Abstract

Acid treatment is an important measure to improve production for horizontal wells of carbonate reservoirs. Acid injection profile of horizontal wells (AIPHWs) is the most critical indicator of the success of the acidification. Currently, most previous works studied AIPHW based on the point source method. However, an inherent singularity exists in the point source solution, and hence, the calculation speed is too slow or the solution does not converge. To solve this problem, a semi-analytical model (coupling the wellbore flow model and reservoir seepage model) by the volumetric source method is presented to determine AIPHW in carbonate reservoirs. In this new coupled model, the permeability heterogeneity, formation contamination, acid-induced wormhole formation, and wellbore pressure drop are all considered. The results of the validations show that the results from the proposed method match well with the model results from the literature. Then, the effects of the acid injection flowrate, acid injection time, and permeability heterogeneity on the AIPHW are studied. According to the sensitivity analysis, we find that the disequilibrium degree of AIPHW becomes stronger as acid injection flowrate increases, acid injection time increases, and permeability heterogeneity coefficient increases. This study provides a guide for the design of horizontal well acidification and the evaluation of acid treatments of horizontal wells in carbonate reservoirs.

References

1.
Nazari
,
R.
,
Bahramian
,
A.
,
Fakhroueian
,
Z.
,
Karimi
,
A.
, and
Arya
,
S.
,
2015
, “
Comparative Study of Using Nanoparticles for Enhanced oil Recovery: Wettability Alteration of Carbonate Rocks
,”
Energy Fuels
,
29
(
4
), pp.
2111
2119
. 10.1021/ef5024719
2.
Rui
,
Z.
,
Wang
,
X.
,
Zhang
,
Z.
,
Lu
,
J.
,
Chen
,
G.
,
Zhou
,
X.
, and
Patil
,
S.
,
2018
, “
A Realistic and Integrated Model for Evaluating Oil Sands Development With Steam Assisted Gravity Drainage Technology in Canada
,”
Appl Energy
,
213
(
3
), pp.
76
91
. 10.1016/j.apenergy.2018.01.015
3.
Huang
,
X.
,
Guo
,
X.
,
Zhou
,
X.
,
Lu
,
X.
,
Shen
,
C.
,
Qi
,
Z.
, and
Li
,
J.
,
2019
, “
Productivity Model for Water-Producing Gas Well in a Dipping Gas Reservoir With an Aquifer Considering Stress-Sensitive Effect
,”
ASME J. Energy Resour. Technol.
,
141
(
2
), p.
022903
. 10.1115/1.4041741
4.
Abdulwahid
,
M. A.
,
Niranjan Kumar
,
I. N.
, and
Dakhil
,
S. F.
,
2014
, “
Influence of Radial Flux Inflow Profile on Pressure Drop of Perforated Horizontal Wellbore
,”
ASME J. Energy Resour. Technol.
,
136
(
4
), p.
042907
. 10.1115/1.4028770
5.
Chen
,
X.
,
Feng
,
Q.
, and
Wang
,
Q.
,
2014
, “
Performance Prediction of Gel Water Shutoff in Horizontal Wells Using a Newly Coupled Reservoir–Wellbore Model
,”
ASME J. Energy Resour. Technol.
,
136
(
2
), p.
022903
. 10.1115/1.4026919
6.
Zhang
,
N.
,
Li
,
H.
,
Zhang
,
Y.
,
Deng
,
Q.
, and
Tan
,
Y.
,
2019
, “
A Numerical Simulation for the Determination of the Shunt Ratio at a T-Junction With Different Branch Angles, Viscosities, and Flow Rates
,”
ASME J. Energy Resour. Technol.
,
141
(
10
), p.
102906
. 10.1115/1.4043635
7.
Adesina
,
F. A.
,
Churchill
,
A.
, and
Olugbenga
,
F.
,
2011
, “
Modeling Productivity Index for Long Horizontal Well
,”
ASME J. Energy Resour. Technol.
,
133
(
3
), p.
033101
. 10.1115/1.4004887
8.
Mishra
,
V.
,
Zhu
,
D.
,
Hill
,
D.
, and
Furui
,
K.
,
2007
, “
An Acid Placement Model for Long Horizontal Wells in Carbonate Reservoirs
,”
European Formation Damage Conference
,
Scheveningen, The Netherlands
,
30 May–1 June
, Paper No. SPE-107780-MS.
