Estimating the Specific Productivity Index in Horizontal Wells From Distributed-Pressure Measurements Using an Adjoint-Based Minimization Algorithm
- Farzad Farshbaf Zinati (Delft University of Technology) | Jan-Dirk Jansen (Delft University of Technology) | Stefan M. Luthi (Delft University of Technology)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2012
- Document Type
- Journal Paper
- 742 - 751
- 2012. Society of Petroleum Engineers
- 5.6.3 Pressure Transient Testing, 5.1.5 Geologic Modeling, 5.3.2 Multiphase Flow
- 2 in the last 30 days
- 505 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
Recent developments in the deployment of distributed-pressure-measurement devices in horizontal wells promise to lead to a new, low-cost, and reliable method of monitoring production and reservoir performance. Practical applicability of distributed-pressure sensing for quantitative-inflow detection will strongly depend on the specifications of the sensors, details of which were not publicly available at the time of publication. Therefore, we theoretically examined the possibility of identifying reservoir inflow from distributed-pressure measurements in the well. The wellbore and near-wellbore region were described by semianalytical steady-state models, and a gradient-based inversion method was applied to estimate the specific productivity index (SPI) as a function of along-well position. We employed the adjoint method to obtain the gradients, which resulted in a computationally efficient inversion scheme. With the aid of two numerical experiments (one of which was based on a real well and reservoir), we investigated the effects of well and reservoir parameters, sensor spacing, sensor resolution, and measurement noise on the quality of the inversion results. In both experiments, we generated synthetic measurements with the aid of a high-resolution reservoir-simulation model and used these to test the semianalytical inversion algorithm. In the first experiment, we considered a 2000-m horizontal well passing through two 300-m high-permeability streaks in a background with a permeability that was 10 times lower. The location of the streaks and the SPIs along the well were detected with fair accuracy using 20 unknown parameters (SPI values) and 20 pressure measurements. Decreasing the number of measurements resulted in a poorer detection of the streaks and their SPIs. The detection performance also decreased for increasing noise levels and deteriorated sensor resolution, though the negative effect of random measurement noise was cancelled out primarily by stacking multiple measurements. The detrimental effects of measurement noise and low sensor resolution were strongest in areas where the inflow was lowest (usually close to the toe). The second experiment concerned a high-rate near-horizontal well with slightly varying inclination that intersected a dipping package of formations with strongly variable permeabilities. Additionally, a satisfactory detection of SPIs was obtained even though the heterogeneities were no longer perpendicular to the well as in the first experiment. As a result of using the simple semianalytical forward model and the adjoint method, the inversions typically required less than 90 seconds on a standard laptop. This offered the opportunity to extend the algorithm to multiphase flow and dynamic applications (pressure-transient testing), while still maintaining sufficient computational speed to perform the inversion in real time.
|File Size||1 MB||Number of Pages||10|
Brill, J.P. and Mukherjee, H. 1999. Multiphase Flow in Wells, No. 17.Richardson, Texas: Monograph Series, SPE.
Brown, G. 2006. Monitoring Multilayered Reservoir Pressures and Gas/Oilratio Changes Over Time Using Permanently Installed Distributed TemperatureMeasurement. Paper SPE 101886 presented at the SPE Annual Technical Conferenceand Exhibition, San Antonio, Texas, USA, 24-27 September. http://dx.doi.org/10.2118/101886-MS.
Bryant, I.D., Chen, M.-Y., Raghuraman, B., et al. 2004. Real-Time Monitoringand Control of Water Influx to a Horizontal Well Using Advanced CompletionEquipped With Permanent Sensors. SPE Drill & Compl 19(4): 253-264. SPE-77522-PA. http://dx.doi.org/10.2118/77522-PA.
Bryson Jr., A.E. and Ho, Y.-C. 1975. Applied Optimal Control:Optimization, Estimation and Control revised edition. Levittown,Pennsylvania: Taylor & Francis.
Colebrook, C.F. 1939. Turbulent Flow in Pipes With Particular Reference tothe Transition Region Between the Smooth and Rough Pipe Laws. Journal of theICE 11 (4): 13-156. http://dx.doi.org/10.1680/ijoti.1939.13150.
Dikken, B.J. 1990. Pressure Drop in Horizontal Wells and Its Effect onProduction Performance. J Pet Technol 42 (11): 1426-1433.SPE-19824-PA. http://dx.doi.org/10.2118/19824-PA.
Drakeley, B.K. and Omdal, S. 2008. Fiber Optics Sensing Systems for SubseaApplications-Sensing Capabilities, Applications, and the Challenges Being Facedin Order to Provide Reliable Transmission of Data for Online ReservoirManagement. Paper SPE 112205 presented at the Intelligent Energy Conference andExhibition, Amsterdam, 25-27 February. http://dx.doi.org/10.2118/112205-MS.
Drakeley, B.K., Johansen, E.S., Zisk, E., and Bostick III, T. 2006.In-Well Optical Sensing--State-of-the-Art Applications and Future Direction forIncreasing Value in Production-Optimization Systems. Paper SPE 99696 presentedat the Intelligent Energy Conference and Exhibition, Amsterdam, 11-13 April. http://dx.doi.org/10.2118/99696-MS.
