Skip to main content
SpringerLink
Log in

Well Interference Model of Multi-fractured Horizontal Wells Considering Non-uniform Fracture Conductivity in Fractured Porous Media

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

Strong interference has been observed due to small well spacing in the well pad of gas reservoirs, and the fracture properties significantly impact the interference degree. However, current well-test model hardly considers the interference among different multi-fractured horizontal wells (MFHWs) in the well pad and the fracture conductivity are assumed to be the same for different fractures. It would cause erroneous interpretation results for well interference and fracture properties using previous models. Thus, this paper presents a semi-analytical well interference model to better describe flow and mass transfer in fractured porous media by incorporating non-uniform fracture conductivity and interference from adjacent wells. The fractures contain two segments which covers difference values of half-length, production and conductivity. Eight flow regimes can be seen on the interference type curves, and interference can be observed obviously on pressure and its derivative curves during multi-well interference flow. Sensitivity analysis is conducted to analyze the effect of well spacing, fracture conductivity and production distribution on the pressure response. Finally, field application indicates that the proposed model can be used to analyze the well interference among MFHWs in fractured reservoirs, which further demonstrate the accuracy and advantages of the established interference-test model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Abbreviations

ψ :

Pressure of gas reservoir, pa

x, y, z :

Cartesian coordinates

z* :

Cartesian coordinates considering permeability anisotropy

η :

Diffusivity, m2/s

t :

Time, s

k h :

Horizontal permeability, m2

k v :

Vertical permeability, m2

η h :

Horizontal diffusivity, m2/s

φ :

Porosity

μ :

Viscosity, Pa∙s

C t :

Total compressibility, Pa−1

η v :

Vertical diffusivity, m2/s

x f :

Fracture half-length, m

x f1 :

Length of the 1st segment of fracture, m

x f2 :

Length of the 2nd segment of fracture, m

B :

Fluid formation volume factor

q fl :

Rates of the 1st segment of fracture, m3/s

q f2 :

Rates of the 2nd segment of fracture, m3/s

h :

Formation thickness, m

q fil :

Rates of the 1st segment of the ith fracture, m3/s

q fi2 :

Rates of the 2nd segment of the ith fracture, m3/s

x fi1 :

Length of the 1st segment of the ith fracture, m

x fi2 :

Length of the 2nd segment of the ith fracture, m

S fi1 :

Skin factor of the 1st segment of the ith fracture

S fi2 :

Skin factor of the 2nd segment of the ith fracture

k fi1 :

Permeability of the 1st segment of the ith fracture, m2

k fi2 :

Permeability of the 2nd segment of the ith fracture, m2

w fi1 :

Fracture width of the 1st segment of the ith fracture, m

w fi2 :

Fracture width of the 2nd segment of the ith fracture, m

L :

Length of horizontal well, m

x iD :

Dimensionless coordinate of the ith fracture

q filD :

Dimensionless rates of the 1st segment of the ith fracture

q fi2D :

Dimensionless rates of the 2nd segment of the ith fracture

x fi1D :

Dimensionless length of the 1st segment of the ith fracture

x fi2D :

Dimensionless length of the 2nd segment of the ith fracture

C fDi1 :

Dimensionless conductivity of the 1st segment of the ith fracture.

C fDi2 :

Dimensionless conductivity of the 2nd segment of the ith fracture.

q obs :

Total gas rates of the observation well, m3/s

q fj Pro :

Gas rates of the jth fracture in adjacent well, m3/s

q fj Pro D :

Dimensionless gas rates of the jth fracture in adjacent well

x f Pro :

Half-length in adjacent well, m

x f Pro D :

Dimensionless half-length in adjacent well

x wj Pro , y wj Pro :

Coordinate of the jth fracture in adjacent well

x wj Pro D , y wj Pro D :

Dimensionless coordinate of the jth fracture in adjacent well.

x obs D , y obs D :

Dimensionless coordinates of the observation well

S :

Skin effect

C D :

Dimensionless well storage coefficient

u :

Laplace variables

References

  • Al-Rbeawi, S., Owayed, J.: Pressure-rate convolution and deconvolution response for fractured conventional and unconventional reservoirs using new decline rate model. Petroleum 7(2), 241–242 (2021). https://doi.org/10.1016/j.petlm.2018.10.001

