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Citation: Luo, Y.; Yang, J.; Chen, M.;
Yang, L.; Peng, H.; Liang, J.; Zhang, L.
Study of Estimated Ultimate
Recovery Prediction and Multi-Stage
Supercharging Technology for Shale
Gas Wells. Separations 2023,10, 432.
https://doi.org/10.3390/
separations10080432
Academic Editor: Sascha Nowak
Received: 17 June 2023
Revised: 18 July 2023
Accepted: 24 July 2023
Published: 29 July 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
separations
Article
Study of Estimated Ultimate Recovery Prediction and
Multi-Stage Supercharging Technology for Shale Gas Wells
Yanli Luo 1, Jianying Yang 1, Man Chen 1, Liu Yang 1, Hao Peng 1, Jinyuan Liang 2and Liming Zhang 2,*
1Sichuan Changning Natural Gas Development Co., Ltd., Yibin 610051, China;
luoyl2017@petrochina.com.cn (Y.L.); yangjianying@petrochina.com.cn (J.Y.);
chenman08@petrochina.com.cn (M.C.); yangliu16@petrochina.com.cn (L.Y.);
peng.hao@petrochina.com.cn (H.P.)
2School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, China;
liangjinyuanupc@163.com
*Correspondence: zhangliming@upc.edu.cn
Abstract:
The development of shale gas reservoirs often involves the utilization of horizontal well
segmental multi-stage fracturing techniques. However, these reservoirs face challenges, such as rapid
initial wellhead pressure and production decline, leading to extended periods of low-pressure produc-
tion. To address these issues and enhance the production during the low-pressure stage, pressurized
mining is considered as an effective measure. Determining the appropriate pressurization target
and method for the shale gas wells is of great practical significance for ensuring stable production in
shale gas fields. This study takes into account the current development status of shale gas fields and
proposes a three-stage pressurization process. The process involves primary supercharging at the
center station of the block, secondary supercharging at the gas collecting station, and the introduction
of a small booster device located behind the platform separator and in front of the outbound valve
group. By incorporating a compressor, the wellhead pressure can be reduced to 0.4 MPa, resulting
in a daily output of 12,000 to 14,000 cubic meters from the platform. Using a critical liquid-carrying
model for shale gas horizontal wells, this study demonstrates that reducing the wellhead pressure
decreases the critical flow of liquid, thereby facilitating the discharge of the accumulated fluid from
the gas well. Additionally, the formation pressure of shale gas wells is estimated using the mass
balance method. This study calculates the cumulative production of different IPR curves based on
the formation pressure. It develops a dynamic production decline model for gas outlet wells and
establishes a relationship between the pressure depletion of gas reservoirs and the cumulative gas
production before and after pressurization of H10
−
2 and H10
−
3 wells. The final estimated ultimate
recovery of two wells is calculated. In conclusion, the implementation of multi-stage pressurization,
as proposed in this study, effectively enhances the production of, and holds practical significance for,
stable development of shale gas fields.
Keywords: shale gas; multi-stage supercharging; EUR; steady yield increase
1. Introduction
Shale gas exhibits inherent traits, such as self-generation and self-storage, water-
sealed reservoir interfaces, extensive and continuous distribution, low porosity, and low
permeability. Typically, it lacks natural production capabilities or possesses low yields,
necessitating the implementation of large-scale hydraulic fracturing and horizontal well
technologies for economically viable exploitation [
1
–
4
]. Nevertheless, after years of shale
gas well development, the pressure experiences a rapid decline, with the wellhead pressure
approaching the transportation pressure, resulting in a minimal production pressure dif-
ference. Consequently, shale gas production experiences a steep decline [
5
,
6
]. Employing
pressurized mining serves as an effective approach to enhance the production performance
of the low-pressure stage. By incorporating a compressor to elevate the pressure energy
Separations 2023,10, 432. https://doi.org/10.3390/separations10080432 https://www.mdpi.com/journal/separations
Separations 2023,10, 432 2 of 16
of low-pressure gas, the flow pressure increases, along with the disparity between the
flow pressure and external transmission pressure. This facilitates a smooth transportation
of the low-pressure gas. Accurately determining the pressurization target and adopting
a reasonable pressurization method for shale gas wells holds practical significance for
ensuring stable production in shale gas fields.
Since the 1970s, Columbia Company in the United States has implemented gas field
pressurization production through the construction of a compressor booster device [
7
].
Most of the coalbed methane fields developed in the United States utilize a centralized
compression system, commonly referred to as the central station level processing [
8
,
9
]. The
coalbed methane field in the San Juan Basin of the United States employs a centralized
pressurization procedure, allowing for the central pressurization and transportation of
coalbed methane by utilizing the wellhead pressure. Each treatment station is outfitted
with a minimum of two skid-mounted reciprocating compressors powered by coalbed
methane engines, utilizing a three-stage compression process [
10
]. The Marcellus shale
gas field in the United States employs a two-stage pressurization mode. A throttle valve
is installed at the wellhead to regulate the flow of shale gas. After passing through the
pipeline following throttling, the shale gas enters the well site. Upon undergoing treat-
ment with a separator and de-sanding device, it proceeds to the gas collection station for
pressurization. Subsequently, the gas undergoes secondary pressurization at the central
processing station [
11
]. The Waddell Ranch [
12
] project conducted an economic comparison
between centralized pressurization and single-well pressurization, ultimately determin-
ing the feasibility of the single-well boosting scheme. The project was implemented in
three phases over a three-year period, involving pressurization tests on 63 wells at the
well sites and the installation of 52 compressors, resulting in increased gas production
from low-pressure wells. However, it was observed that although gas well production
significantly increased after pressurization, the production decline rate also escalated ac-
cordingly. The Ranger field and the Panham gas field [
13
] have also achieved positive
application results by employing pressurization devices and utilizing negative pressure
gas gathering processes for production.
