multivariate production systems optimization - Stanford University

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[35] Greenstadt, J. L.: “On the Relative Efficiencies of Gradient Methods,” Mathematics of Computation, 21 (1967) 360-67. [36] Gregory, M., Aziz, K., and Fogarasi, M.: “Analysis of Vertical Two-Phase Flow Calculations, Crude Oil, Gas Flow in Well Tubing,” J. Canad. Petro. Tech. (Jan 1980) 86- 92. [37] Griffith, P., and Wallis, G. B.: “Two-Phase Slug Flow,” J. Heat Transfer, ASME (Aug. 1961) 307-320. [38] Guzhov, A. J., and Medeiediev, V. F.: “Critical Flow of Two-Phase Liquids Through Wellhead Chokes,” Nieftianoie Xoziastva-Moskva No. 11 (1962) in Russian. [39] Hagedorn, A. R., and Brown, K. E.: “Experimental Study of Pressure Gradients Occurring During Continuous Two-Phase Flow in Small-Diameter Vertical Conduits,” J. Petro. Tech. (April 1965) 475-484. [40] Hazim, S. H. Al-Najjar, and Nimat, B. Abu Al-Soof: “Alternative Flow-Pattern Maps Can Improve Pressure-Drop Calculations of the Aziz et al. Multiphase-Flow Correlation,” SPEPE (August 1989) 327-334. [41] Hunt, J. L.: “Production-Systems Analysis for Fractured Wells,” SPEPE (Nov. 1988) 608-614. [42] Huppler, J. D.: “Scheduling Gas Field Production for Maximum Profit,” SPEJ (June 1974) 274-279. [43] IMSL Inc., IMSL MATH/LIBRARY User’s Manual, 3, Chapter 8, IMSL, Houston (1987). [44] Kuller, R. G., and Cummings, R. G.: “An Economic Model for Investment and Production for Petroleum Reservoirs,” Am. Econ. Rev. 64 (1974) 66-79. [45] Lang, Z. X., and Horne, R. N.: “Optimum Production Scheduling Using Reservoir Simulators: A Comparison of Linear Programming and Dynamic Programming 128
Techniques,” SPE Paper 12159, presented at the 1983 SPE Annual Technical Conference and Exhibition, San Francisco, October 5-8. [46] Lasdon, L., Coffman, P. E., MacDonald, R., McFarland, J. W., and Sepehrnoori, K.: “Optimal Hydrocarbon Reservoir Production Policies,” Operations Research (Jan. 1986) 34, 40-54. [47] Lea, J. F., and Brown, K. E.: “Production Optimization Using a Computerized Well Model,” SPE Paper 14121, presented at the SPE 1986 International Meeting on Petroleum Engineering, Beijing (March 1986). [48] Marquardt, D. W.: “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” J. SIAM (June 1963) 11, No. 2, 431-41. [49] McFarland, J. W., Lasdon, L., and Loose, V.: “Development Planning and Management of Petroleum Reservoirs Using Tank Models and Nonlinear Programming,” Operations Research (Mar. 1984) 32, 270-289. [50] Murray, J. E., III, and Edgar, T. F.: “Optimal Scheduling of Production and Compression in Gas Fields,” J. Petro. Tech. (Jan. 1979) 109-116. [51] Nelder, J. A., and Mead, R.: “A Simplex Method for Function Minimization,” Computer Journal 7, 308-313. [52] O’Dell, P. M., Steubing, N. W., and Gray, J. W.: “Optimization of Gas Field Operation,” J. Petro. Tech. (April 1973) 419-425. [53] Omana, R. et al.: “Multiphase Flow Through Chokes,” SPE Paper 2682 presented at the 1969 SPE Annual Meeting, Denver, Sept. 28 - Oct. 1. [54] Orkiszewski, J.: “Predicting Two-Phase Pressure Drops in Vertical Pipes,” J. Petro. Tech. (June 1967) 829-838. [55] Poettman, F. H., and Carpenter, P. G.: “The Multiphase Flow of Gas, Oil and Water Through Vertical Flow Strings with Application to the Design of Gas Lift Installations,” Drill. and Prod. Prac., API (1952) 257-317. 129
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MULTIVARIATE PRODUCTION SYSTEMS OPT
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iii Approved for the Department: Ro
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Acknowledgements I would like to th
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5.2.4 Determine Partial Fugacities
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List of Figures Figure 1.1 Graphica
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Chapter 1 INTRODUCTION The performa
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eservoir model. Kuller and Cummings
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optimization, it is merely the proc
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Chapter 2 RESERVOIR AND INFLOW PERF
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where RS = V GO S 9 V OO S rS = V O
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The source-sink term of Equation 2.
