Abstract
In order to clarify reservoir characteristics and identify pressure build-up characteristics resulting from the offset effect, well test models of bottomhole pressure in the multi-well system of infinite homogeneous and double porosity reservoirs were derived in consideration of effective radius. For a testing well in the model, skin and wellbore storage effect were considered, while for offset wells, skin and wellbore storage were ignored. The exact solution to Bessel function in the Laplace space was derived with Laplace transform method. Two-type curves were plotted for offset wells being online or offline simultaneously. In addition, characteristics of the type curve were analysed and the method for pressure build-up analysis was established. Under both scenarios mentioned above, long-term asymptotic solutions show that the curves of the pressure derivative rise stepwise, and there appears a multi-radial flow stabilization line. The ratio of height of each stabilization line to that of the first stabilization line is the algebraic sum of the dimensionless production combining the testing well and the effective offset wells. In the meanwhile, the curves of pressure derivatives descend under the scenario of the testing well build-up when the offset wells are producing simultaneously.
Copyright 2017, Shaanxi Petroleum Society.
This paper was prepared for presentation at the 2017 International Field Exploration and Development Conference in Chengdu, China, 21–22 September 2017.
This paper was selected for presentation by the IFEDC&IPPTC Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the IFEDC&IPPTC Committee and are subject to correction by the author(s). The material does not necessarily reflect any position of the IFEDC&IPPTC Committee, its members. Papers presented at the Conference are subject to publication review by Professional Committee of Petroleum Engineering of Shaanxi Petroleum Society. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of Shaanxi Petroleum Society is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgement of IFEDC&IPPTC. Contact email: paper@ifedc.org or paper@ipptc.org.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Abbreviations
- \( B \) :
-
Formation-volume factor
- C :
-
WBS coefficient, m3/Pa
- C t :
-
Total compressibility, Pa−1
- h :
-
Net-pay thickness, m
- K :
-
Permeability, m2
- K 0 :
-
Bessel function
- K 1 :
-
Bessel function
- m :
-
\( m = 2\int {\frac{p}{\mu Z}} {\text{d}}p \), MPa2/mPa s
- p i :
-
Initial pressure, Pa
- q j :
-
Rate, m3/s
- \( r_{\text{w}} \) :
-
Wellbore radius, m
- S :
-
Skin factor
- z:
-
Laplace variable
- \( C_{\text{D}} \) :
-
\( C_{\text{D}} = \frac{C}{{2\uppi\varphi hC_{\text{t}} r_{\text{w}}^{2} }} \)
- \( p_{\text{D}} \) :
-
\( p_{{j{\text{D}}}} = \frac{{2\,\uppi\,Kh\left( {p_{\text{i}} - p_{\text{wf}} } \right)}}{{q_{1} \mu B}} \)
- \( q_{{j{\text{D}}}} \) :
-
\( q_{{j{\text{D}}}} = \frac{{q_{j} }}{{q_{1} }} \)
- \( r_{\text{D}} \) :
-
\( r_{\text{D}} = \frac{r}{{r_{\text{w}} {\text{e}}^{ - S} }} \)
- \( t_{\text{D}} \) :
-
Dimensionless time, \( t_{\text{D}} = \frac{Kt}{{\varphi \mu C_{\text{t}} r_{\text{w}}^{2} }} \)
- \( t_{\text{p}} \) :
-
Production time, hour
- t pD :
-
Dimensionless production time
- ΔtD:
-
Dimensionless shut in time
- a:
-
\( \frac{{\lambda C_{\text{D}} }}{{\omega \left( {1 - \omega } \right)}} \)
- \( b \) :
-
\( \frac{{\lambda C_{\text{D}} }}{{\left( {1 - \omega } \right)}} \)
- \( D \) :
-
Diffusivity ratio for composite reservoir, \( D = {{\left( {{k \mathord{\left/ {\vphantom {k {\phi \mu c_{t} }}} \right. \kern-0pt} {\phi \mu c_{t} }}} \right)_{2} } \mathord{\left/ {\vphantom {{\left( {{k \mathord{\left/ {\vphantom {k {\phi \mu c_{t} }}} \right. \kern-0pt} {\phi \mu c_{t} }}} \right)_{2} } {\left( {{k \mathord{\left/ {\vphantom {k {\phi \mu c_{t} }}} \right. \kern-0pt} {\phi \mu c_{t} }}} \right)_{1} }}} \right. \kern-0pt} {\left( {{k \mathord{\left/ {\vphantom {k {\phi \mu c_{t} }}} \right. \kern-0pt} {\phi \mu c_{t} }}} \right)_{1} }} \)
- \( D \) :
-
Non-Darcy flow coefficient
- \( M \) :
-
Mobility ratio for composite reservoir, \( M = {{\left( {{k \mathord{\left/ {\vphantom {k \mu }} \right. \kern-0pt} \mu }} \right)_{2} } \mathord{\left/ {\vphantom {{\left( {{k \mathord{\left/ {\vphantom {k \mu }} \right. \kern-0pt} \mu }} \right)_{2} } {\left( {{k \mathord{\left/ {\vphantom {k \mu }} \right. \kern-0pt} \mu }} \right)_{1} }}} \right. \kern-0pt} {\left( {{k \mathord{\left/ {\vphantom {k \mu }} \right. \kern-0pt} \mu }} \right)_{1} }} \)