Josifovic et al. [14]
found that reducing the cut
diameter and running the pump at a higher speed can increase pump efficiency by as
much as 4.6%. In China, the adoption of pressurization processes commenced relatively
late. The first use of a compressor in the pressurization process took place in 1982 in the
Sichuan Xing3 well [
7
]. Since then, the domestic utilization of pressurization processes has
become widespread. Field development practices have indicated that when the pressure
of a gas well approaches the pipeline network pressure, production starts to decline, and
the gas well lacks the ability to maintain stable production. Studying the dynamics of
production indicators such as gas field production and pressure decline is a crucial aspect
of the second phase of pressurization. Production history fitting serves as the basis for
forecasting production dynamics [
15
]. ARPS [
16
] proposed a systematic approach to the
decline laws of oil and gas fields in the 1950s. Yu et al. [
17
] defined three new capacity
reduction rates based on the instantaneous decline rate, derived the expression for capacity
reduction under the three types of reductions in Arps’ decline theory, and provided a
clearer representation of the relationship among capacity, pressure, and production degree.
Chen et al. [
18
] proposed a method to detect the reservoir volumetric fracturing effect
by using longitudinal wave velocity radial sequence imaging technology and shear wave
remote exploration and processing technology. Zhang et al. [
19
] proposed a new production
optimization framework combining advanced deep reinforcement learning techniques.
Zhang et al. [
20
] proposed a new multi-scale fracture network characterization method
and a strong dimensionality reduction method based on a model parameter autoencoder.
Zhang et al. [
21
] established a deep learning model based on FNO for three types of PDE
control problems of two-dimensional subsurface oil–water two-phase flow. Meng et al. [
22
]
analyzed the fundamental characteristics and exploitation status of the West Sichuan gas
reservoir and employed ReO software and linear programming principles to determine
the optimal pressurization scheme based on parameters such as maximum production
Separations 2023,10, 432 3 of 16
output and minimal unit energy consumption. However, their study did not delve into the
research of early-stage pressurization processes. Hu et al. [
23
] adopted a process known
as “drainage gas production, low-pressure gas gathering, inter-well connection, wellhead
measurement, composite material utilization, dual-site pressurization, station–site sep-
aration, and centralized treatment”. However, this mode is applicable only when the
wellhead pressures are equal. In the later stages of production, when the wellhead pres-
sures vary, inter-well interference occurs, and the gas backflow prevents it from entering
the gas collection station. Shang et al. [
24
] and others implemented a pressurization process
with “regional pressurization as the primary approach, supplemented by single-station
pressurization” during the middle and late stages of the Jingbian gas field. However,
the regional pressurization operation was inflexible and not applicable to more complex
scenarios. Liu et al. [
25
] implemented a second-phase booster project at the gas gathering
station in Daniudi, building upon the first phase of centralized pressurization. This allowed
for the realization of a two-stage pressurization and transportation system. However, this
pressurization mode focused on the location and method of pressurization within the
long-distance natural gas pipeline network gathering and transmission system, without
addressing the timing of pressurization. Shi et al. [
26
] adopted the gas gathering station
pressurization and production mode in the Fuling shale gas field. This method minimized
the waste pressure of the pressurized gas well and met the transmission requirements
of the gas gathering station’s new regulating well. However, it neglected the inter-well
disturbance caused by different pressures between the wells due to long-term mining or
the blockage of long-term operating pipelines, resulting in a significant pressure loss. This
led to the failure of gas from well to well to reach the gas collection station and incurred
substantial economic losses. China’s shale gas exploration and development started later,
and the geological environment and exploitation methods of shale gas fields differ from
those in the United States. Therefore, it is not feasible to simply replicate advanced foreign
technologies for boosting and increasing production. Consequently, this study incorporated
the development status of the Xx shale gas field. Based on primary supercharging at the
central station of the Xx block and secondary supercharging at the gas gathering station,
a small piece of pressurization equipment was installed behind the platform separator
and in front of the outbound valve group to create a three-stage pressurization process.
The critical liquid-carrying model of shale gas horizontal wells was used to determine the
influence of wellhead pressure on the critical flow of liquid carrying in wellheads. Through
the analysis of field test data, the inflow dynamic relationship (IPR) curve was successfully
established. The mass balance method was applied to the estimation of the formation
pressure in shale gas wells. By calculating the cumulative yield of different IPR curves, the
dynamic decline model of gas outlet well production revealed the relationship between the
waste pressure and the pressurization effect of the gas well’s gas reservoir. Based on the
above, we predicted the estimated ultimate recovery of the gas well.
2. Theoretical Research
2.1. The Selection of the Supercharging Mechanism and Mode
The addition of a compressor is intended to augment the pressure energy of gas
with low pressure levels by means of a supplementary apparatus, thereby elevating the
flow pressure and the pressure differential between the flow pressure and the external
transmission pressure. This facilitates the smooth transportation of low-pressure gas.
The purpose is to improve the starting transmission pressure of the gas pipeline and
compensate for resistance losses during fluid flow within the pipeline. It also ensures that
the transmission pressure meets the requirements of the gas gathering pipeline network.
As the development of the gas fields progresses, the pressure in the gas wells gradually
decreases over time. In the later stages of development, the well pressure may no longer
meet the requirements of the gathering pipeline network’s gas inlet pressure. Therefore,
pressurization is necessary to increase the gas pressure for transmission into the pipeline
network. By utilizing the suction action of the compressor at the inlet, the wellhead
Separations 2023,10, 432 4 of 16
pressure of the gas well can be reduced over a period of time, while the reservoir pressure
remains unchanged. This increases the pressure difference between the bottom of the well
and the wellhead. Due to long-term exploitation, some gas wells experience relatively
low wellhead pressures and gas production rates, which hinders the export of natural
gas and severely impacts the normal production operations. Hence, it is imperative to
study the pressurization processes. Common pressurization methods employed both
domestically and internationally include single-well pressurization, pressurization at gas
gathering stations, and regional pressurization [
27
]. Single-well pressurization refers to
the installation of a compressor at the wellhead to pressurize the raw gas for transmission
into the gas pipeline network [
28
]. This process offers operational flexibility and can
be customized based on the specific conditions of each gas field. It is highly adaptable.
