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The Analysis and Interpretation of Water-Oil Ratio Performance in Petroleum Reservoirs

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## The Analysis and Interpretation of Water-Oil Ratio Performance in Petroleum Reservoirs

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**The Analysis and Interpretation of Water-Oil Ratio**Performance in Petroleum Reservoirs Valentina Bondar Texas A&M University Harold Vance Department of Petroleum Engineering 12 January 2001**Outline**• Introduction • Conventional WOR Analysis (Steady-State WOR Model) • Pseudosteady-State WOR Model • Analysis of WOR • Conclusions and Recommendations**Outline**• Introduction • Conventional WOR Analysis (Steady-State WOR Model) • Pseudosteady-State WOR Model • Analysis of WOR • Conclusions and Recommendations**Objective**• Provide the development of a pseudo-steady-state WOR equation. • Estimate and compare values of "movable" oil using various straight-line extrapolation methods. • Introduce two new methods for esti-mating Np,mov. • Perform "qualitative" analysis of oil and water production data.**Introduction**• 20 Wells in the North Robertson Unit (West Texas) • 8 Wells in the West White Lake Field (South Louisiana)**Outline**• Introduction • Conventional WOR Analysis (Steady-State WOR Model) • Pseudosteady-State WOR Model • Analysis of WOR • Conclusions and Recommendations**Linear log(krw/kro) versus Sw**Conventional WOR Analysis Steady-State WOR Model**fw**Np Conventional WOR Analysis log(fw) versus Np**fw = 1**Conventional WOR Analysis log(fw) versus Np**Outline**• Introduction • Conventional WOR Analysis (Steady-State WOR Model) • Pseudosteady-State WOR Model • Analysis of WOR • Conclusions and Recommendations**Blasingame and Lee**bpss m Pseudosteady-State WOR Model**mw**mo fw tw to bppsw bppso Pseudosteady-State WOR Model log(fw) versus Np**fw**tw to Pseudosteady-State WOR Model log(fw) versus Np**Pseudosteady-State WOR Model**Results from the PSS WOR modelversus the field production data**Pseudosteady-State WOR Model**log(fw) versus Np**Pseudosteady-State WOR Model**Results from the PSS WOR modelversus the field production data**Outline**• Introduction • Conventional WOR Analysis (Steady-State WOR Model) • Pseudosteady-State WOR Model • Analysis of WOR • Conclusions and Recommendations**Analysis of WOR Data**Estimation of Movable Oil • Conventional techniques • log(qo) versusproduction time, t • qo versus cumulative oil production, Np • fo versus cumulative oil production, Np • log(fw) versus cumulative oil production, Np • Ershagi's X-function • New techniques • 1/fw versus cumulative oil production, Np • 1/qo versus oil material balance time, to**Analysis of WOR Data**Qualitative Analysis • log(fwc) versus cumulative oil production, Np • log(WORc) versus cumulative oil production, Np • log(WOR) versus total production, (Np+Wp) • log(fo) versus total material balance time, tt • WOR and WOR associated functions versus time, t (to)**Analysis of WOR Data**Estimation of Movable Oil • Conventional techniques • log(qo) versusproduction time, t • qo versus cumulative oil production, Np • fo versus cumulative oil production, Np • log(fw) versus cumulative oil production, Np • Ershagi's X-function • New techniques • 1/fw versus cumulative oil production, Np • 1/qo versus oil material balance time, to**Analysis of WOR Data**log(qo) and log(qw) versus t**qo=0**Analysis of WOR Data qo versus Np**fo=0**Analysis of WOR Data fo versus Np**fw = 1**Analysis of WOR Data log(fw ) versus Np**X-function= -5.6**@ fw = 0.99 Analysis of WOR Data Ershagi’s X-plot Np=145,000 STB X = ln((1/fw)-1)-1/fw**Analysis of WOR Data**Estimation of Movable Oil • Conventional techniques • log(qo) versusproduction time, t • qo versus cumulative oil production, Np • fo versus cumulative oil production, Np • log(fw) versus cumulative oil production, Np • Ershagi's X-function • New techniques • 1/fw versus cumulative oil production, Np • 1/qo versus oil material balance time, to**1/fw=1**Analysis of WOR Data 1/fw versus Np**1/qo**Np /qo Analysis of WOR Data 1/qo versus Np/qo**Analysis of WOR Data**Reciprocal of qo versus oil material balance time**b**Analysis of WOR Data 1/qo versus Np/qo**Analysis of WOR Data**1/qo versus Np/qo Np,mov = 164,500 STB**Analysis of WOR Data**fwc versus Np Np,mov = 164,500 STB**Analysis of WOR Data**Comparison of the estimated Np values**Analysis of WOR Data**Qualitative Analysis • log(fwc) versus cumulative oil production, Np • log(WORc) versus cumulative oil production, Np • log(WOR) versus total production, (Np+Wp) • log(fo) versus total material balance time, tt • WOR and WOR associated functions versus time, t (to)**Analysis of WOR Data**WORversus (Np+Wp)**Analysis of WOR Data**fo versus (Np+Wp)/(qo+qw)**Analysis of WOR Data**WOR and WOR' versus (Np/qo)**Analysis of WOR Data**WOR integral andintegral-derivative versus (Np/qo)**Outline**• Introduction • Conventional WOR Analysis (Steady-State WOR Model) • Pseudosteady-State WOR Model • Analysis of WOR • Conclusions and Recommendations**Conclusions**Pseudosteady-state WOR model • We have developed a new pss WOR model for boundary-dominated reservoir behavior. • The proposed pss WOR model provides the best representation of the oil and water production data for the cases that we in-vestigated. • The only significant limitation of the our model is that it does not provide a mechan-ism for the prediction of future production**Conclusions (cont.)**Estimation of Movable Oil • We provide a compilation of the "conven-tional" straight-line extrapolation methods. These techniques should be applied simultaneously in order to obtain consis-tent estimates of movable oil. • We proposed two new methods for estimating movable oil reserves: • 1/fw versus Np • 1/qo versus Np/qo**Conclusions (cont.)**Estimation of Movable Oil • The results obtained by these new methods correspond quite well to the results obtained "conventional" WOR techniques. Analysis of Oil and Water Production Data • We note a straight-line behavior for the fwc and WORc functions plotted versus Np. However, the extrapolation of these straight-line trends does not lead to similar result for movable oil as the "conventional" extrapolation techniques.**Conclusions (cont.)**Analysis of Oil and Water Production Data • We have extended the diagnostic plots proposed by Chan. The following obser-vations are noted: • unit slope of the WOR and WOR integral and integral-derivative functions when plotted versus t, to, tt. • the WOR' function is typically very erratic and can not be used for routine analysis due to poor overall behavior.**Conclusions (cont.)**Analysis of Oil and Water Production Data • We believe that the X-plot method provides no substantive advantage over the "conventional" extrapolation techniques. The extrapolation of the X-function tends to significantly overestimate the value of movable oil.**Recommendations**• Investigate the possibility of using the proposed pss WOR model for the estimation of movable oil. • Examine a possibility to develop an analysis scheme to estimate pss parameters (bpsso, bpssw, mo, and mw). We suggest that the para-meters can be further used for reservoir analysis. • We suggest further qualitative and quantitative analysis for the various WOR trends as a function of time, cumulative production, material balance time. A”type curve" approach may be possible.**The Analysis and Interpretation of Water-Oil Ratio**Performance in Petroleum Reservoirs Valentina Bondar Texas A&M University Harold Vance Department of Petroleum Engineering 12 January 2001