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: uqmdenni@uq.edu.au

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