn’t flow while it’s base synthetic type curve is zero
flow (before it’s dewatered or after depletion) or a shut-in has occurred by x(t)shut;
- Lij is the distance between wells i and j;
- κ is the transmissibility constant used as a global constant between all wells; and
- Pres is the reservoir pressure, as calculated in the previous section.
7 Fixed Parameters
7.1 Temperature
The parameter T is defined as the temperature of the gas flow at the input boundary, which is
constant over time for the synthetic type curve.
7.2 Composition
The composition of the gas at the input boundary is a key parameter as this will impact on the
surface network design as the flow rate itself, by way of fluid transport properties (density,
viscosity), potential for multiphase flow through the network (eg liquids condensing from
cooling in the pipe network or entrained as liquid droplets in the gas phase) and can impact
on the hydraulic performance of the surface network.
Describing fluid composition, temperature, pressure and phase transitions requires a
thermodynamic method to be introduced, though this is an issue for the surface network
system modelling and the synthetic type curve parameterisation is independent of those
decisions.
The synthetic type curve fluid composition will be defined as an array of, denoted as z1, z2, z-
3…zn , where zn is the mole fraction for component n given as a number between 0 and 1.
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8 Using synthetic type curves
The synthetic type curves defined in this work can be used to mimic the uncertain and
variable input boundaries of unconventional gas surface networks by randomising the input
parameters to form a set of unique type curves. This is done by specifying a probability
distribution (e.g. Gaussian, log-normal, triangular, equal probability to name a few) and the
required parameters, such as mean, variance and upper and lower bounds for each parameter.
A surface network design that is based on a set of synthetic type curves identical to the base
case can then be tested for performance on the set of synthetic type curves generated from
randomisation of the parameters used to construct them to enable evaluation of surface
network designs against uncertain input boundaries.
It is important to note that synthetic type curves do not account for any mass balance on the
reservoirs as it’s around modelling the input boundary response over time rather than
providing a model for the reservoir. For example, if a well is consistently operating below its
reference pressure Pref, actual cumulative production will be higher than the base type curve
but have no impact on the reservoir pressure Pres rate of decline.
9 Conclusions
A synthetic type curve based on input parameterisation independent of reservoir properties
for use in describing the input boundaries of surface facilities and gas gathering networks for
unconventional gas developments has been developed and described. The synthetic type
curve has been demonstrated to adequately reproduce actual unconventional gas type curves
found in literature. Means to incorporate instabilities, disturbances and discontinuous
uncertainties observed in production history data have been incorporated. A mechanism for
inflow performance relationships has been established including the flexibility to model
different types of reservoirs. Subsurface communication between individual wells has been
accounted for with a simplified model that provides a relationship between flow, difference in
reservoir pressure and distance.
The synthetic type curve can be used as an input boundary to mimic the flow profile, inflow
performance response and flow irregularities of a coal bed methane well. They will be used in
future work to rapidly generate sets of type curves built with random variations of input
parameters to test surface facility and gas gathering network designs against uncertainty and
variability and explore both the downsides of the risk and also find and exploit the upside
opportunities.
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10 Acknowledgement
This research was financially supported by INTELICS Pty Ltd (www.intelics.com.au) with
academic guidance from Prof Brian Towler and Dr Mahshid Firouzi from University of
Queensland School of Chemical Engineering (www.chemeng.uq.edu.au) and Prof Andrew
Garnett and Prof Jim Underschultz from Centre for Coal Seam Gas (www.ccsg.uq.edu.au).
The author is also very gracious of the generous amount of time David Hazle from Arrow
Energy afforded to support this work and valuable contributions from Ashok Mishra from
ConocoPhilips.
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11 Nomenclature
a flow decline constant
b flow decline exponent
c1 variance of noise function
c2 amplitude of frequency based noise function as fraction of flow
c3 frequency of frequency based noise function in time units
c4 major flow disturbance average, as fraction of flow rate
c5 variance of major flow disturbance as fraction of flow rate
c6 maximum fraction of flow that can be from subsurface communication
Gtot Total gas content of a reservoir, scf / tonne
Grec Gas recoverable, fraction of Gtot
k interpolation degree between linear and sinusoidal ramp to peak
L length, linear distance between two wells
m slope of ramp to peak, MMSCFD / month
n exponent for well deliverability
p probability of event occurring, month-1
P pressure, kPag
q standard volume flow, MMSCFD
t time, months
T Temperature, °C
U sample from a uniform probability distribution
V Volume, standard cubic feet
w number of wells in the field
x multiplicative factor to modify well flow q
z mole fraction of molecular component
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λ coefficient for well deliverability
κ global subsurface flow resistivity
Φ sample from a user defined probability distribution function
11.1 Subscripts
0 time zero
A intermediate result A
B intermediate result B
C intermediate result C
decline result during decline flow period
dist major disturbance to well flowrate
i well i
j well j
lin result of linear function
L Langmuir constant
noise signal noise
peak result during peak flow conditions
plat result during synthetic type flow plateau period
ramp result within the ramp to peak period of synthetic type curve
ref reference conditions
res reservoir conditions
shut well shut-in, zero flow
sin result of sine function
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Highlights:
- A framework to develop synthetic type curves is proposed, using qualitative
parameters and some theoretical basis, but require little knowledge from the reservoir
engineering domain to construct
- The synthetic type curves are demonstrated to mimic reservoir model outputs and
actual operating data
- A mechanism to incorporate pressure flow performance relationships is described
- A mechanism to incorporate subsurface communication between reservoirs is
proposed
- The synthetic type curves are primarily for using as input boundaries to
unconventional gas surface networks, with the larger intent of being able to quickly
produce many sets of synthetic type curves by randomisation of the input parameters
to test designs against uncertain inputs