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Thomas Alwin Blasingame - One of the best experts on this subject based on the ideXlab platform.

  • Estimating the Stabilized Deliverability of a Gas Well Using the Rawlins and Schellhardt Method: An Analytical Approach
    SPE Eastern Regional Meeting, 1991
    Co-Authors: J L Johnston, Thomas Alwin Blasingame
    Abstract:

    duration of the shut-in tiis often is not long enough to reach the . , This paper introduces a direct method to use the results of true average reservoir pressure in the well% drainage area. HoupeuztDeliverability analysis to derive the constants “C” and Although isochronaland modifkd isochronalTests weredevelo P “n” in the Rawlins and Schellhardt gas well deiiversbllity to circumvent the long flow times required in low permesbl ity equation. The motivation for this effort is the need to report the reservoirs, these Tests may still require a single, stabili=d fiOW resultsof Rawlins and ScheUhardtanalysisto regulatory agencies, period at the end of the Test in order to estimate the srrzfdfized and the widespread use of their deliverabi lity equation by producingcapacityof the well. engineers. We present a detailed procedure which shows how these results can be applied to Deliverability forecasting. This The Conventional Deliverability Test analysis technique was paper includes an ?lustmtive example in which the new nwthod is proposed by Rawlins and Schellhardt.} They observedthat a logapplied to field data from the literature. This example presents log plot of the difference between the squares of the average comparisons between Houpeurt and Rawlins and Schellhsrdt reservoir pressure and the bottomhole flowing pressure against analysesand showsthe correlation betweenthe two methods. gas flow rate can be representedby a straightline defined by qg = c G* “P;f)n . . .. . . .. . . . . . . . . , ..,.,,,,....,,, . . . . . . . . . . . .(1) INTRODUCTION The purpose of Deliverability Testing is to determine a gas well’s where C is defined as the stabdizai performancecoefficient,and n is the reciprocal of the slope of the straight line, Extrapolation of production capabilities under’specific reservoir conditions. A this line to the difference between the squares of ths average common prmiuctivity indicator obtained from these Tests is the reservoir pressure and the bottomhole flowing pressure equal to absolute open flow (AOF) potential, which is defined as the atmosphericpressuredefines the AOF. maximum rate at which a well could flow against a theoretical atmospheric backpressure at the sandface. Although in practice Eq, 1 was developed empirically from the observation of a the well cannot produce at this rate, the AOF is often used by number of gas well Tests. Extrapolation of Eq. 1 over large regulatory agencies for establis%tg field proration schedulesand variationsin pmssum can result in incorrecTestimatesof the AOF, settingmaximumallowableproductionrates for individualwells. Subsequent theoretical developments by Houpeurd have shown A number of Testing techniques have been developed to assess a that a more accurateanalysisfor gas flow is possiblewith gas well’sDeliverabilitycharacteristics, Flow+fter-flowl Tests am P2-p~f=aq8+bqi ,,, ., .. . . . . . . . . . . . .. . .. . . . . .. . . . ,, .,4,.. (2) conducted by producin$ the well at a seriesof different flow rates and measuring the stabdized bottomholeflowin$ pressures, Each where the flowcoefficients,a and b, are defined by flowrate is establishedin successionwithoutan intermediateshutin period. The primary limitation of these Tests is the long time a= L422x106~ Z T required to reach stabilization in low permeability reservoirs. Consequently, the isochrorta12and modified isochronal Tests k,ll g ‘ [’151’~g(%)-i+’] .b.,(3, were developed to shotten Test times. ~ = L422x106 jit Et TD kt h An isochronal Testis conductedby alternativelyproducing the .,, ,!,.,.,.,,, ,,, ,,, ,,, ,,, ,, ., .,... (4) well, then shutting it in md allowing it to build up to the average 7 2 is a solution to the diffusivity equation for radial flow, reservoir ressure prior to the beginning of the next flow period. R A ;hough t$e Houpeurt equation has a theoretical basis and is The rnodi ed isochronal Test is conducted similsriy, except the rigorously correct, the more famiiiw but em ifically b~ed Rawlins and Schellhardt equation continues to L used, inkd Referencesm~Uustradons at end of paper favored, b I the natural gas industry. Consequently, we have i combined e two analysistechn4uea and havedevelopeda mm 2 Estimatingthe Stabtized Deliverabilityof a Gss WellUsing the SPE 23440 Rawtinsand SchellhardtMethod: An AnalyticalAppioach . accurate version of the Rswlins-Schellhardtmethod which can be used in Deliverability forecasting. Our technique can be used to estimate the stabihzed performance coefficient, C, without requiring stabilizedflowingconditions and is especiallyuseful for analyzing isochronal and modified isochronal Tests without a stabilized flow period. This is a simple method which rquires only data from a modified isochronal Test to develop a performance prediction for the well without a priori estimates of reservoir properties. I?ZFINITIONS AND THEORETICAL DEVELOPMENT Our Deliverability Test analysis technique is derived by equating derivatives of log (qg) with respect to log (AP ) from both the Rawlins-Schellhardt and Houpeurt equations, 1 similar method was used by Brigham,s Duong,s and Poettmann and KazemiTto develop quations in terms of pressures-squared for estimating reservoir properties from gas Deliverability Tests. Because of the pressure-dependentgas properties, the pressure-squaredforms of the Deliverability equations (Eqs, 1 and 2) often are inaccurate at high pressures. Therefore, in the subsquent derivation, we use the pseudopressure transformation introduced by A1-Hussainy,et al,a J P pp=2 P& pb /404 ‘go) . . . . . . . . . . . . ! ..,...,.,,, . . . . . . . . . . . . . . .(5) Our method is a!su applicable, however, for Deliverability quations written with pnssure-squared as the dependentvariable. In terms of pseudopressure,the Rawlins and Schellhardtequation becomes qg = C ~P@) PP@wf)l” %’ ,,, ., .,,.,,... . . . . . . . . . . . . . . . . . . . . . . .(6) Similarly, the Houpeurtquation is Pp@) PP(IW) = a qg + b q~ . . . . . .. . . . . .. . .. . .. . . . . . .. . .. ...(7) where the flowcoefficients,u and b, are defined by 6 b ~x10 = D kg h , .,, ., ...,..,, . . . . . . . . . . . . . . ,.! ...,,,0,,,, (9) Taking the logarithmof both sidesof Eq, 6 yields /og(q8) =/og(C)+ fl/og~~@ -PP@w/)] .. ...0.. . .. .. ..