However, for large low-pressure gas fields, a significant number of compressors may
be required, resulting in high investment costs. Pressurization at gas gathering stations
involves the centralized installation of compressors at the stations to provide increased
pressure. This approach reduces investment costs. However, it is only applicable to gas
fields where the wellhead pressure is sufficient to reach the gas gathering station without
the need for additional pressurization. This method is not suitable for gas fields with low
wellhead pressures [
29
]. This mode involves the independent establishment of a booster
station, which increases the flexibility of scheduling for the gas gathering network. In this
study, a comprehensive pressurization scheme was developed by combining the advantages
of various pressurization modes. According to the Xx H10 platform gas gathering process
(Figure 1a), the gas flowed from the platform (gas well) to the gathering station and then
to the centralized booster station before being transported externally. The pressurization
equipment was installed behind the separator and before the outbound valve group. It was
connected to the reserved manifold of the pipeline at the back end of the separator, and the
pressurized gas was then connected to the outbound manifold through the pipeline. The
modified process flow included a bypass function that determined whether the gas entered
the pressurization device based on the production conditions of each individual well. This
allowed low-pressure natural gas to be transported to the next station and reduced the cost
of transporting non-pressurized gas. Within the gas gathering station, the installation of
mobile-type two-stage boosting equipment was determined based on the inlet pressure.
For example, the gas produced from the Xx H10 platform was pressurized and transported
to the central station of the Xx well area for centralized boosting and external transmission
through the Xx H3 platform. The gas was then transported to the central station for
centralized pressurization and subsequent external transmission (Figure 1b).
Separations 2023, 10, x FOR PEER REVIEW 5 of 18
(a)
(b)
Figure 1. (a) Xx H10 platform gas delivery process flow diagram; (b) Xx station gas transmission
process flow diagram.
2.2. Calculation Method of the IPR Curve
Determining the inflow performance relationship (IPR) curve is an essential step in
the calculation of gas well production. This involves integrating the geological properties
of shale gas and the seepage characteristics of fractured horizontal wells, taking into ac-
count the variable mass flow from the formation to the fracture. By applying the
Figure 1. Cont.
Separations 2023,10, 432 5 of 16
Separations 2023, 10, x FOR PEER REVIEW 5 of 18
(a)
(b)
Figure 1. (a) Xx H10 platform gas delivery process flow diagram; (b) Xx station gas transmission
process flow diagram.
2.2. Calculation Method of the IPR Curve
Determining the inflow performance relationship (IPR) curve is an essential step in
the calculation of gas well production. This involves integrating the geological properties
of shale gas and the seepage characteristics of fractured horizontal wells, taking into ac-
count the variable mass flow from the formation to the fracture. By applying the
Figure 1.
(
a
) Xx H10 platform gas delivery process flow diagram; (
b
) Xx station gas transmission
process flow diagram.
2.2. Calculation Method of the IPR Curve
Determining the inflow performance relationship (IPR) curve is an essential step in the
calculation of gas well production. This involves integrating the geological properties of
shale gas and the seepage characteristics of fractured horizontal wells, taking into account
the variable mass flow from the formation to the fracture. By applying the superposition
principle, a steady-state stage production capacity equation was proposed for multi-stage
fractured horizontal wells in shale gas reservoirs.
The flow rate at any given position within the artificial fracture [30]:
vf(x)=−M
RT
P
Z
Kf
µ
dPf
dx =−1
2Kf
M
RT
dψf
dx (1)
Considering the additional pressure drop caused by the high-speed non-Darcy effect
and the epidermal effect [30]:
ψe−ψw f =qg f sc
Ze√c
hkm
1
1−e−√cx f
Psc T
Z0Tsc 1+S+Dqg f sc (2)
Assuming that a shale gas multi-stage fractured horizontal well has n uniformly
distributed fractures, the total gas production from the well is q
gsc
, the gas production
from each fractured fracture is q
gsc
/n, and the shale gas well capacity equation satisfies the
binomial form [30]:
P2
e
µeZe−P2
w f
µw f Zw f
=Aqgsc +Bq2
gsc (3)
Thereinto:
A=1
4n
Ze√c
hkm
1
1−e−√cx f
psc T
Z0Tsc
(1+S)(4)
B=1
8n2
Ze√c
h√km
1
1−e−√cx f
Psc T
Z0Tsc
D(5)
c=2km
kfzeω(6)
In the case of well Xx H10
−
1, the fundamental formation parameters are presented in
Table 1, sourced from the pressure recovery test conducted on well Xx 10
−
1. The measured
Separations 2023,10, 432 6 of 16
PVT (pressure–volume–temperature) curve is fitted, as shown in Figure 2. The goal was to
calculate the product of compression factor and viscosity at various pressures.
Table 1. Basic stratigraphic parameters of well Xx H10 −1.
Stratigraphic
Temperature
(K)
Crack
Height/Shale
Thickness
(cm)
Uncaused
Fracture
Infusion
Capacity
Shale
Matrix
Permeability
(µm2)
Crack
Half-Length
(cm)
Fracturing
Section
Length
(cm)
Number of
Cracks
Total
Epidermal
Coefficient
364.93 3500 10.04 3.1 ×10−510,750 136,200 19 0.0133
Separations 2023, 10, x FOR PEER REVIEW 7 of 18
relative error indicated the accuracy and correctness of the IPR (inflow performance rela-
tionship) curve of well Xx H10
−
1.
Table 2. Pressure test data of well Xx H10 −1 in 2021.
Date Testing Central
Pressure (MPa)
Boom Hole Flow
Pressure (MPa)
Daily Gas Production Ca-
pacity
(10
5
m
3
/d)
Average Calculated
Formation Pressure (MPa)
20 August 2021 2.733 2.743 1.66 3.210
23 August 2021 Well shutdown pressure recovery
17 September 2021 3.344 (Measuring
static pressure) None 0 3.379 (Static pressure)
(a) (b)
(c)
Figure 2. (a) Graphs of different formation pressures and compression factors; (b) graphs of different
formation pressures and viscosities; (c) product plot of different formation pressures with compres-
sion factors and viscosity.
