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1、5.7 Analysis of Gas Well Buildup Tests5.7 Analysis of Gas Well Buildup Tests-2 2Discrete Change in Rate Before Shut InDiscrete Change in Rate Before Shut In1、Superposition MethodWe can develop an analysis technique for buildup tests with discreterate changes before shut-in using superposition in tim

2、e for(n-1)ratespreceding the pressure-buildup testFig.5.19-Rate history for buildup test following n-1 different flow ratessrcktkhBqppwtggggwfaia869.023.3log)log(6.1622,For the general case where qn=0 and for(n-1)different rates beforeshut-in,12231221121111loglog.loglog6.162nnnnnnnnnwsittttttttqqttt

3、tqqtttqqkhBqppAnalysis procedure in terms of adjusted variables:（1）Calculate the plotting function.12111log.lognnntttttttqqX（3）Determine the slope m of the straight line.mhBqkggn16.162（2）Plot pa,wsvs.X on Cartesian coordinate graph paper.（4）Calculate permeability to gas using the slope from Step 3.1

4、232121,1112121162.6loglog.loglognnnna ia wsnnnnnqBqttttqqtttppkhqttqttqtttt,162.6lgpa wsa ittqBppkht（5）Calculate the skin factor.,1,21.151log3.23ahra wfgt wppksmc r（6）The initial adjusted formation pressure,iap,is thevalue ofwsap,on the straight line extrapolated to X=0.2、Odeh-Selig MethodFig.5.19-R

5、ate history for buildup test following n-1 different flow rates,162.6()loggggpaa wsa iaqBttppkht Asanalternativetosuperposition,OdehandSeligsuggested that a buildup test following n different rates couldbe analyzed by a method similar to the Horner method.aapggwsaiatttkhBqpp*,log6.162The shut-in pre

6、ssure response is where the modified production time,，and flow rate,*q，arenjjjjnjjjjnpttqttqtt111212*22njjjjpttqtq11*1The Odeh-Selig method,approximate butaccurate,is applicable only for pressuresatvalues greater than actual producingtime.This condition is likely only in a drillstem test or short pr

7、oduction test.*ptat3、Horners MethodFig.5.19-Rate history for buildup test following n-1 different flow ratesHorner reported an approximation that can be used in many cases to avoid theuse of superposition in modeling the production history of a variable-rate well.He defined a producing time,lastppqG

8、t/Where，pG=cumulative production from the well,Mscf,lastq=the most recent production rate,Mscf/D.Horner proposed to model the effect of the entire rate history by869.023.3log6.1622,srcktkhBqppwtgpgglastiawfa,22162.6log3.230.869 162.6log3.230.869 gpaglasta wsa itgwgglastatgwk ttqBppskhc rqBktskhc raa

9、pgglastiawsatttkhBqpplog6.162,Combining terms and simplifying yieldsmhBqkgglast6.16223.3log151.12,1,wtgwsahrarckmpps To calculate permeability,we use the absolute value of m of the semilog straight line.The apparent skin factor is estimated from From the semilog graph，the original reservoir pressure

10、,pa.i,isestimated by extrapolating the straight line to infinite shut-in timewhere,1/)(aaptttWith slight modification,conventional Horner and type-curve analysescan be used to analyze buildup test data following production at constantBHP.Constant BHP Before Shut InConstant BHP Before Shut InConventi

11、onal buildup test analysis techniques have been developedprimarily for wells producing at a constant rate before shut-in.However,some common situations involve production at constant BHPrather than at constant rate.Using Horners MethodThe actual producing time,actualt,rather than defined.lastppqGt/,

12、162.6loggglastactualaa wsa iaqBttppkhtgives the correct semilog straight line with slope m.k is computed withmhBqkgglast6.162The skin factor also is calculated in the usual way,23.3log151.12,1,wtgwsahrarckmppsUsing Horners MethodConstant BHP Before Shut InConstant BHP Before Shut InDiscrete Change in Rate Before Shut InDiscrete Change in Rate Before Shut In1、Superposition Method2、Odeh-Selig Method3、Horners MethodSummarySummaryDiscrete Change in Rate Before Shut In（End)