(lO) Reatmnging Eq. 10 and solving for n shows that n is the slope of a log-log plot of qg vs. *P Alternatively, n can be expressed as the derivativeof log (q8) with respect to log (A@: ‘=m&3i$m=hm#kz-T”( ll) Similarly, taking the logaxithmof both sides of E@7 yields ‘OtiP@-pp@~j)] =10~aq8+ bql]... !...!..! . .. ..!. (12) Differentiatinglog (@P) with respect to q, gives . a+2bq r ,,..,.,.,,,..,.,,,,,., (13) aqg+bq~ Substituting F@ 13 into Eq 11 yields an quation for n in terms of the Houpeurtflow eoefftciem [1 ~=1 ~g+%l -a+bg qg a+2bqg (14) a+2bqg To develop an expression for the performance coefficient, C, in terms of the Houpeurt flow coefficients,we combine Eqs, 10 and 12to obtain In c‘(a~,~bqf~ = (a f~qg)” . . . . . . . . . . . . . . , ...,,...,,, (15) Eq. 15 is similar to a result derived by Poettmann and Kazemi.T We show the applications and importance of this development in the procedure in the next section of this paper, The flow rate required in Eq, 15 is defined by solving Eq. 14 for the gas flowrate, qg, a(l -n) ‘g= b(2n-1) .. ... .. . . . . . .. . .. . . . . . . . .. . . .. . .. . . . . .. . ... ... (16) Implicit in our derivation is the assumption of radial flow of a single-phase gas in a homogeneous, isotropic reservoir, For naturally fractured reservoirs, our method, like Conventional Deliverability analysis techniques, is valid only after the matrixfracture system has begun to behave like a single, homogeneous unit. Similarly, our method is valid only after pseudoradial flow is exhibited in hydraulically fractured wells, We also assume wellborestorageeffects are negligible. I“ Deliverability Test ANALYSIS Application of our method assumes that the slo~, l/n, of the empirical Deliverability plot remains constant wnh time. This assumption implies that, if we can calculate values of a and b (I@. 8 and 9, respectively) for given reservoir properties, we also can calculatea flow rate with@. 16, We then substitute this flow rate into Eq. 15 and calculate a stabilized C value, and assuminga constantvalue for n, calculatethe AOF AOF = C ~p(ji) Pp@b)r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (17) To apply our new Deliverability analysis technique to field data, we present an analysis procedure below. We will then apply this procedureto a fieldexample, General Analysis Procedure. We recommend the following proceduro to analyze isochronal and modified isochronal Tests using our technique, Although presented in terms of pseudopressures, this procedure also is applicable with the pressure-squaredvariables, 1. Plot 4P = Pp@) Pp@wf) vs. qg on log-log graph paper for the measuredflow data. 2, For each flow time, construct the best tit line through the data points, Typically, some of the earl data points will not J’ agree with the general trend of the ata, so these points should be ignored in all subsequentanalyses. 3. Determine the Deliverability exponent, n, for each best-fit line by least-squaresregressionanalysis using the following equation: I !i1OW.5(10,4P)J N$(fOgq810g&p~-, , ‘=-$=’’”(’8) 4, For M isochronal Tests, compute the arithmeti~ average Deliverabilityexportcn4ii,