Element, D.J., Goodyear, S.G., and Jayasera, A.J. 2002. The Use ofDistributed Well Temperature Measurements in Water-flood Management. PaperIOR-06 presented at the IEA EOR Collaborative Agreement--23rd Annual Workshopand Symposium, Caracas, Venezuela, 8-11 September.
Flecker, M.J., Thompson, S.J., McKay, C.S., and Buchwalter, J.L. 2000.Maximizing Reservoir Production Using New Technologies for Permanent ContinuousDownhole Sensors. Paper OTC 12153 presented at the Offshore TechnologyConference, Houston, 1-4 May. http://dx.doi.org/10.4043/12153-MS.
Intel. 2011. Intel® Core™2 Duo Processor T7300 (4M Cache, 2.00 GHz, 800 MHzFSB), http://ark.intel.com/Product.aspx?id=29760(accessed 2010).
Jansen, J.-D. 2003. A Semianalytical Model for Calculating Pressure DropAlong Horizontal Wells With Stinger Completions. SPE J. 8(2): 138-146. SPE-74212-PA. http://dx.doi.org/10.2118/74212-PA.
Kragas, T.K., Williams, B.A., and Myers, G.A. 2001. The Optic OilField: Deployment and Application of Permanent In-well Fiber Optic SensingSystems for Production and Reservoir Monitoring. Paper SPE 71529 presented atthe SPE Annual Technical Conference and Exhibition, New Orleans, 30 September-3October. http://dx.doi.org/10.2118/71529-MS.
Li, Z. and Zhu, D. 2009. Predicting Flow Profile of Horizontal Well byDownhole Pressure and DTS Data for Water-Drive Reservoir. Paper SPE 124873presented at the SPE Annual Technical Conference and Exhibition, New Orleans,4-7 October. http://dx.doi.org/10.2118/124873-MS.
MathWorks. 2010. MATLAB R2011a Documentation - Optimization Toolbox.fmincon: Find minimum of constrained nonlinear multivariable function, http://www.mathworks.com/help/toolbox/optim/ug/fmincon.html(accessed 01 June 2011).
Moody, L.F. 1944. Friction Factors for Pipe Flow. Trans ASME 66 (8): 671-684.
Nocedal, J. and Wright, S.J. 2006. Numerical Optimization, secondedition. New York: Series in Operations Research and Financial Engineering,Springer.
Oliver, D.S., Reynolds, A.C., and Liu, N. 2008. Inverse Theory forPetroleum Reservoir Characterization and History Matching. Cambridge, UK:Cambridge University Press.
Ouyang, L.-B. and Belanger, D. 2006. Flow Profiling by DistributedTemperature Sensor (DTS) System--Expectation and Reality. SPE Prod &Oper 21 (1): 269-281. SPE-90541-PA. http://dx.doi.org/10.2118/90541-PA.
Peaceman, D.W. 1978. Interpretation of Well-Block Pressures in NumericalReservoir Simulation(includes associated paper 6988 ). SPE J. 18 (3): 183-194. SPE-6893-PA. http://dx.doi.org/10.2118/6893-PA.
Schroeder, R.J., Yamate, T., and Udd, E. 1999. High Pressure andTemperature Sensing for the Oil Industry using Fiber Bragg Gratings Writtenonto Side Hole Single Mode Fiber (Proc. SPIE Vol. 3746), https://docs.google.com/viewer?url=http%3A%2F%2Fwww.bluerr.com%2Fpapers%2FBRR-1999_SPIE_Vol3746_p42.pdf.
Stengel, R.F. 1994. Optimal Control and Estimation. Mineola, NewYork: Dover Publications (repr. Wiley, 1986).
Udd, E. ed. 1991. Fiber Optic Sensors: An Introduction for Engineers andScientists New York: Wylie Series in Pure and Applied Optics, John Wiley& Sons.
van Gisbergen, S.J.C.H.M. and Vandeweijer, A.A.H. 2001. Reliability Analysisof Permanent Downhole Monitoring Systems. SPE Drill & Compl 16 (1): 60-63. SPE-57057-PA. http://dx.doi.org/10.2118/57057-PA.
Wang, X., Lee, J., Thigpen, B., Vachon, G., Poland, S., and Norton, D.2008. Modeling Flow Profile Using Distributed Temperature Sensor (DTS) System.Paper SPE 111790 presented at the Intelligent Energy Conference and Exhibition,Amsterdam, 25-27 January. http://dx.doi.org/10.2118/111790-MS.
Yoshioka, K., Zhu, D., Hill, A.D., and Lake, L.W. 2009. A NewInversion Method to Interpret Flow Profiles From Distributed Temperature andPressure Measurements in Horizontal Wells. SPE Prod & Oper 24 (4): 510-521. SPE-109749-PA. http://dx.doi.org/10.2118/109749-PA.
Zhu, D., Achinivu, O.I., and Furui, K. 2008. An Interpretation Method ofDownhole Temperature and Pressure Data for Flow Profiles in Gas Wells. PaperSPE 116292 presented at the SPE Russian Oil and Gas Technical Conference andExhibition, Moscow, 28-30 October. http://dx.doi.org/10.2118/116292-MS.
Zisk, E.J. 2005. Optical In-Well Permanent Monitoring--Initial Promise Now AReality? Paper OTC 17529 presented at the Offshore Technology Conference,Houston, 2-5 May. http://dx.doi.org/10.4043/17529-MS.