multivariate production systems optimization - Stanford University

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$Drilling-induced tensile wall-fractures - Stanford University$

Chapter 5 PHASE SEPARATION The well stream that arrives at the surface consists of multiple phases such as oil, gas, water, and possibly sand. Before the hydrocarbon well stream may be directed to storage facilities or delivered to market, it must first be separated into the discrete phases present. Gas pipelines stipulate maximum levels of water vapor content and contaminants. Oil purchase contracts specify the maximum amount of basic sediment and water that is allowable in the crude. The most common form of isolating the gas and liquid phases present in a well stream is to pass the stream through a separator (see Figure 5.1). A separator is typically maintained at a constant operating pressure by controlling the effluence from the separator with backpressure valves. A separator is designed to provide sufficient time for the various phases of the well stream to equilibrate and separate by means of gravity Inlet Inlet Diverter Figure 5.1: Schematic of Horizontal Separator. 49 Mist Extractor Gas Liquid Interface Pressure Control Valve Gas Out Level Control Valve Liquid Out
segregation. The gas phase must exit from the top of the separator whereas the liquid phase must exit from the bottom. The resulting gas may then be passed to a glycol dehydrator for further removal of water vapor and contaminants before being delivered to a pipeline. The liquid stream coming out of a separator may be passed through additional separators operating at successively lower pressures before finally being delivered to the stock tank (see Figure 5.2). Alternatively, the liquid stream may be passed through gunbarrels, free water knock-outs, skim tanks, and heater treaters depending on the specific treating requirements. Any solids present in the well stream are usually removed by the force of gravity which may be augmented by hydrocyclones. PC Feed High Pressure Separator 1 psig Stock Tank Gas Out PC Intermediate Pressure Separator Figure 5.2: Stage Separation (from Arnold 1986). 50 Gas Out PC Low Pressure Separator Gas Out
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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
Page 7 and 8: 5.2.4 Determine Partial Fugacities
Page 9 and 10: List of Figures Figure 1.1 Graphica
Page 11 and 12: Chapter 1 INTRODUCTION The performa
Page 13 and 14: eservoir model. Kuller and Cummings
Page 15 and 16: optimization, it is merely the proc
Page 17 and 18: Chapter 2 RESERVOIR AND INFLOW PERF
Page 19 and 20: where RS = V GO S 9 V OO S rS = V O
Page 21 and 22: The source-sink term of Equation 2.
Page 23 and 24: Δ φ SG BG + SO RS BO ρGO S S ρG
Page 25 and 26: 3. Estimate the average reservoir p
Page 27 and 28: which is valid for steady-state, ra
Page 29 and 30: Chapter 3 VERTICAL MULTIPHASE FLOW
Page 31 and 32: μNS = μL λL + μG λG 21 (3.8) T
Page 33 and 34: -dP = 1 Qα + Q β Mα + Mβ g gC d
Page 35 and 36: • The term NGV NL 0.38 ND 2.14 is
Page 37 and 38: HL = 1 - 1 2 1 + VM VS - 1 + VM VS
Page 39 and 40: A paper by Hazim and Nimat (1989) p
Page 41 and 42: NV ≤ 18 25 18 < NV < 250 69 NV -0
Page 43 and 44: NWE Nμ > 0.005 ε = 0.3713 σL D 3
Page 45 and 46: NLV 100. 10. 1.0 0.1 Bubble Griffit
Page 47 and 48: V M < 10 δ ≥ -0.065 VM V M > 10
Page 49 and 50: RETURN ΔZ=.95 Δ Z ΔP=.95 Δ Pnew
Page 51 and 52: • maintain stable pressure downst
Page 53 and 54: R P = producing gas-liquid ratio, M
Page 55 and 56: flowrate is straightforward. Fortun
Page 57: Mass Flux Residual G1 - G2 0 Spurio
Page 61 and 62: API, GOR, Bo API Gravity First Stag
Page 63 and 64: Zi = Xi L + Yi V (5.3) where V and
Page 65 and 66: aα m = ∑ ∑ YiYj aα ij i j bm
Page 67 and 68: ψ1 = 2 cos θ 3 - Ω 3 (5.28) ψ2
Page 69 and 70: Chapter 6 NONLINEAR OPTIMIZATION Th
Page 71 and 72: IMSL (1987). For a broad overview o
Page 73 and 74: The minimum of a function can occur
Page 75 and 76: F(x + hj ej - hi ei) F(x - hi ei) F
Page 77 and 78: 6.2.1 The Method of Steepest Descen
Page 79 and 80: The second step of the Greenstadt (
Page 81 and 82: 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
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Figure 7.21: First Derivative of Tu
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Figure 7.23: Second Mixed-Partial D
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Figure 7.24: Minimum Eigenvalue of
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Figure 7.26: Curvature of Hessian M
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Figure 7.27: Convergence Path of Un
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Figure 7.29: Convergence Path of Po
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Figure 7.31: Convergence Path of Tr
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• Nonlinear optimization may be u
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Nomenclature Α Area. B Flow regime
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xe Expansion point. xr Reflection p
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Bibliography [1] Achong, I.: “Rev
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[23] Charnes, A., and Cooper, W. W.
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Techniques,” SPE Paper 12159, pre
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[67] Strang, G.: Introduction to Ap
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