J L Johnston - One of the best experts on this subject based on the ideXlab platform.

  • Estimating the Stabilized Deliverability of a Gas Well Using the Rawlins and Schellhardt Method: An Analytical Approach
    SPE Eastern Regional Meeting, 1991
    Co-Authors: J L Johnston, Thomas Alwin Blasingame
    Abstract:

    duration of the shut-in tiis often is not long enough to reach the . , This paper introduces a direct method to use the results of true average reservoir pressure in the well% drainage area. HoupeuztDeliverability analysis to derive the constants “C” and Although isochronaland modifkd isochronalTests weredevelo P “n” in the Rawlins and Schellhardt gas well deiiversbllity to circumvent the long flow times required in low permesbl ity equation. The motivation for this effort is the need to report the reservoirs, these Tests may still require a single, stabili=d fiOW resultsof Rawlins and ScheUhardtanalysisto regulatory agencies, period at the end of the Test in order to estimate the srrzfdfized and the widespread use of their deliverabi lity equation by producingcapacityof the well. engineers. We present a detailed procedure which shows how these results can be applied to Deliverability forecasting. This The Conventional Deliverability Test analysis technique was paper includes an ?lustmtive example in which the new nwthod is proposed by Rawlins and Schellhardt.} They observedthat a logapplied to field data from the literature. This example presents log plot of the difference between the squares of the average comparisons between Houpeurt and Rawlins and Schellhsrdt reservoir pressure and the bottomhole flowing pressure against analysesand showsthe correlation betweenthe two methods. gas flow rate can be representedby a straightline defined by qg = c G* “P;f)n . . .. . . .. . . . . . . . . , ..,.,,,,....,,, . . . . . . . . . . . .(1) INTRODUCTION The purpose of Deliverability Testing is to determine a gas well’s where C is defined as the stabdizai performancecoefficient,and n is the reciprocal of the slope of the straight line, Extrapolation of production capabilities under’specific reservoir conditions. A this line to the difference between the squares of ths average common prmiuctivity indicator obtained from these Tests is the reservoir pressure and the bottomhole flowing pressure equal to absolute open flow (AOF) potential, which is defined as the atmosphericpressuredefines the AOF. maximum rate at which a well could flow against a theoretical atmospheric backpressure at the sandface. Although in practice Eq, 1 was developed empirically from the observation of a the well cannot produce at this rate, the AOF is often used by number of gas well Tests. Extrapolation of Eq. 1 over large regulatory agencies for establis%tg field proration schedulesand variationsin pmssum can result in incorrecTestimatesof the AOF, settingmaximumallowableproductionrates for individualwells. Subsequent theoretical developments by Houpeurd have shown A number of Testing techniques have been developed to assess a that a more accurateanalysisfor gas flow is possiblewith gas well’sDeliverabilitycharacteristics, Flow+fter-flowl Tests am P2-p~f=aq8+bqi ,,, ., .. . . . . . . . . . . . .. . .. . . . . .. . . . ,, .,4,.. (2) conducted by producin$ the well at a seriesof different flow rates and measuring the stabdized bottomholeflowin$ pressures, Each where the flowcoefficients,a and b, are defined by flowrate is establishedin successionwithoutan intermediateshutin period. The primary limitation of these Tests is the long time a= L422x106~ Z T required to reach stabilization in low permeability reservoirs. Consequently, the isochrorta12and modified isochronal Tests k,ll g ‘ [’151’~g(%)-i+’] .b.,(3, were developed to shotten Test times. ~ = L422x106 jit Et TD kt h An isochronal Testis conductedby alternativelyproducing the .,, ,!,.,.,.,,, ,,, ,,, ,,, ,,, ,, ., .,... (4) well, then shutting it in md allowing it to build up to the average 7 2 is a solution to the diffusivity equation for radial flow, reservoir ressure prior to the beginning of the next flow period. R A ;hough t$e Houpeurt equation has a theoretical basis and is The rnodi ed isochronal Test is conducted similsriy, except the rigorously correct, the more famiiiw but em ifically b~ed Rawlins and Schellhardt equation continues to L used, inkd Referencesm~Uustradons at end of paper favored, b I the natural gas industry. Consequently, we have i combined e two analysistechn4uea and havedevelopeda mm 2 Estimatingthe Stabtized Deliverabilityof a Gss WellUsing the SPE 23440 Rawtinsand SchellhardtMethod: An AnalyticalAppioach . accurate version of the Rswlins-Schellhardtmethod which can be used in Deliverability forecasting. Our technique can be used to estimate the stabihzed performance coefficient, C, without requiring stabilizedflowingconditions