ISSN 0253-2778

CN 34-1054/N

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Open AccessOpen Access JUSTC Original Paper

Application of response surface method and BFGS algorithm in well test analysis

  • School of Mathematics, Hefei University of Technology, Hefei 236009, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2018.05.009
  • Received Date: 26 June 2017
  • Accepted Date: 07 December 2017
  • Rev Recd Date: 07 December 2017
  • Publish Date: 31 May 2018
    Abstract

  • Abstract

    Well test analysis is a typical inverse problem that analyzes the formation and wellbore parameters using the time-varying data of the bottom hole pressure measured during shut-in. Based on the response surface method， a new method for automatically evaluating parameters was presented to solve the numerical well test interpretation. Select the uncertain parameters and their scope， the experimental examples were determined， and then the polynomial approximation function was obtained by matching method， that is， constructing the response surface model. Using the response surface model， the objective function of the deviation between the calculated value and the actual observation value was constructed. The minimum value of the objective function was obtained by using the BFGS algorithm and the Latin hypercube sampling to obtain the uncertain parameter value. The numerical examples show that the method can effectively match the bottom hole pressure and the pressure derivative， and thus has a good potential for application.

    Abstract

    Well test analysis is a typical inverse problem that analyzes the formation and wellbore parameters using the time-varying data of the bottom hole pressure measured during shut-in. Based on the response surface method， a new method for automatically evaluating parameters was presented to solve the numerical well test interpretation. Select the uncertain parameters and their scope， the experimental examples were determined， and then the polynomial approximation function was obtained by matching method， that is， constructing the response surface model. Using the response surface model， the objective function of the deviation between the calculated value and the actual observation value was constructed. The minimum value of the objective function was obtained by using the BFGS algorithm and the Latin hypercube sampling to obtain the uncertain parameter value. The numerical examples show that the method can effectively match the bottom hole pressure and the pressure derivative， and thus has a good potential for application.
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    • References(22)
  • [1]
    LI Daolun，ZHA Wenshu，LIU Shufeng，et al.Pressure transient analysis of low permeability reservoir with pseudo threshold pressure gradient[J].J Petrol Science and Engineering，2016，147: 308-316.
    [2]
    LI Daolun，ZHANG Longjun，LU Detang.Effect of distinguishing apparent permeability on flowing gas composition，composition change and composition derivative in tight- and shale-gas reservoir[J].J Petrol Science and Engineering，2015，128: 107-114.
    [3]
    李道伦，查文舒.数值试井理论与方法[M].北京：石油工业出版社，2013.
    [4]
    OLIVER D S，CHEN Y.Recent progress on reservoir history matching: A review[J].Computational Geosciences，2011，15(1): 185-221.
    [5]
    闫霞，张凯，姚军，等.油藏自动历史拟合方法研究现状与展望[J].油气地质与采收率，2010，17(4): 69-73.
    YAN Xia，ZHANG Kai，YAO Jun，et al.Review on automatic history matching methods for reservoir simulation[J].Petroleum Geology and Recovery Efficiency，2010，17(4): 69-73.
    [6]
    张凯，路然然，周文胜，等.无梯度多参数自动历史拟合方法[J].中国石油大学学报(自然科学版)，2014，38(5): 109-115.
    ZHANG Kai，LU Ranran，ZHOU Wensheng，et al.Multi-parameter gradient-free automatic history matching method[J].Journal of China University of Petroleum (Edition of Natural Science)，2014，38(5): 109-115.
    [7]