Figure 2.
(
a
) Graphs of different formation pressures and compression factors; (
b
) graphs of different
formation pressures and viscosities; (
c
) product plot of different formation pressures with compression
factors and viscosity.
After substituting the given data from Table 1into the binomial equation for gas wells,
the values A = 124.754377 and B = 0.037499 were obtained. The gas well capacity equation
can be expressed as follows:
P2
e−P2
w f =(µZ)p124.754377qgsc +0.037499q2
gsc(7)
Separations 2023,10, 432 7 of 16
Based on the 2021 pressure test data of well Xx H10
−
1 (as shown in Table 2), the
formation static pressure test value was recorded as 3.379 MPa, while the model-calculated
value was 3.210 MPa. This resulted in a relative error of 5.0%. The relatively low relative
error indicated the accuracy and correctness of the IPR (inflow performance relationship)
curve of well Xx H10 −1.
Table 2. Pressure test data of well Xx H10 −1 in 2021.
Date Testing Central
Pressure (MPa)
Bottom Hole Flow
Pressure (MPa)
Daily Gas
Production Capacity
(105m3/d)
Average Calculated
Formation Pressure
(MPa)
20 August 2021 2.733 2.743 1.66 3.210
23 August 2021 Well shutdown pressure recovery
17 September 2021 3.344 (Measuring
static pressure) None 0 3.379 (Static pressure)
In order to analyze the impact of pressurization measures on EUR, the decay process
of the formation pressure in gas wells under different cumulative gas production scenar-
ios needs to be clarified. In this study, based on shale gas reserves and an analysis of
the mechanism, we fitted shale gas well reserves based on the material balance method,
and then predicted the variation of the formation pressure under different cumulative
production scenarios.
The material balance equation for shale gas wells [31]:
GpBg=GmBg−Bgi+GfBg−Bgi +GmBgi Bgρb
(1−Smi )Φm−ΦaVLP0
PL+P0−VLP
PL+P
−GmBgi ρbρsc
[(1−Smi )Φm−Φa]ρSmi x VLP0
PL+P0−VLP
PL+P+GmBgiΦm
(1−Smi )Φm−Φa(cx+cwSm)(P0−P)
+GfBgi
1−Sfcf+cwSf(P0−P)
(8)
Y
M=Gf+F
MGm(9)
Y=GpBg(10)
M=Bg−Bgi +Bgi
1−Sf i cf+cwSf i (P0−P)(11)
F=Bg−Bgi +Bgi BgVL
(1−Smi)Φm−ΦaP0
PL+P0−P
PL+PBg−ρsc
ρSmix +BgiΦm
(1−Smi)Φm−Φa
(cx+cwSm)(P0−P)(12)
Based on the formation pressure and dynamic production data obtained during the
production of well Xx H10
−
1 (Table 3), the well reserves were calculated using the material
balance equation. The calculated values of Y/Mand F/Mwere plotted (Figure 3). By
applying Equation (11), the slope was determined as the matrix-free gas storage volume
G
m
= 0.5271
×
10
8
m
3
, and the intercept represented as the fracture-free gas storage volume
G
f
= 0.0691
×
10
8
m
3
. The adsorbed gas storage capacity was calculated as
1.3226 ×108m3
.
The total storage capacity was determined to be
1.9188 ×108m3
. To predict the decay
process of the average formation pressure under different cumulative production scenarios,
the reserves of well Xx H10
−
1 (Table 4) were used. The predicted results were then
compared with the actual measured data (Figure 4) to verify the accuracy of the calcu-
lations. The comparison showed a close resemblance between the predicted and actual
decay processes of the average formation pressure under different cumulative production
scenarios. By establishing the correspondence between the cumulative production and the
average formation pressure, the IPR curve under different cumulative production levels
Separations 2023,10, 432 8 of 16
was calculated. This curve served as a basis for determining gas well production under
various formation pressures.
Table 3. Dynamic production data of well Xx H10 −1.
Date Testing Central
Pressure (MPa)
Discounted
Bottomhole Flow
Pressure
(MPa)
Daily Gas
Production
Capacity
(105m3)
Average Calculated
Formation Pressure
(MPa)
Cumulative Gas
Production (105m3)
14 October 2016 7.748 8.132 12.082 9.391 5619.912
8 December 2016 7.25 7.524 7.999 8.726 6125.840
24 March 2017 7.563 7.889 7.236 8.992 6843.317
19 June 2017
8.026 (Static pressure) 8.226 (Static pressure)
0 None 7451.635
19 July 2018 5.132 5.905 5.261 6.610 9209.911
20 August 2021 2.733 2.743 1.66 3.210 11,792.283
17 September 2021
3.344 (Static pressure) 3.379 (Static pressure)
0 None 11,797.364
Separations 2023, 10, x FOR PEER REVIEW 9 of 18
Figure 3. Relationship between Y/M and F/M.
Table 3. Dynamic production data of well Xx H10 −1.
Date Testing Central
Pressure (MPa)
Discounted Boomhole
Flow Pressure
(MPa)
Daily Gas
#break#Production
#break#Capacity
(10
5
m
3
)
Average Calculated
Formation Pressure
(MPa)
Cumulative
Gas
#break#Pro-
duction (10
5
m
3
)
14 October 2016 7.748 8.132 12.082 9.391 5619.912
8 December 2016 7.25 7.524 7.999 8.726 6125.840
24 March 2017 7.563 7.889 7.236 8.992 6843.317
19 June 2017 8.026 (Static pres-
sure) 8.226 (Static pressure) 0 None 7451.635
19 July 2018 5.132 5.905 5.261 6.610 9209.911
20 August 2021 2.733 2.743 1.66 3.210 11,792.283
17 September 2021 3.344 (Static pres-
sure) 3.379 (Static pressure) 0 None 11,797.364
Figure 3. Relationship between Y/M and F/M.
Table 4.
Decay process of the average formation pressure under different cumulative production
scenarios for the reservoir prediction of well Xx H10 −1.