and is especiallyuseful for analyzing isochronal and modified isochronal Tests without a stabilized flow period. This is a simple method which rquires only data from a modified isochronal Test to develop a performance prediction for the well without a priori estimates of reservoir properties. I?ZFINITIONS AND THEORETICAL DEVELOPMENT Our Deliverability Test analysis technique is derived by equating derivatives of log (qg) with respect to log (AP ) from both the Rawlins-Schellhardt and Houpeurt equations, 1 similar method was used by Brigham,s Duong,s and Poettmann and KazemiTto develop quations in terms of pressures-squared for estimating reservoir properties from gas Deliverability Tests. Because of the pressure-dependentgas properties, the pressure-squaredforms of the Deliverability equations (Eqs, 1 and 2) often are inaccurate at high pressures. Therefore, in the subsquent derivation, we use the pseudopressure transformation introduced by A1-Hussainy,et al,a J P pp=2 P& pb /404 ‘go) . . . . . . . . . . . . ! ..,...,.,,, . . . . . . . . . . . . . . .(5) Our method is a!su applicable, however, for Deliverability quations written with pnssure-squared as the dependentvariable. In terms of pseudopressure,the Rawlins and Schellhardtequation becomes qg = C ~P@) PP@wf)l” %’ ,,, ., .,,.,,... . . . . . . . . . . . . . . . . . . . . . . .(6) Similarly, the Houpeurtquation is Pp@) PP(IW) = a qg + b q~ . . . . . .. . . . . .. . .. . .. . . . . . .. . .. ...(7) where the flowcoefficients,u and b, are defined by 6 b ~x10 = D kg h , .,, ., ...,..,, . . . . . . . . . . . . . . ,.! ...,,,0,,,, (9) Taking the logarithmof both sidesof Eq, 6 yields /og(q8) =/og(C)+ fl/og~~@ -PP@w/)] .. ...0.. . .. .. ..(lO) Reatmnging Eq. 10 and solving for n shows that n is the slope of a log-log plot of qg vs. *P Alternatively, n can be expressed as the derivativeof log (q8) with respect to log (A@: ‘=m&3i$m=hm#kz-T”( ll) Similarly, taking the logaxithmof both sides of E@7 yields ‘OtiP@-pp@~j)] =10~aq8+ bql]... !...!..! . .. ..!. (12) Differentiatinglog (@P) with respect to q, gives . a+2bq r ,,..,.,.,,,..,.,,,,,., (13) aqg+bq~ Substituting F@ 13 into Eq 11 yields an quation for n in terms of the Houpeurtflow eoefftciem [1 ~=1 ~g+%l -a+bg qg a+2bqg (14) a+2bqg To develop an expression for the performance coefficient, C, in terms of the Houpeurt flow coefficients,we combine Eqs, 10 and 12to obtain In c‘(a~,~bqf~ = (a f~qg)” . . . . . . . . . . . . . . , ...,,...,,, (15) Eq. 15 is similar to a result derived by Poettmann and Kazemi.T We show the applications and importance of this development in the procedure in the next section of this paper, The flow rate required in Eq, 15 is defined by solving Eq. 14 for the gas flowrate, qg, a(l -n) ‘g= b(2n-1) .. ... .. . . . . . .. . .. . . . . . . . .. . . .. . .. . . . . .. . ... ... (16) Implicit in our derivation is the assumption of radial flow of a single-phase gas in a homogeneous, isotropic reservoir, For naturally fractured reservoirs, our method, like Conventional Deliverability analysis techniques, is valid only after the matrixfracture system has begun to behave like a single, homogeneous unit. Similarly, our method is valid only after pseudoradial flow is exhibited in hydraulically fractured wells, We also assume wellborestorageeffects are negligible. I“ Deliverability Test ANALYSIS Application of our method assumes that the slo~, l/n, of the empirical Deliverability plot remains constant wnh time. This assumption implies that, if we can calculate values of a and b (I@. 8 and 9, respectively) for given reservoir properties, we also can calculatea flow rate with@. 16, We then substitute this flow rate into Eq. 15 and calculate a stabilized C value, and assuminga constantvalue for n, calculatethe AOF AOF = C ~p(ji) Pp@b)r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (17) To apply our new Deliverability analysis technique to field data, we present an analysis procedure below. We will then apply this procedureto a fieldexample, General Analysis Procedure. We recommend the following proceduro to analyze isochronal and modified isochronal Tests using our technique, Although presented in terms of pseudopressures, this procedure also is applicable with the pressure-squaredvariables, 1. Plot 4P = Pp@) Pp@wf) vs. qg on log-log graph paper for the measuredflow data. 2, For each flow time, construct the best tit line through the data points, Typically, some of the earl data points will not J’ agree with the general trend of the ata, so these points should be ignored in all subsequentanalyses. 3. Determine the Deliverability exponent, n, for each best-fit line by least-squaresregressionanalysis using the following equation: I !i1OW.5(10,4P)J N$(fOgq810g&p~-, , ‘=-$=’’”(’8) 4, For M isochronal Tests, compute the arithmeti~ average Deliverabilityexportcn4ii,