    KHURI A I，MUKHOPADHYAY S.Response surface methodology[J].Wiley Interdisciplinary Reviews: Computational Statistics，2010，2(2): 128-149.
    [8]
    DEJEAN J P，BLANC G.Managing uncertainties on production predictions using integrated statistical methods[C]// SPE Annual Technical Conference and Exhibition.Houston，Texas: Society of Petroleum Engineers，1999.
    [9]
    MANCEAU E，MEZGHANI M，ZABALZA-MEZGHANI I，et al.Combination of experimental design and joint modeling methods for quantifying the risk associated with deterministic and stochastic uncertainties: An integrated test study[C]// SPE Annual Technical Conference and Exhibition.New Orleans，Louisiana: Society of Petroleum Engineers，2001.
    [10]
    DEHGHAN MONFARED A，HELALIZADEH A，PARVIZI H.Automatic history matching using the integration of response surface modeling with a genetic algorithm[J].Petroleum Science and Technology，2012，30(4): 360-374.
    [11]
    BERTOLINI A C，SCHIOZER D J.Influence of the objective function in the history matching process[J].Journal of Petroleum Science and Engineering，2011，78(1): 32-41.
    [12]
    THOMAS L K，HELLUMS L J，REHEIS G M.A nonlinear automatic history matching technique for reservoir simulation models[J].Society of Petroleum Engineers Journal，1972，12(6): 508-514.
    [13]
    CHEN W H，GAVALAS G R，SEINFELD J H，et al.A new algorithm for automatic history matching[J].Society of Petroleum Engineers Journal，1974，14(6): 593-608.
    [14]
    KOLDA T G，O’LEARY D P，NAZARETH L.BFGS with update skipping and varying memory[J].SIAM Journal on Optimization，1998，8(4): 1060-1083.
    [15]
    ZHANG F，REYNOLDS A C.Optimization algorithms for automatic history matching of production data[C]// ECMOR VIII-8th European Conference on the Mathematics of Oil Recovery.Houten，The Netherlands: European Association of Geoscientists & Engineers，2002.
    [16]
    OUENES A，BREFORT B，MEUNIER G，et al.A new algorithm for automatic history matching: Application of simulated annealing method (SAM) to reservoir inverse modeling[R].Houston，Texas: Society of Petroleum Engineers，1993.
    [17]
    GOMEZ S，GOSSELIN O，BARKER J W.Gradient-based history-matching with a global optimization method[C]// SPE Annual Technical Conference and Exhibition.Houston，Texas: Society of Petroleum Engineers，1999.
    [18]
    XAVIER C R，DOS SANTOS E P，DA FONSECA VIEIRA V，et al.Genetic algorithm for the history matching problem[J].Procedia Computer Science，2013，18: 946-955.
    [19]
    ZHANG X，HOU J，WANG D，et al.An automatic history matching method of reservoir numerical simulation based on improved genetic algorithm[J].Procedia Engineering，2012，29: 3924-3928.
    [20]
    闫术，李道伦，王磊.基于多井试井解释的数值试井方法及其应用[J].油气井测试，2013,22(1): 27-31.
    YAN Shu，LI Daolun，WANG Lei.Method of multi well test and its application[J].Well Testing，2013，22(1):27-31.
    [21]
    IMAN R L.Latin hypercube sampling[J].Encyclopedia of Quantitative Risk Analysis and Assessment，2008: DOI: 10.1002/9780470061596.risk0299.
    [22]
    MONFARED A D，HELALIZADEH A，PARVIZI H，et al.A global optimization technique using gradient information for history matching[J].Energy Sources，Part A: Recovery，Utilization，and Environmental Effects，2014，36(13): 1414-1428.)
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    [1]
    LI Daolun，ZHA Wenshu，LIU Shufeng，et al.Pressure transient analysis of low permeability reservoir with pseudo threshold pressure gradient[J].J Petrol Science and Engineering，2016，147: 308-316.
    [2]
    LI Daolun，ZHANG Longjun，LU Detang.Effect of distinguishing apparent permeability on flowing gas composition，composition change and composition derivative in tight- and shale-gas reservoir[J].J Petrol Science and Engineering，2015，128: 107-114.
    [3]
    李道伦，查文舒.数值试井理论与方法[M].北京：石油工业出版社，2013.
    [4]
    OLIVER D S，CHEN Y.Recent progress on reservoir history matching: A review[J].Computational Geosciences，2011，15(1): 185-221.