Stratigraphic Pressure
(MPa)
Cumulative Yield
(108m3)
Stratigraphic Pressure
(MPa)
Cumulative Yield
(108m3)
22 0 4.5 1.03712
20 0.06689 4 1.09471
18 0.15571 3.5 1.15672
16 0.25955 3 1.22405
14 0.36432 2.5 1.29787
12 0.46852 2 1.37972
10 0.58169 1.5 1.47155
8 0.7171 1 1.57597
6 0.88468 0.5 1.69641
5 0.98323 0.1 1.8074
Separations 2023,10, 432 9 of 16
Separations 2023, 10, x FOR PEER REVIEW 9 of 18
Figure 3. Relationship between Y/M and F/M.
Table 3. Dynamic production data of well Xx H10 −1.
Date Testing Central
Pressure (MPa)
Discounted Boomhole
Flow Pressure
(MPa)
Daily Gas
#break#Production
#break#Capacity
(10
5
m
3
)
Average Calculated
Formation Pressure
(MPa)
Cumulative
Gas
#break#Pro-
duction (10
5
m
3
)
14 October 2016 7.748 8.132 12.082 9.391 5619.912
8 December 2016 7.25 7.524 7.999 8.726 6125.840
24 March 2017 7.563 7.889 7.236 8.992 6843.317
19 June 2017 8.026 (Static pres-
sure) 8.226 (Static pressure) 0 None 7451.635
19 July 2018 5.132 5.905 5.261 6.610 9209.911
20 August 2021 2.733 2.743 1.66 3.210 11,792.283
17 September 2021 3.344 (Static pres-
sure) 3.379 (Static pressure) 0 None 11,797.364
Figure 4.
Comparison between predicted and measured data of the decay process of the average
formation pressure under different cumulative production cases.
2.3. Establishment of a Critical Fluid-Carrying Model for Horizontal Shale Gas Wells
Statistical data show that [
32
] water-bearing gas reservoirs in the Sichuan gas field
account for more than 80% of the total reserves. As gas fields are developed, the proportion
of water-producing gas wells has been increasing annually. Most water-producing gas
wells exhibit a ring fog flow during normal production. In instances where the flow rate of
the gas phase is insufficient to consistently lift the fluid out of the wellbore, a fluid pool
is formed at the bottom of the well. This accumulation of fluid in the wellbore results in
an elevation in back pressure on the gas formation, thereby restricting the productivity
of the well. Excessive fluid in the wellbore can even result in wellbore liquid loading,
causing the gas well to cease flowing. Furthermore, when the actual gas flow rate in the
wellbore is lower than the critical flow rate, the airflow becomes unable to remove all the
liquid from the wellhead, resulting in liquid accumulation at the bottom of the well. The
flow pattern in the wellbore will change, including the emergence of segment plug flow,
necessitating a comprehensive examination of the multi-phase tubular flow pattern theory.
This investigation holds significant value in accurately comprehending the fluid-carrying
and accumulation characteristics within gas wellbores and in providing guidance for gas
well production. In 2019, Liu et al. [
33
] conducted a study on wellbore flow calculation
methods based on pressure and temperature test data from 40 wells in shale gas fields. They
proposed using the modified Hagedorn–Brown model for sections with well slope angles
<45
◦
and the modified Beggs–Brill model for sections with well slope angles >45
◦
. The use
of horizontal wells in tight gas reservoirs has become increasingly common in recent years.
This is mainly because horizontal wells can significantly increase the drainage area of the
reservoir, thereby enhancing the productivity of a single well. However, due to the different
borehole trajectories and complex flow patterns in horizontal wells, conventional prediction
models, such as the Turner model and the Li Min model [
34
], which are based on straight
wells, are not applicable to horizontal wells. In this study, a combination of research from
the literature [
34
] and field experience was employed to select the modified Min model for
calculating the critical velocity of liquid carry (Equation (13)) and the flow (Equation (14)).
By comparing the critical flow rates of fluid carry at oil pressures of 1.83 MPa and 1.0 MPa
(Figure 5), it was found that lowering the wellhead pressure reduced the critical flow rate
of fluid carrying, thus facilitating the discharge of fluid accumulation from the gas wells.
υcrit =5"σρl−ρg
ρ2
g#0.25 [sin(1.7β)]0.38
0.74 (13)
Separations 2023,10, 432 10 of 16
Qcrit =2.5 ×104×APυcr
ZT (14)
Separations 2023, 10, x FOR PEER REVIEW 11 of 18
υ =5𝜎𝜌−𝜌
𝜌
.𝑠𝑖𝑛(1.7𝛽).
0.74 (13)
Q =2.5×10
×
𝐴
𝑃𝜐
𝑍𝑇 (14)
Figure 5. Effect of wellhead pressure on fluid-carrying critical flow rate.
2.4. Establishment of Booster Timing
Currently, there is a consensus among scholars [27–29,32–35] that during the normal
production of gas wells, the gas and liquid phases in the wellbore typically exhibit an
annular flow, with the gas phase carrying the liquid phase in an upward movement. This
state is known as continuous liquid carry. However, if the gas flow rate falls below the
critical gas flow rate for continuous liquid carry, liquid accumulation occurs in the gas
well. To prevent liquid accumulation, gas production from the well must exceed the crit-
ical flow rate for liquid carry. The decline in gas well production and liquid carry capacity
was determined by considering both the gas reservoir’s supply capacity and the well-
bore’s production capacity. Using the nodal analysis method, the inflow curve (gas well
IPR curve) and the outflow curve (wellbore TPR curve) were ploed, with the boom of
the well as the reference point for the solution. The gas well production was determined
by the intersection of these two curves. Taking well Xx H10 −1 as an example, based on
the pressure recovery interpretation results on 17 September 2021, the formation pressure
pr was 4.1 MPa, and when the wellhead pressure pt was 1.83 MPa, the nodal analysis re-
sults (Figure 6) indicated a gas production of 1.47 × 104 m3/d. By reducing the wellhead
pressure to 1.0 MPa through pressure boosting measures, the TPR curve moved down-
ward, and the intersection of the TPR curve and IPR curve shifted to the right. As a result,
the gas production of the well increased, reaching 3.72 × 104 m3/d. Lowering the wellhead
pressure enhanced the wellbore delivery capacity. The improvement in wellbore delivery
capacity also relied on the gas reservoir’s supply capacity to achieve stable production. As
well Xx H10 −1 continued to produce, its formation pressure gradually decreased, causing
the IPR curve of the gas well to shift downward (Figure 7). Even if the wellhead pressure
remained constant (TPR curve remained constant), the intersection of the IPR curve and
Figure 5. Effect of wellhead pressure on fluid-carrying critical flow rate.