- \( N \) :
-
Number of wells
- \( r \) :
-
Distance from the well test wellbore, m
- \( R_{i} \) :
-
Outer radius of inner zone annulus in radial-composite model, m
- \( t \) :
-
Time, h
- \( \Delta t \) :
-
Shut in time, h
- \( \phi \) :
-
Porosity
- \( \lambda \) :
-
Interporosity flow coefficient
- \( \mu \) :
-
Viscosity, cp
- \( \omega \) :
-
Storativity ratio
- \( {\text{D}} \) :
-
Dimensionless variable
- \( {\text{f}} \) :
-
Fracture
- \( {\text{m}} \) :
-
Matrix
- \( {\text{j}} \) :
-
Index
- \( {\text{w}} \) :
-
Wellbore conditions
- \( {\text{wf}} \) :
-
Flowing wellbore conditions
- \( {\text{ws}} \) :
-
Shut in wellbore conditions
References
Spivey JP, Lee WJ (2013) Applied well test interpretation. Society of Petroleum Engineers, Richardson, pp 1–30
Sun H (2015) Advanced production decline analysis and application. Gulf Professional Publishing, Oxford, pp 263–290
Lin J, Liu W, Chen Q (1993) Pressure buildup analysis for a well in a pressure-maintained system. Well Test 2(4):51–58
Lin J, Liu W, Chen Q (1996) Application of the well test analysis theory to a multiwell water flooding system. Pet Explor Dev 23(3):58–63
Onur M, Serra KV, Reynolds AC (1991) Analysis of pressure buildup data from a well in a multiwell system. SPE Formation Eval 6(1):101–110
Dong J, Zhai Y, Yang J, Zhao C (1999) Determination of injection production ratio size by type curve analysis. In: Paper SPE 57320 presented at the SPE Asia Pacific improved oil recovery conference, Kuala Lumpur, Malaysia, 25–26 Oct 1999. http://dx.doi.org/10.2118/57320-MS
Lin J, Yang H (2005) Pressure buildup analysis for a well in a closed, bounded multiwell reservoir. Chin J Chem Eng 13(4):441–450
Lin J, Yang H (2005) Analysis of two phase flow pressure buildup data from well in an infinite multiwell reservoir. J Hydrodynam Series B 17(4):489–497
Lin J, Yang H (2007) Analysis of well test data in a multiwell reservoir with water injection. In: Paper SPE 110349 presented at SPE annual technical conference and exhibition, Anaheim, California, USA, 11–14 Nov 2007. http://dx.doi.org/10.2118/110349-MS
Li X, Luo J (2009) Application of well test analysis model influenced by neighbouring wells. Well Test 18(2):5–7,11
Liu Y, Chen H, Zhang D, Zhou R, Liu Y (2002) Numerical well test analysis for oil wells in condition of adjacent wells influences. Well Test 11(5):4–7
Zhang L, Xiang Z, Li Y, Li X, Liu Q (2006) The interwell interference effect on numerical well test curve of oil-water phase. J Hydrodynam Series A 21(6):805–810
Marhaendrajana T, Kaczorowski NJ, Blasingame TA (1999) Analysis and interpretation of well test performance at Arun field, Indonesia. In: Paper SPE 56487 presented at the SPE annual technical conference and exhibition, Houston, TX, USA, 3–7 Oct 1999. http://dx.doi.org/10.2118/56487-MS
Qiguo L, Yanli C, Liehui Z, Wei W (2006) Study for disturbing test model with the well opening and its interpreting method. Well Testing 15(1):10–12
Zeng T, Jia Y, Wang H, Tang D, Wu Z (2006) Well testing model for finite multiwell system and type curve analysis. Xinjiang Pet Geol 27(1):86–88
Liu Y, Jia Y, Kang Y, Huo J (2008) Finite multiwell testing model for heavy oil thermal recovery under consideration heat loss. Drill Prod Technol 31(1):79–81
Deng Q, Nie R, Jia Y, Wang X, Chen Y, Xiong Y (2015) A new method of pressure buildup analysis for a well in a multiwell reservoir. In: Paper SPE 175866 presented at SPE North Africa technical conference and exhibition, Cairo, Egypt, 14–16 Sept 2015. http://dx.doi.org/10.2118/175866-MS
Stehfest H (1970) Algorithm 368: numerical inversion of Laplace transforms. Commun ACM 13(1):47–49
Abramowitz M, Stegun IA (1966) Handbook of mathematical functions. Dover Publications, New York, pp 374–375
Bourdet D, Whittle TM, Douglas AA, Pirard YM (1983) A new set of type curves simplifies well test analysis. World Oil 196(6):95–106
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Sun, H., Cui, Y., Wang, X., Zhang, J., Cao, W. (2019). Build-up Analysis of Multi-Well System in Naturally Fractured HTHP Gas Reservoirs. In: Qu, Z., Lin, J. (eds) Proceedings of the International Field Exploration and Development Conference 2017. Springer Series in Geomechanics and Geoengineering. Springer, Singapore. https://doi.org/10.1007/978-981-10-7560-5_166
Download citation
DOI: https://doi.org/10.1007/978-981-10-7560-5_166
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-7559-9
Online ISBN: 978-981-10-7560-5
eBook Packages: EngineeringEngineering (R0)