    [5]
    闫霞，张凯，姚军，等.油藏自动历史拟合方法研究现状与展望[J].油气地质与采收率，2010，17(4): 69-73.
    YAN Xia，ZHANG Kai，YAO Jun，et al.Review on automatic history matching methods for reservoir simulation[J].Petroleum Geology and Recovery Efficiency，2010，17(4): 69-73.
    [6]
    张凯，路然然，周文胜，等.无梯度多参数自动历史拟合方法[J].中国石油大学学报(自然科学版)，2014，38(5): 109-115.
    ZHANG Kai，LU Ranran，ZHOU Wensheng，et al.Multi-parameter gradient-free automatic history matching method[J].Journal of China University of Petroleum (Edition of Natural Science)，2014，38(5): 109-115.
    [7]
    KHURI A I，MUKHOPADHYAY S.Response surface methodology[J].Wiley Interdisciplinary Reviews: Computational Statistics，2010，2(2): 128-149.
    [8]
    DEJEAN J P，BLANC G.Managing uncertainties on production predictions using integrated statistical methods[C]// SPE Annual Technical Conference and Exhibition.Houston，Texas: Society of Petroleum Engineers，1999.
    [9]
    MANCEAU E，MEZGHANI M，ZABALZA-MEZGHANI I，et al.Combination of experimental design and joint modeling methods for quantifying the risk associated with deterministic and stochastic uncertainties: An integrated test study[C]// SPE Annual Technical Conference and Exhibition.New Orleans，Louisiana: Society of Petroleum Engineers，2001.
    [10]
    DEHGHAN MONFARED A，HELALIZADEH A，PARVIZI H.Automatic history matching using the integration of response surface modeling with a genetic algorithm[J].Petroleum Science and Technology，2012，30(4): 360-374.
    [11]
    BERTOLINI A C，SCHIOZER D J.Influence of the objective function in the history matching process[J].Journal of Petroleum Science and Engineering，2011，78(1): 32-41.
    [12]
    THOMAS L K，HELLUMS L J，REHEIS G M.A nonlinear automatic history matching technique for reservoir simulation models[J].Society of Petroleum Engineers Journal，1972，12(6): 508-514.
    [13]
    CHEN W H，GAVALAS G R，SEINFELD J H，et al.A new algorithm for automatic history matching[J].Society of Petroleum Engineers Journal，1974，14(6): 593-608.
    [14]
    KOLDA T G，O’LEARY D P，NAZARETH L.BFGS with update skipping and varying memory[J].SIAM Journal on Optimization，1998，8(4): 1060-1083.
    [15]
    ZHANG F，REYNOLDS A C.Optimization algorithms for automatic history matching of production data[C]// ECMOR VIII-8th European Conference on the Mathematics of Oil Recovery.Houten，The Netherlands: European Association of Geoscientists & Engineers，2002.
    [16]
    OUENES A，BREFORT B，MEUNIER G，et al.A new algorithm for automatic history matching: Application of simulated annealing method (SAM) to reservoir inverse modeling[R].Houston，Texas: Society of Petroleum Engineers，1993.
    [17]
    GOMEZ S，GOSSELIN O，BARKER J W.Gradient-based history-matching with a global optimization method[C]// SPE Annual Technical Conference and Exhibition.Houston，Texas: Society of Petroleum Engineers，1999.
    [18]
    XAVIER C R，DOS SANTOS E P，DA FONSECA VIEIRA V，et al.Genetic algorithm for the history matching problem[J].Procedia Computer Science，2013，18: 946-955.
    [19]
    ZHANG X，HOU J，WANG D，et al.An automatic history matching method of reservoir numerical simulation based on improved genetic algorithm[J].Procedia Engineering，2012，29: 3924-3928.
    [20]
    闫术，李道伦，王磊.基于多井试井解释的数值试井方法及其应用[J].油气井测试，2013,22(1): 27-31.
    YAN Shu，LI Daolun，WANG Lei.Method of multi well test and its application[J].Well Testing，2013，22(1):27-31.
    [21]
    IMAN R L.Latin hypercube sampling[J].Encyclopedia of Quantitative Risk Analysis and Assessment，2008: DOI: 10.1002/9780470061596.risk0299.
    [22]
    MONFARED A D，HELALIZADEH A，PARVIZI H，et al.A global optimization technique using gradient information for history matching[J].Energy Sources，Part A: Recovery，Utilization，and Environmental Effects，2014，36(13): 1414-1428.)
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