2.4. Establishment of Booster Timing
Currently, there is a consensus among scholars [
27
–
29
,
32
–
35
] that during the normal
production of gas wells, the gas and liquid phases in the wellbore typically exhibit an
annular flow, with the gas phase carrying the liquid phase in an upward movement. This
state is known as continuous liquid carry. However, if the gas flow rate falls below the
critical gas flow rate for continuous liquid carry, liquid accumulation occurs in the gas
well. To prevent liquid accumulation, gas production from the well must exceed the critical
flow rate for liquid carry. The decline in gas well production and liquid carry capacity was
determined by considering both the gas reservoir’s supply capacity and the wellbore’s
production capacity. Using the nodal analysis method, the inflow curve (gas well IPR
curve) and the outflow curve (wellbore TPR curve) were plotted, with the bottom of the
well as the reference point for the solution. The gas well production was determined by
the intersection of these two curves. Taking well Xx H10
−
1 as an example, based on
the pressure recovery interpretation results on 17 September 2021, the formation pressure
p
r
was 4.1 MPa, and when the wellhead pressure p
t
was 1.83 MPa, the nodal analysis
results (Figure 6) indicated a gas production of 1.47
×
10
4
m
3
/d. By reducing the wellhead
pressure to 1.0 MPa through pressure boosting measures, the TPR curve moved downward,
and the intersection of the TPR curve and IPR curve shifted to the right. As a result, the
gas production of the well increased, reaching 3.72
×
10
4
m
3
/d. Lowering the wellhead
pressure enhanced the wellbore delivery capacity. The improvement in wellbore delivery
capacity also relied on the gas reservoir’s supply capacity to achieve stable production. As
well Xx H10
−
1 continued to produce, its formation pressure gradually decreased, causing
the IPR curve of the gas well to shift downward (Figure 7). Even if the wellhead pressure
remained constant (TPR curve remained constant), the intersection of the IPR curve and
TPR curve shifted to the left, leading to a decrease in the gas well production. For instance,
when the formation pressure dropped to 3.5 MPa, the gas well production decreased to
2.05
×
10
4
m
3
/d, even with a constant wellhead pressure of 1.0 Mpa. In such cases, the
production can be increased by reducing the wellhead pressure and shifting the intersection
of the TPR and IPR curves to the right.
Separations 2023,10, 432 11 of 16
Separations 2023, 10, x FOR PEER REVIEW 12 of 18
TPR curve shifted to the left, leading to a decrease in the gas well production. For instance,
when the formation pressure dropped to 3.5 MPa, the gas well production decreased to
2.05 × 10
4
m
3
/d, even with a constant wellhead pressure of 1.0 Mpa. In such cases, the
production can be increased by reducing the wellhead pressure and shifting the intersec-
tion of the TPR and IPR curves to the right.
Figure 6. Effect of wellhead pressure on fluid-carrying critical flow rate (black line meas IPR(Bot-
tom pressure 4.1 MPa)).
Figure 7. Effect of wellhead pressure on fluid-carrying critical flow rate.
3. Actual Production Research
3.1. Equipment Selection
The compressor unit is the core piece of equipment in the booster station, with high
investment and complex operating conditions, and the rationality of the unit selection is
closely related to the booster program. Combined with the characteristics of the Xx gas
Figure 6.
Effect of wellhead pressure on fluid-carrying critical flow rate (black line meas IPR (Bottom
pressure 4.1 MPa)).
Separations 2023, 10, x FOR PEER REVIEW 12 of 18
TPR curve shifted to the left, leading to a decrease in the gas well production. For instance,
when the formation pressure dropped to 3.5 MPa, the gas well production decreased to
2.05 × 10
4
m
3
/d, even with a constant wellhead pressure of 1.0 Mpa. In such cases, the
production can be increased by reducing the wellhead pressure and shifting the intersec-
tion of the TPR and IPR curves to the right.
Figure 6. Effect of wellhead pressure on fluid-carrying critical flow rate (black line meas IPR(Bot-
tom pressure 4.1 MPa)).
Figure 7. Effect of wellhead pressure on fluid-carrying critical flow rate.
3. Actual Production Research
3.1. Equipment Selection
The compressor unit is the core piece of equipment in the booster station, with high
investment and complex operating conditions, and the rationality of the unit selection is
closely related to the booster program. Combined with the characteristics of the Xx gas
Figure 7. Effect of wellhead pressure on fluid-carrying critical flow rate.
3. Actual Production Research
3.1. Equipment Selection
The compressor unit is the core piece of equipment in the booster station, with high
investment and complex operating conditions, and the rationality of the unit selection is
closely related to the booster program. Combined with the characteristics of the Xx gas field,
the matching compressor was selected.
1
Because the natural gas in the Xx booster station
often contains water, condensate oil, sand, and so on, and the gas well production varies
widely, the compressor to be used in the gas field gathering system should be selected from
the compressor with strong adaptability to the gas medium and a wide range of working
conditions.
2
The Xx platform collection network covers a small area, so compressor sets
should be skid-mounted equipment, as far as possible, to reduce the footprint.
3
Suitable
for multi-stage pressurization requirements, the ability to create negative pressure should
be strong—the stronger the ability to create negative pressure, the greater the production
pressure difference and the higher the output.