Walter K. Sawyer - One of the best experts on this subject based on the ideXlab platform.

  • Novel Surveillance Helps Operators Track Damage
    All Days, 2002
    Co-Authors: Kenneth G. Brown, Walter K. Sawyer
    Abstract:

    Abstract As part of an ongoing study sponsored by the Gas Technology Institute, new technology has been developed that provides storage operators with a cost effective method to frequently monitor wellbore damage with reasonable accuracy. Two procedures were developed and Tested, the Sawyer-Brown Method (SB Method) and the Minute-Rise Deconvolution Method (MRD Method). These procedures are inexpensive, since no service company personnel or down-hole equipment is required. Consequently, the wells can be Tested at much more frequent intervals than is typical of current Testing methods. The theoretical basis of each method is developed. The successful application of the SB Method is demonstrated using Conventional Deliverability Test data and verified using multiple rate pressure transient Tests in which bottom hole pressure gauges were used. The theoretical basis of the MRD Method is validated using simulated data. Difficulties encountered in the practical application of the MRD Method are presented and discussed. Areas of additional work are identified and guidelines for the implementation of these methods are presented. Introduction It is typical for many underground gas storage operators to perform surface backpressure Testing annually, bi-annually, or even less frequently to evaluate damage levels in their storage wells. Such infrequent Testing using surface data is often attributed to the high cost of contracting a service company to run down-hole pressure gauges. Consequently, timely identification of damaged wells may not occur, which results in delayed well remediation and lost Deliverability. In addition, the path of damage development over time - which may provide considerable insight to the source of the damage - cannot be determined with such infrequent Testing. Fig. 1 illustrates three possible histories of the damage level in a storage well, each suggesting very different sources of damage. Path #1 suggests injection operations induce damage, path #2 suggests both injection and withdrawal operations induce damage, and path #3 suggests damage is created as a result of switching from withdrawal to injection. Typically, we only have two points derived from pressure transient Tests spaced a considerable time apart (represented by the two points labeled "PTA Skin" in Fig. 1). The need to increase operators' understanding of the path of damage development was a major motivation for development of the surveillance techniques discussed in this paper. The two techniques described in this paper have the potential to allow operators to track damage much more frequently than in the past. These new techniques use bottom-hole pressures calculated from surface data and short flow and/or shut-in periods to identify deterioration in well performance over time. The Testing procedures are inexpensive and easily implemented by the operator, and therefore can be performed much more frequently than currently employed Testing methods.

Kenneth G. Brown - One of the best experts on this subject based on the ideXlab platform.

  • Novel Surveillance Helps Operators Track Damage
    All Days, 2002
    Co-Authors: Kenneth G. Brown, Walter K. Sawyer
    Abstract:

    Abstract As part of an ongoing study sponsored by the Gas Technology Institute, new technology has been developed that provides storage operators with a cost effective method to frequently monitor wellbore damage with reasonable accuracy. Two procedures were developed and Tested, the Sawyer-Brown Method (SB Method) and the Minute-Rise Deconvolution Method (MRD Method). These procedures are inexpensive, since no service company personnel or down-hole equipment is required. Consequently, the wells can be Tested at much more frequent intervals than is typical of current Testing methods. The theoretical basis of each method is developed. The successful application of the SB Method is demonstrated using Conventional Deliverability Test data and verified using multiple rate pressure transient Tests in which bottom hole pressure gauges were used. The theoretical basis of the MRD Method is validated using simulated data. Difficulties encountered in the practical application of the MRD Method are presented and discussed. Areas of additional work are identified and guidelines for the implementation of these methods are presented. Introduction It is typical for many underground gas storage operators to perform surface backpressure Testing annually, bi-annually, or even less frequently to evaluate damage levels in their storage wells. Such infrequent Testing using surface data is often attributed to the high cost of contracting a service company to run down-hole pressure gauges. Consequently, timely identification of damaged wells may not occur, which results in delayed well remediation and lost Deliverability. In addition, the path of damage development over time - which may provide considerable insight to the source of the damage - cannot be determined with such infrequent Testing. Fig. 1 illustrates three possible histories of the damage level in a storage well, each suggesting very different sources of damage. Path #1 suggests injection operations induce damage, path #2 suggests both injection and withdrawal operations induce damage, and path #3 suggests damage is created as a result of switching from withdrawal to injection. Typically, we only have two points derived from pressure transient Tests spaced a considerable time apart (represented by the two points labeled "PTA Skin" in Fig. 1). The need to increase operators' understanding of the path of damage development was a major motivation for development of the surveillance techniques discussed in this paper. The two techniques described in this paper have the potential to allow operators to track damage much more frequently than in the past. These new techniques use bottom-hole pressures calculated from surface data and short flow and/or shut-in periods to identify deterioration in well performance over time. The Testing procedures are inexpensive and easily implemented by the operator, and therefore can be performed much more frequently than currently employed Testing methods.