响应面法和BFGS算法在试井分析中的应用

doi:10.3969/j.issn.0253-2778.2018.05.009

中国科学技术大学学报 ›› 2018, Vol. 48 ›› Issue (5): 400-408.DOI: 10.3969/j.issn.0253-2778.2018.05.009

响应面法和BFGS算法在试井分析中的应用

李道伦，陈刚，查文舒，许恩华

合肥工业大学数学学院，安徽合肥 236009

收稿日期:2017-06-26 修回日期:2017-12-07 接受日期:2017-12-07 出版日期:2018-05-31 发布日期:2017-12-07
通讯作者: 李道伦
作者简介:李道伦（通讯作者），男，1972年生，博士/教授.研究方向：数值试井和油藏数值模拟.E-mail: LdaoL@ustc.edu.cn
基金资助:
中国石油-中国科学院战略合作项目(2015A-4812)，中国科学院战略性先导科技专项(XDB10030402)资助

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

LI Daolun, CHEN Gang, ZHA Wenshu, XU Enhua

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

Received:2017-06-26 Revised:2017-12-07 Accepted:2017-12-07 Online:2018-05-31 Published:2017-12-07

摘要/Abstract

摘要： 试井分析是利用关井所测的井底压力随时间变化的资料来分析地层和井筒参数，是一个典型的反问题.基于响应面法提出了一种新的参数自动反求的数值试井解释方法.选定不确定参数及其范围，确定试算算例，然后利用拟合方法得到多项式逼近函数，即构造响应面模型.利用响应面模型构建计算值与实际观测值偏差的目标函数，再利用BFGS算法以及拉丁超立方抽样搜索目标函数的最小值，得到不确定参数值.算例表明该方法能有效地对井底压力以及压力导数进行拟合，因而具有很好的应用前景.

关键词: 试井分析, 响应面法, 目标函数, BFGS算法, 拉丁超立方抽样

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.

Key words: well test analysis, response surface method, objective function, BFGS algorithm, Latin hypercube sampling

中图分类号:

TE312

李道伦，陈刚，查文舒，许恩华. 响应面法和BFGS算法在试井分析中的应用[J]. 中国科学技术大学学报, 2018, 48(5): 400-408.

LI Daolun, CHEN Gang, ZHA Wenshu, XU Enhua. Application of response surface method and BFGS algorithm in well test analysis[J]. Journal of University of Science and Technology of China, 2018, 48(5): 400-408.

参考文献

［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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响应面法和BFGS算法在试井分析中的应用

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

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