9.
Guo
,
T.
,
Li
,
Y.
,
Ding
,
Y.
,
Qu
,
Z.
, and
Gai
,
N.
,
2017
, “
Evaluation of Acid Fracturing Treatments in Shale Formation
,”
Energy Fuels
,
31
(
10
), pp.
10479
10489
. 10.1021/acs.energyfuels.7b01398
10.
Tan
,
Y.
,
Li
,
H.
,
Zhou
,
X.
,
Jiang
,
B.
,
Wang
,
Y.
, and
Zhang
,
N.
,
2018
, “
A Semi-Analytical Model for Predicting Horizontal Well Performances in Fractured gas Reservoirs With Bottom-Water and Different Fracture Intensities
,”
ASME J. Energy Res. Technol.
,
140
(
10
), p.
102905
. 10.1115/1.4040201
11.
Leong
,
V.
,
Ben
,
M.
,
Law
,
M.
,
Foo
,
H.
, and
Tan
,
I.
,
2018
, “
A Comparison and Assessment of the Modelling and Simulation of the Sandstone Matrix Acidizing Process: A Critical Methodology Study
,”
J. Nat. Gas Sci. Eng.
,
57
(
9
), pp.
52
67
. 10.1016/j.jngse.2018.06.044
12.
Chen
,
Y.
,
Sari
,
A.
,
Xie
,
Q.
, and
Saeedi
,
A.
,
2019
, “
Insights Into the Wettability Alteration of CO2-Assisted EOR in Carbonate Reservoirs
,”
J. Mol. Liq.
,
279
(
4
), pp.
420
426
. 10.1016/j.molliq.2019.01.112
13.
Liu
,
P.
,
Xue
,
H.
,
Zhao
,
L.
,
Fu
,
Y.
,
Luo
,
Z.
, and
Qu
,
Z.
,
2015
, “
Analysis and Simulation of Rheological Behavior and Diverting Mechanism of In Situ Self-Diverting Acid
,”
J. Petrol. Sci. Eng.
,
132
(
8
), pp.
39
52
. 10.1016/j.petrol.2015.04.042
14.
Jones
,
A. T.
, and
Davies
,
D. R.
,
1998
, “
Quantifying Acid Placement: The key to Understanding Damage Removal in Horizontal Wells
,”
SPE Prod. Oper.
,
13
(
3
), pp.
163
169
. 10.2118/50975-PA
15.
Eckerfield
,
L.
,
Zhu
,
D.
,
Hill
,
A.
,
Robert
,
J.
, and
Bartko
,
K.
,
1998
, “
Fluid Placement Model for Horizontal Well Stimulation
,”
SPE International Oil and Gas Conference and Exhibition in China
,
Beijing, China
,
Nov. 2–6
, Paper No. SPE-48861-MS.
16.
Gdanski
,
R.
,
2005
, “
Recent Advances in Carbonate Stimulation
,”
International Petroleum Technology Conference
,
Doha, Qatar
,
Nov. 21–23
, Paper No. IPTC-10693-MS.
17.
Li
,
X.
,
Gomaa
,
A.
,
Nino-Penaloza
,
A.
, and
Chaudhary
,
S.
,
2015
, “
Integrated Carbonate Matrix Acidizing Model for Optimal Treatment Design and Distribution in Long Horizontal Wells
,”
SPE Production and Operations Symposium
,
Oklahoma City, OK
,
Mar. 1–5
, Paper No. SPE-173607-MS
.
18.
Zou
,
H.
,
Cui
,
M.
,
Liu
,
H.
,
Liang
,
C.
,
Liu
,
P.
, and
Xue
,
H.
,
2018
, “
An Uneven Acid Injection Technology for Long-Lateral Horizontal Wells in Complex Carbonate Reservoirs: Simulation, Optimization and Practice
,”
SPE Asia Pacific Oil and Gas Conference and Exhibition
,
Brisbane, Australia
,
Oct. 23–25
, Paper No. SPE-191991-MS.
19.
Li
,
H.
,
Tan
,
Y.
,
Jiang
,
B.
,
Wang
,
Y.
, and
Zhang
,
N.
,
2018
, “
A Semi-Analytical Model for Predicting Inflow Profile of Horizontal Wells in Bottom-Water Gas Reservoir
,”
J. Petrol. Sci. Eng.
,
160
(
10
), pp.
