multivariate production systems optimization - Stanford University

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5.1 Optimization of Phase Separation The <strong>optimization</strong> of phase separation practices is important because by varying the blend of surface oil and gas produced per reservoir volume, an operator may markedly affect the total value of the mix. The total value of the mix is affected by the fractional volumes produced of each phase as well as the quality of each phase. The fractional volume of each phase is important because traditionally the market has paid a significant premium for hydrocarbons in the liquid phase. At times, the vapor phase was considered to be of no economic value, prompting operators to flare the gas rather than attempt to find a market for it. In addition to the gross volume produced of the oil and gas phases, the total value is affected by the quality of the phases. A gas price is adjusted for the BTU content while the price paid for crude varies with the API gravity of the oil. An important concept in surface phase separation is that the fractional liquid recovery will always be enhanced by adding more separators between the wellhead and the stock tank. By increasing the number of separators, the liberation process between the wellhead and the stock tank is essentially transformed from a flash liberation process to a differential liberation process, thus improving the fractional liquid recovery. In a stage separation process, the light hydrocarbons molecules that flash are removed at relatively high pressure, keeping the partial pressure of the intermediate hydrocarbons lower at each stage. As the number of stages approaches infinity, the lighter molecules are removed as soon as they are formed and the partial pressure of the intermediate components is maximized at each stage. An equally important concept is that for a finite number of separators, there is an optimal combination of discrete separator pressures that will maximize the fractional liquids recovery. At the optimal combination of separator pressures, the API gravity of the crude will be maximized and the gas-oil ratio will minimized (see Figure 5.3). To mimic the behavior of surface facilities, this study elected to model the performance of a two-stage separation process. A two-stage separation process involves flashing the well stream initially at the separator operating conditions and then flashing the resulting liquid stream at stock tank conditions. Assuming the temperatures of the two stages to be constant and by setting the stock tank pressure to atmospheric pressure, the separator pressure can be optimized to yield the most beneficial mix of oil and gas fractional recoveries. 51
API, GOR, Bo API Gravity First Stage Separator Pressure, psi 52 Total Gas-Oil Ratio Formation Volume Factor Figure 5.3: Effect of Separator Pressure in a Two-Stage Separation Process (from Amyx, Bass, &Whiting 1960). 5.2 Flash Equilibria A mixture is flashed by being suddenly exposed to a new temperature and pressure at which it must re-equilibrate. A flash calculation takes the overall composition of a mixture and determines the resulting phase equilibria at a new temperature and pressure, such as the number of phases present and the composition and amount of each phase. The procedure of performing a flash calculation is iterative and converges when the fugacity of each component is the same in both phases. The basic procedure of a flash calculation involves six steps: 1) Given the composition of the mixture, Zi , at a temperature T and pressure P, guess the resulting compositions of the gas and liquid phases, Yi and Xi respectively.
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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
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 and 58: Mass Flux Residual G1 - G2 0 Spurio
Page 59: segregation. The gas phase must exi
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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