    Article  Google Scholar 

  • Chen, Z., Liao, X., Yu, W., Sepehrnoori, K.: Pressure-transient behaviors of wells in fractured reservoirs with natural-and hydraulic-fracture networks. SPE J. 24(01), 375–394 (2018). https://doi.org/10.2118/194013-PA

    Article  Google Scholar 

  • Chen, Z., Shi, L.: Parameter estimations of complex fracture networks using pressure transient analysis in fracturing-shutting data from shale oil wells. Paper presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Virtual (2020). https://doi.org/10.15530/urtec-2020-1093

  • Dawood, M.A., Aziz, A.A., Rahim, Z., Al-Omair, A., Rahman, A.: Well testing analysis of horizontal open hole multistage fracturing wells in tight gas condensate reservoirs in Saudi Arabia to characterize production performance and fracture behavior: case studies. Paper presented at the SPE Middle East Oil & Gas Show and Conference, Manama, Bahrain (2015). https://doi.org/10.2118/172697-MS

  • Dong, P., Chen, Z., Liao, X., Yu, W.: A deep reinforcement learning (DRL) based approach for well-testing interpretation to evaluate reservoir parameters. Pet. Sci. 19, 264–278 (2022). https://doi.org/10.1016/j.petsci.2021.09.046

    Article  Google Scholar 

  • Dong, J., Zhai, Y., Yang, J., Zhao, C.: Determination of injection-production ratio size by type-curve analysis. Paper presented at the SPE Asia Pacific Improved Oil Recovery Conference, Kuala Lumpur, Malaysia (1999). https://doi.org/10.2118/57320-MS

  • Duhamel, J.M.C.: Éléments de calcul infinitésimal. Mallet-Bachelier, Paris (1860)

    Google Scholar 

  • Giegbefumwen, P.U., Adewole, E.S.: Interference test pressures of a reservoir with vertical and horizontal wells. Paper presented at the SPE Nigeria Annual International Conference and Exhibition, Lagos, Nigeria (2015). https://doi.org/10.2118/178338-MS

  • Giger, F.M.: Horizontal wells production techniques in heterogeneous reservoirs. Paper presented at the Middle East Oil Technical Conference and Exhibition, Bahrain (1985). https://doi.org/10.2118/13710-MS

  • Gringarten, A.C., Ramey, H.J.: The use of source and Green’s functions in solving unsteady-flow problems in reservoirs. Soc. Petrol. Eng. J. 13(05), 285–296 (1973). https://doi.org/10.2118/3818-PA

    Article  Google Scholar 

  • He, Y., Cheng, S., Qin, J., Chai, Z., Wang, Y., Patil, S., Li, M., Yu, H.: Analytical interference testing analysis of multi-segment horizontal well. J. Petrol. Sci. Eng. 171, 919–927 (2018). https://doi.org/10.1016/j.petrol.2018.08.019

    Article  Google Scholar 

  • Huang, Y., Cheng, S., Yu, H., He, Y., Lin, B., Feng, N.: A semianalytical approach to estimate fracture closure and formation damage of vertically fractured wells in tight gas reservoir. J Pet Sci Eng 150, 85–90 (2017). https://doi.org/10.1016/j.petrol.2016.10.049

    Article  Google Scholar 

  • Huang, L., Liu, X., Xiong, J., Liang, L.: Experimental on the pore structure characteristics of Longmaxi Formation shale in southern Sichuan Basin, China. Petroleum 7(2), 135–141 (2021). https://doi.org/10.1016/j.petlm.2020.07.006

    Article  Google Scholar 

  • Ji, Q., Vernon, G., Mata, J., Klier, S., Perry, M., Garcia, A., Coenen, E.: Joint pressure and production analysis to understand inter-and intra-zone well interference: A midland basin case study. Paper presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition, Virtual (2021). https://doi.org/10.2118/204179-MS

  • Kasumov, M., Liu, Y., Farthing, A., Miller, M., Attar, A.E.: Bakken unconventional well production interference test analysis. Paper presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Houston, Texas (2022). https://doi.org/10.15530/urtec-2022-3715180

  • Li, J., Li, B., Cheng, Q., Gao, Z.: Characterization of the fracture compressibility and its permeability for shale under the effects of proppant embedment and compaction: a preliminary study. Pet. Sci. 19, 1125–1138 (2022). https://doi.org/10.1016/j.petsci.2021.12.021