351
362
. 10.1016/j.petrol.2017.10.067
20.
Luo
,
W.
,
Li
,
H.
,
Wang
,
Y.
, and
Wang
,
J.
,
2015
, “
A New Semi-Analytical Model for Predicting the Performance of Horizontal Wells Completed by Inflow Control Devices in Bottom-Water Reservoirs
,”
J. Nat. Gas Sci. Eng.
,
27
, pp.
1328
1339
. 10.1016/j.jngse.2015.03.001
21.
Xue
,
H.
,
2017
, “
The Simulation Research of Horizontal Well Efficient Acidizing in Complex Carbonate Reservoir
,”
Dissertation
,
Southwest Petroleum University
,
Chengdu, China
.
22.
Penmatcha
,
V.
, and
Aziz
,
K.
,
1999
, “
A Comprehensive Reservoir/Wellbore Model for Horizontal Wells
,”
SPE J.
,
4
(
3
), pp.
224
234
. 10.2118/57194-PA
23.
Tian
,
F.
,
Wang
,
X.
, and
Xu
,
W.
,
2019
, “
A Semi-Analytical Model for Multiple-Fractured Horizontal Wells in Heterogeneous Gas Reservoirs
,”
J. Petrol. Sci. Eng.
,
183
(
11
), pp.
469
479
.
24.
Wang
,
W.
,
Fan
,
D.
,
Sheng
,
G.
,
Chen
,
Z.
, and
Su
,
Y.
,
2019
, “
A Review of Analytical and Semi-Analytical Fluid Flow Models for Ultra-Tight Hydrocarbon Reservoirs
,”
Fuel
,
256
(
11
), pp.
1
7
.
25.
Wu
,
Y.
,
Cheng
,
L.
,
Huang
,
S.
,
Bai
,
Y.
,
Jia
,
P.
,
Wang
,
S.
,
Xu
,
B.
, and
Chen
,
L.
,
2019
, “
An Approximate Semianalytical Method for Two-Phase Flow Analysis of Liquid-Rich Shale Gas and Tight Light-Oil Wells
,”
J. Petrol. Sci. Eng.
,
176
(
5
), pp.
562
572
. 10.1016/j.petrol.2019.01.085
26.
Zhang
,
F.
, and
Yang
,
D.
,
2018
, “
Effects of Non-Darcy Flow and Penetrating Ratio on Performance of Horizontal Wells With Multiple Fractures in a Tight Formation
,”
ASME J. Energy Res. Technol.
,
140
(
3
), p.
032903
. 10.1115/1.4037903
27.
Tian
,
L.
,
Yang
,
D.
,
Zheng
,
S.
, and
Feng
,
B.
,
2018
, “
Parametric Optimization of Vector Well Patterns for Hydraulically Fractured Horizontal Wells in Tight Sandstone Reservoirs
,”
J. Petrol. Sci. Eng.
,
162
(
3
), pp.
469
479
. 10.1016/j.petrol.2017.12.054
28.
Furui
,
K.
,
Burton
,
C.
,
Burkhead
,
W.
,
Abdelmalek
,
A.
,
Hill
,
D.
, and
Zhu
,
D.
,
2012
, “
A Comprehensive Model of High-Rate Matrix-Acid Stimulation for Long Horizontal Wells in Carbonate Reservoirs
,”
SPE J.
,
17
(
1
), pp.
280
291
. 10.2118/155497-PA
29.
Amini
,
S.
, and
Valkó
,
P.
,
2010
, “
Using Distributed Volumetric Sources to Predict Production From Multiple-Fractured Horizontal Wells Under Non-Darcy-Flow Conditions
,”
SPE J.
,
15
(
1
), pp.
105
115
. 10.2118/120110-PA
30.
Jiang
,
B.
,
Li
,
H.
,
Zhang
,
Y.
,
Wang
,
Y.
,
Wang
,
J.
, and
Patil
,
S.
,
2016
, “
Multiple Fracturing Parameters Optimization for Horizontal Gas Well Using a Novel Hybrid Method
,”
J. Nat. Gas Sci. Eng.
,
34
(
8
), pp.
604
615
. 10.1016/j.jngse.2016.07.023
31.
Wang
,
J.
,
Xu
,
J.
,
Wang
,
Y.