4
It is necessary to meet the requirements of
the Xx platform wellhead pressure, gas production, and the pressure differential between
the compressor inlet pressure and the external transmission pressure.
5
The Xx platform
Separations 2023,10, 432 12 of 16
location is remote, so if the equipment failure rate is high, maintenance experts will be
required to visit often, resulting in higher maintenance costs; thus, this selection must have
simple installation, a simple system, easy maintenance, and a low failure rate. Based on the
above requirements, this study considered the star rotary mixed air pump as the booster
equipment of this platform and compared it with the traditional equipment in Table 5to
highlight the superiority of the equipment.
Table 5. Comparison of equipment selection.
Type Advantages and Disadvantages
Reciprocating Compressors
Advantages
1. Strong applicability to variable conditions. Reciprocating
compressor is not limited by the booster pressure and
volume range, can be adjusted by adjusting the
compressor cylinder size and speed to adjust and control
the flow rate.
2. Low material requirements, conventional steel can meet
the requirements, low price, simple installation system.
3. Low noise.
4. Highly serviceable and easy to modify when used in
different working conditions.
Disadvantages
1. Needs more installation space, heavy weight is not
conducive to operation.
2. The output airflow has a certain pulsation and vibration
during operation.
3. Reciprocating motion can easily cause damage to parts,
and routine maintenance is more complicated.
Screw compressors
Advantages
1. Simple structure, not easy to damage, stable operation,
high volumetric efficiency, easy maintenance.
2. Unique cooling method to ensure the stability of the gas
compression process, can meet the requirements of low
exhaust temperature.
3.
Uniform air flow with good stability and easy installation
4. Simple structure, not easy to damage, stable operation,
high volumetric efficiency, easy maintenance.
Disadvantages
1. Low pump efficiency.
2. Short life, high price, screw pump stator using rubber
material, easy to damage.
Star rotary mixer pump
Advantages
1. Simplify crude oil gathering process and saves capital
investment in oil and gas separation and transfer.
2. Reduces wellhead back pressure and increases
production.
3. Small footprint and easy skid-mounting.
4. Automatic control, the protection function is perfect,
realizes unattended and remote control.
5. The form of motion of the piston and cylinder by rolling
friction instead of the traditional sliding friction, and has
two high-pressure compression type functions to solve the
existing technology of various compressors and pumps of
low efficiency, energy consumption, can be used in the
need for higher pressure occasions.
Disadvantages Does not smoke gases containing weak corrosion
3.2. Platform Pressurization Process Effect Analysis
The Xx platform conducted a test run from 18–28 August on wells 2 and 3 to increase
the pressure while suspending bubble row refilling. During this test period, the wellhead
Separations 2023,10, 432 13 of 16
pressure decreased, resulting in increased production from the platform, and no abnormal
gas well production was observed. Subsequently, on 21 October, the platform officially
began pressurizing, this time including three wells simultaneously, while discontinuing
bubble row refilling. After approximately 15 days of operation, wells 2 and 3 were flooded
successively, and gas lift operations were resumed. To maintain continuous production
from the gas wells, a combination of pressurization with bubble drainage and plunger gas
lift techniques was employed. This refined the cooperation between the bubble drainage
and plunger gas lift processes, which allowed for the reduction in the minimum wellhead
pressure to 0.4 MPa under the full load of the booster unit (as shown in Figure 8). So far,
the production has been relatively smooth, and the platform has achieved an increase in
production by 12 to 14 thousand cubic meters per day, effectively achieving the expected
results of the implemented measures.
Separations 2023, 10, x FOR PEER REVIEW 14 of 18
2. Reduces wellhead back pressure and increases pro-
duction.
3. Small footprint and easy skid-mounting.
4. Automatic control, the protection function is perfect,
realizes unaended and remote control.
5. The form of motion of the piston and cylinder by roll-
ing friction instead of the traditional sliding friction,
and has two high-pressure compression type func-
tions to solve the existing technology of various com-
pressors and pumps of low efficiency, energy con-
sumption, can be used in the need for higher pressure
occasions.
Disadvantages Does not smoke gases containing weak corrosion
3.2. Platform Pressurization Process Effect Analysis
The Xx platform conducted a test run from 18–28 August on wells 2 and 3 to increase
the pressure while suspending bubble row refilling. During this test period, the wellhead
pressure decreased, resulting in increased production from the platform, and no abnormal
gas well production was observed. Subsequently, on 21 October, the platform officially
began pressurizing, this time including three wells simultaneously, while discontinuing
bubble row refilling. After approximately 15 days of operation, wells 2 and 3 were flooded
successively, and gas lift operations were resumed. To maintain continuous production
from the gas wells, a combination of pressurization with bubble drainage and plunger gas
lift techniques was employed. This refined the cooperation between the bubble drainage
and plunger gas lift processes, which allowed for the reduction in the minimum wellhead
pressure to 0.4 MPa under the full load of the booster unit (as shown in Figure 8). So far,
the production has been relatively smooth, and the platform has achieved an increase in
production by 12 to 14 thousand cubic meters per day, effectively achieving the expected
results of the implemented measures.
Figure 8. Change in oil pressure and gas production before and after pressurization of Xx H10 −3
well.
3.3. Platform Pressurization Process Predictive Analysis
Figure 8.
Change in oil pressure and gas production before and after pressurization of
Xx H10 −3 well.
3.3. Platform Pressurization Process Predictive Analysis
If the economic limit production of Xx shale gas well is 2890 m3/day, the minimum
wellhead pressure before boosting is 1.5 Mpa, and the minimum wellhead pressure after
depressurization is 0.9 MPa. According to the relationship between gas reservoir abandon-
ment pressure and cumulative gas production established by the research, the changes of
reservoir abandonment pressure and cumulative gas production (EUR) in well H10
−
2
and well H10
−
3 were calculated in Table 6. Calculations showed that the abandoned
formation pressure in wells H10
−
2 and H10
−
3 decreased from 3.03 MPa and 3.16 MPa to
2.34 MPa and 2.43 MPa, respectively, as a result of the pressure boosting measures, and
the EUR of the two wells increased by 10.33 million cubic meters and 10.43 million cubic
meters, respectively.