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Δ φ SG BG + SO RS BO ρGO S S ρG
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3. Estimate the average reservoir p
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which is valid for steady-state, ra
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Chapter 3 VERTICAL MULTIPHASE FLOW
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μNS = μL λL + μG λG 21 (3.8) T
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-dP = 1 Qα + Q β Mα + Mβ g gC d
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• The term NGV NL 0.38 ND 2.14 is
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HL = 1 - 1 2 1 + VM VS - 1 + VM VS
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A paper by Hazim and Nimat (1989) p
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NV ≤ 18 25 18 < NV < 250 69 NV -0
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NWE Nμ > 0.005 ε = 0.3713 σL D 3
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NLV 100. 10. 1.0 0.1 Bubble Griffit
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V M < 10 δ ≥ -0.065 VM V M > 10
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RETURN ΔZ=.95 Δ Z ΔP=.95 Δ Pnew
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• maintain stable pressure downst
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R P = producing gas-liquid ratio, M
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flowrate is straightforward. Fortun
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Mass Flux Residual G1 - G2 0 Spurio
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segregation. The gas phase must exi
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API, GOR, Bo API Gravity First Stag
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Zi = Xi L + Yi V (5.3) where V and
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aα m = ∑ ∑ YiYj aα ij i j bm
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ψ1 = 2 cos θ 3 - Ω 3 (5.28) ψ2
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Chapter 6 NONLINEAR OPTIMIZATION Th
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IMSL (1987). For a broad overview o
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The minimum of a function can occur
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F(x + hj ej - hi ei) F(x - hi ei) F
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6.2.1 The Method of Steepest Descen
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The second step of the Greenstadt (
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direct search method is simple to u
Page 83 and 84: Original Triangular Polytope Worst
Page 85 and 86: Chapter 7 RESULTS Each of the prece
Page 87 and 88: Figure 7.2: Flow Rate Surface of Si
Page 89 and 90: more stable than unmodified Newton
Page 91 and 92: Figure 7.5: Hagedorn and Brown Grad
Page 93 and 94: Figure 7.7: Aziz, Govier, and Fogar
Page 95 and 96: Figure 7.9: Orkeszewski Gradient Ma
Page 97 and 98: The Sachdeva et al. (1986) model wa
Page 99 and 100: Figure 7.11: Constrained Present Va
Page 101 and 102: At the end of each time step, the w
Page 103 and 104: Figure 7.13: Present Value Surface
Page 105 and 106: Figure 7.15: Profile of Tubing Diam
Page 107 and 108: Figure 7.17: Close-up of Tubing Dia
Page 109 and 110: Figure 7.19: First Derivative of Se
Page 111 and 112: Figure 7.21: First Derivative of Tu
Page 113 and 114: Figure 7.23: Second Mixed-Partial D
Page 115 and 116: Figure 7.24: Minimum Eigenvalue of
Page 117 and 118: Figure 7.26: Curvature of Hessian M
Page 119 and 120: Figure 7.27: Convergence Path of Un
Page 121 and 122: Figure 7.29: Convergence Path of Po
Page 123 and 124: Figure 7.31: Convergence Path of Tr
Page 125 and 126: • Nonlinear optimization may be u
Page 127 and 128: Nomenclature Α Area. B Flow regime
Page 129 and 130: xe Expansion point. xr Reflection p
Page 131 and 132: Bibliography [1] Achong, I.: “Rev
Page 133: [23] Charnes, A., and Cooper, W. W.
Page 137: [67] Strang, G.: Introduction to Ap
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