    Article  Google Scholar 

  • Lin, J., Yang, H.: Analysis of well-test data from a well in a multiwell reservoir with water injection. Paper presented at the SPE Annual Technical Conference and Exhibition, Anaheim, California (2007a). https://doi.org/10.2118/110349-MS

  • Lin, J., Yang, H.: Analysis of two-phase flow pressure buildup data from well in an infinite multiwell reservoir. J. Hydrodyn. Ser. B 17(4), 489–497 (2005)

    Google Scholar 

  • Lin, J., Yang, H.: Pressure buildup analysis using type curves for a well in a pressure-maintained system. Chin. J. Chem. Eng. 15(1), 6–11 (2007b). https://doi.org/10.1016/S1004-9541(07)60026-3

    Article  Google Scholar 

  • Lu, J., Cunha, L.B., Lu, T.: New solutions for well test analysis of horizontal wells. Paper presented at the SPE International Thermal Operations and Heavy Oil Symposium and International Horizontal Well Technology Conference, Alberta, Canada (2002). https://doi.org/10.2118/78972-MS

  • Luo, L., Cheng, S., John, L.: Integrating multiple pressure build-up tests to characterize the behavior of dynamically-closed fractures. Paper presented at the SPE Western Regional Meeting, San Jose, California (2019). https://doi.org/10.2118/195308-MS

  • Malekzadeh, D., Tiab, D.: Interference testing of horizontal wells. Paper presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas (1991). https://doi.org/10.2118/22733-MS

  • Malekzadeh, D.: Deviation of horizontal well interference testing from the exponential integral solution. Paper presented at the SPE Rocky Mountain Regional Meeting, Casper, Wyoming (1992). https://doi.org/10.2118/24372-MS

  • Meng, M., Chen, Z., Liao, X., Wang, J., Shi, L.: A well-testing method for parameter evaluation of multiple fractured horizontal wells with non-uniform fractures in shale oil reservoirs. Adv Geo-Energy Res 4(2), 187–198 (2020). https://doi.org/10.26804/ager.2020.02.07

    Article  Google Scholar 

  • Miranda, C., Cipolla, C., Murray, M.: Analysis of well interference tests in the Bakken Shale, a fully communicated system. Paper presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Houston, Texas (2022). https://doi.org/10.15530/urtec-2022-3717749

  • Newman, A.B.: Heating and cooling rectangular and cylindrical solids. Ind. Eng. Chem. 28(5), 545–548 (1936). https://doi.org/10.1021/ie50317a010

    Article  Google Scholar 

  • Qin, J., Cheng, S., He, Y., Wang, Y., Feng, D., Qin, G., Yu, H.: A novel well-testing model to analyze production distribution of multi-stage fractured horizontal well. J. Nat. Gas Sci. Eng. 59, 237–249 (2018). https://doi.org/10.1016/j.jngse.2018.09.004

    Article  Google Scholar 

  • Qin, J., Cheng, S., Li, P., He, Y., Lu, X., Yu, H.: Interference well-test model for vertical well with double-segment fracture in a multi-well system. J. Petrol. Sci. Eng. 183, 106412 (2019). https://doi.org/10.1016/j.petrol.2019.106412

    Article  Google Scholar 

  • Raghavan, R.S., Chen, C.C., Agarwal, B.: An analysis of horizontal wells intercepted by multiple fractures. SPE J. 2(03), 235–245 (1997). https://doi.org/10.2118/27652-PA

    Article  Google Scholar 

  • Sheng, J.J.: Horizontal well performance evaluation and well test analysis-a case study. Paper presented at the International Oil Conference and Exhibition in Mexico, Veracruz, Mexico (2007). https://doi.org/10.2118/102666-MS

  • Stehfest, H.: Numerical inversion of Laplace transforms. Commun. ACM 13(1), 47–49 (1970)

    Article  Google Scholar 

  • Tang, X., Chen, Z., Chu, H., Liao, X., Chen, H., Zhang, J.: Well testing interpretation for horizontal well with hydraulic fractures and interconnected micro-fractures. J. Petrol. Sci. Eng. 179, 546–557 (2019). https://doi.org/10.1016/j.petrol.2019.04.074

    Article  Google Scholar 

  • Thompson, L., Reynolds, A.: Analysis of variable-rate well-test pressure data using Duhamel's principle. SPE Form. Eval. 1(05), 453–469 (1986). https://doi.org/10.2118/13080-PA