Table 6. Comparison of booster measure yield and EUR.
Serial Number Well Number
Before Booster After Pressurization EUR
Incremental/
108m3
Abandoned
Stratigraphic
Pressure/MPa
EUR/108m3
Abandoned
Stratigraphic
Pressure/MPa
EUR/108m3
1 Xx H10 −2 3.03 1.2198 2.34 1.3231 0.1033
2 Xx H10 −3 3.16 1.6269 2.43 1.6312 0.1043
Separations 2023,10, 432 14 of 16
4. Conclusions
This study focused on the development of the Xx shale gas field and proposed a three-
stage pressurization process to address the specific conditions of the field. The primary
pressurization occurred at the central station of the Xx block, followed by secondary
pressurization at the gas gathering station. Finally, small pressure boosting equipment
was installed after the platform separator and in front of the outlet valve group, forming
a three-stage pressurization process. The main objective of this pressurization process
was to lower the wellhead pressure, which, in turn, reduced the critical liquid-carrying
flow rate of gas wells and enhanced their liquid-carrying capacities. By introducing a
compressor, the wellhead pressure could be reduced to 0.4 MPa, resulting in a daily
output of 12,000 to 14,000 cubic meters from the platform. Through the utilization of the
critical liquid-carrying model for shale gas horizontal wells, it has been determined that
reducing the pressure at the wellhead had a positive impact on the critical flow of liquid
carrying. This reduction facilitated the discharge of accumulated fluids from the gas wells,
allowing for improved operational efficiency. This study successfully established an inflow
performance relationship (IPR) curve by analyzing the field test data, demonstrating a
high level of accuracy, with an error value of only 5%. Furthermore, the mass balance
method was applied to estimate the formation pressure of shale gas wells, which exhibited
a strong correlation with the actual values, indicating the reliability of the estimation
process. By calculating the cumulative production based on different IPR curves and
fitting a dynamic production decline model for gas outlet wells, this study revealed the
relationship between the waste pressure of the gas reservoirs and the boost effect on wells
H10
−
2 and H10
−
3. The results showed a significant decrease in the waste formation
pressure of H10
−
2 and H10
−
3 wells from 3.03 MPa and 3.16 MPa to 2.34 MPa and
2.43 MPa, respectively. Additionally, the estimated ultimate recovery (EUR) of these wells
demonstrated a considerable increase of 103.3 million cubic meters and 104.3 million cubic
meters, respectively. Consequently, the implementation of multi-stage pressurization, as
investigated in this study, proved to be an effective approach for enhancing the production
in shale gas fields. This finding holds practical significance for ensuring stable production
and development in the shale gas industry. By achieving lower well waste pressure, the
production time of gas wells can be extended, leading to improved recovery rates in the gas
fields. However, it is important to note that due to the late stage of platform development
and low formation pressure, the pressurized gas wells may not meet the requirements
for continuous liquid carrying. Therefore, drainage gas production processes must still
be maintained to mitigate the risk of flooded wells. If there is still a possibility of fluid
accumulation after pressurization, it is crucial to combine pressurization measures with
drainage techniques, such as bubble drainage or plunger gas lift. To maximize the gas
well capacity, it is necessary to make timely adjustments to the drainage process regime.
This includes coordinating the switch-on and switch-off well regime for platform plunger
gas lift wells. Additionally, the timing of pressurization should be based on the critical
liquid-carrying yield of the gas wells with fluid, and a reasonable interval for pressurization
timing should be analyzed. From the perspectives of formation pressure, cumulative gas
production, gas production, and EUR increment, the reasonable interval of pressurization
timing was explored.
Author Contributions:
Conceptualization, Y.L., J.Y. and M.C.; methodology, Y.L. and L.Z.; validation,
Y.L. and L.Z.; formal analysis, Y.L., J.Y. and L.Y.; writing—original draft, Y.L., M.C. and J.L.; writing—
review and editing, M.C., L.Y., H.P., J.L. and L.Z.; supervision, L.Y. and H.P.; project administration,
Y.L., J.Y. and M.C.; funding acquisition, Y.L. and L.Z. All authors have read and agreed to the
published version of the manuscript.
Separations 2023,10, 432 15 of 16
Funding:
This research was funded by the National Natural Science Foundation of China under
Grants 52325402, 51874335, 52274057, and 52074340; the Major Scientific and Technological Projects
of CNPC under Grant ZD2019-183-008; the Major Scientific and Technological Projects of CNOOC
under Grant CCL2022RCPS0397RSN; the Science and Technology Support Plan for Youth Innovation
of University in Shandong Province under Grant 2019KJH002; and 111 Project under Grant B08028.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
Nomenclature
Gforiginal free gas reserves of the gas reservoir, 104m3
Gmfree gas reserves in the matrix system, m3
Bgi gas volume factor at primordial formation pressure, m3/m3
VLvolume constant, m3/t
P formation pressure, MPa
PLpressure constant, MPa
ρbapparent density of matrix rocks, g/m3
ϕmmatrix system porosity
Bggas volume coefficient at formation pressure P, m3/m3
ρsc natural gas density in the standard state, g/m3
Cffracture system compression coefficient, MPa−1
Cwformation water compression coefficient, MPa−1
Gpcumulative gas production, 104m3
qgsc daily gas production in shale gas wells under standard conditions, 104 m3
psc standard pressure, MPa
Tsc standard temperature, K
S epidermal coefficient
D high-speed non-Darcy coefficient
νf(x)gas flow rate, cm/s
ψequasi-pressure corresponding to the formation pressure of the two
adjacent fracture centerlines (at the choke boundary), (0.1 MP)2/(mPa·s)
ψfquasi-pressure corresponding to the crack pressure at the fracturing
fracture x position, (0.1 MP)2/(mPa·s)
υcrit critical flow rate of gas well discharge, m/s
A tank cross-sectional area, m2
Z gas deviation coefficient under P and T conditions
R universal gas constant, j/(mol·k)
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