, and
Li
,
H.
,
2016
, “
A New Production Predicting Model of Fractured Horizontal Wells in Dual-Porosity Gas Reservoirs on Non-Darcy Flow Conditions
,”
J. Petrol. Sci. Eng.
,
146
(
10
), pp.
670
676
. 10.1016/j.petrol.2016.06.039
32.
Wang
,
J.
,
Xu
,
W.
,
Wang
,
Y.
,
Li
,
H.
,
Liu
,
T.
, and
Wen
,
X.
,
2018
, “
Productivity of Hydraulically-Fractured Horizontal Wells in Tight Oil Reservoirs Using a Linear Composite Method
,”
J. Petrol. Sci. Eng.
,
164
(
5
), pp.
450
458
. 10.1016/j.petrol.2017.08.071
33.
Ouyang
,
L. B.
,
Arbabi
,
S.
, and
Aziz
,
K.
,
1998
, “
A Single-Phase Wellbore-Flow Model for Horizontal, Vertical, and Slanted Wells
,”
SPE J.
,
3
(
1
), pp.
124
133
. 10.2118/36608-PA
34.
Buijse
,
M.
, and
Glasbergen
,
G.
,
2005
, “
A Semi-Empirical Model to Calculate Wormhole Growth in Carbonate Acidizing
,”
SPE Annual Technical Conference and Exhibition
,
Dallas, TX
,
Oct. 9–12
, Paper No. SPE-96892-MS.
35.
Budek
,
A.
, and
Szymczak
,
P.
,
2012
, “
Network Models of Dissolution of Porous Media
,”
Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys.
,
86
(
2
), pp.
3419
3432
.
36.
Golfier
,
F.
,
Zarcone
,
C.
,
Bazin
,
B.
,
Lenormand
,
R.
,
Lasseux
,
D.
, and
Quintard
,
M.
,
2002
, “
On the Ability of a Darcy-Scale Model to Capture Wormhole Formation During the Dissolution of a Porous Medium
,”
J. Fluid Mech.
,
457
(
10
), pp.
213
254
. 10.1017/S0022112002007735
37.
Kamal
,
M.
,
Buhidma
,
I.
,
Smith
,
S.
, and
Jones
,
W.
,
1993
, “
Pressure-Transient Analysis for a Well With Multiple Horizontal Sections
,”
SPE Annual Technical Conference and Exhibition
,
Houston, TX
,
Oct. 3–6
, Paper No. SPE-26444-MS.
38.
Furui
,
K.
,
Burton
,
C.
,
Burkhead
,
W.
,
Abdelmalek
,
A.
,
Hill
,
D.
,
Zhu
,
D.
, and
Nozaki
,
M.
,
2012
, “
A Comprehensive Model of High-Rate Matrix-Acid Stimulation for Long Horizontal Wells in Carbonate Reservoirs: Part I—Scaling Up Core-Level Acid Wormholing to Field Treatments
,”
SPE J.
,
17
(
1
), pp.
271
279
. 10.2118/134265-PA
39.
Yildiz
,
T.
,
2006
, “
The Impact of Nonuniform Formation Damage on Horizontal Well Performance
,”
SPE International Symposium and Exhibition on Formation Damage Control
,
Lafayette, LA
,
Feb. 15–17
, Paper No. SPE-98123-MS.
40.
Wolfsteiner
,
C.
,
Durlofsky
,
L. J.
, and
Khalid
,
A.
,
2000
, “
Approximate Model for Productivity of Nonconventional Wells in Heterogeneous Reservoirs
,”
SPE J.
,
5
(
2
), pp.
218
226
. 10.2118/62812-PA
41.
Tan
,
Y.
,
Li
,
H.
,
Li
,
Q.
,
Zhou
,
X.
,
Jiang
,
B.
,
Zhang
,
N.
, and
Wang
,
X.
,
2020
, “
Experimental Evaluation Method for Acid Injection Profiles of Horizontal Wells During a Carbonate Acidizing Process
,”
J. Petrol. Sci. Eng.
,
192
(
9
), p.
107245
. 10.1016/j.petrol.2020.107245
42.
Frick
,
T. P.
, and
Economides
,
M. J.
,
1993
, “
Horizontal Well Damage Characterization and Removal
,”
SPE J.
,
26
(
1
), pp.
75
87
.
You do not currently have access to this content.