  • Tiab, D.: Analysis of pressure and pressure derivative without type-curve matching: vertically fractured wells in closed systems. J. Petrol. Sci. Eng. 11(4), 323–333 (1994). https://doi.org/10.1016/0920-4105(94)90050-7

    Article  Google Scholar 

  • Tiab, D.: Analysis of pressure derivative data of hydraulically fractured wells by the Tiab’s direct synthesis technique. J. Petrol. Sci. Eng. 49(1–2), 1–21 (2005). https://doi.org/10.1016/j.petrol.2005.07.001

    Article  Google Scholar 

  • Tiab, D.: Analysis of pressure and pressure derivative without using type-curve matching: I-skin and wellbore storage. SPE Production Operations Symposium. 12, 17–181 (1993). https://doi.org/10.2118/25426-MS

  • Van Everdingen, A.F.: The skin effect and its influence on the productive capacity of a well. J. Petrol. Technol. 5(06), 171–176 (1953). https://doi.org/10.2118/203-G

    Article  Google Scholar 

  • Vincent, P., Eric P.: A new methodology for naturally fractured reservoir characterization: Use of multi-well interference tests interpretation. Paper presented at the SPE Europec, Virtual (2020). https://doi.org/10.2118/200622-MS

  • Volz, R., Pinto, E., Soto, O., Jones, J.R.: An approach to practical pressure transient testing of multiple fracture completed horizontal wells in low permeability reservoirs. Paper presented at the SPE Unconventional Gas Conference and Exhibition, Muscat, Oman (2013). https://doi.org/10.2118/163983-MS

  • Xie, W., Yang, H., Wu, J., Feng, X., Zhang, X., Zheng, M.: Two-phase flow model and well testing analysis for multi-stage fractured horizontal well in shale gas reservoirs. Paper presented at the SPE Argentina Exploration and Production of Unconventional Resources Symposium, Aires, Argentina (2016). https://doi.org/10.2118/180995-MS

  • Xiong, J., Liu, K., Shi, C., Liu, X., Huang, L.: Logging prediction and evaluation of fracture toughness for the shales in the Longmaxi Formation, Southern Sichuan Basin. Petroleum. 7(3), 254–262 (2021). https://doi.org/10.1016/j.petlm.2020.10.003

    Article  Google Scholar 

  • Xu, Y.: Implementation and application of the embedded discrete fracture model (EDFM) for reservoir simulation in fractured reservoirs. (2015). http://hdl.handle.net/2152/34216

  • Yan, J., Shi, L., Zheng, R., Wang, S., Shi, W., Zhang, Y., Li, D.: Development and application of the modern production decline analysis method in consideration of partial closure of hydraulic fracture. Oil Drill. Prod. Technol. 40(06), 787–793 (2018)

    Google Scholar 

  • Zeng, H., Jin, Y., Qu, H., Lu, Y.: Experimental investigation and correlations for proppant distribution in narrow fractures of deep shale gas reservoirs. Pet. Sci. 19, 619–628 (2022). https://doi.org/10.1016/j.petsci.2021.10.019

    Article  Google Scholar 

  • Zerzar, A., Bettam, Y.: Interpretation of multiple hydraulically fractured horizontal wells in closed systems. Paper presented at the Canadian International Petroleum Conference, Alberta (2004). https://doi.org/10.13639/j.odpt.2018.06.018

Download references

Acknowledgements

The authors are grateful to the financial support from China Postdoctoral Science Foundation (2022M712645) and Opening Fund of Key Laboratory of Enhanced Oil Recovery (Northeast Petroleum University), Ministry of Education (NEPU-EOR-2021-03), and we would also like to acknowledge KAPPA Engineering for providing the Saphir for this study.

Author information

Authors and Affiliations

  1. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, 610500, Sichuan, China

    Jiazheng Qin, Jichang Long, Yong Tang & Zhiyue He

Authors
  1. Jiazheng Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jichang Long
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yong Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhiyue He
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yong Tang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qin, J., Long, J., Tang, Y. et al. Well Interference Model of Multi-fractured Horizontal Wells Considering Non-uniform Fracture Conductivity in Fractured Porous Media. Transp Porous Med 149, 229–250 (2023). https://doi.org/10.1007/s11242-022-01891-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-022-01891-4

Keywords

Search

Navigation