Persamaan Umum Material BalanceN Np Bo ( Rp Rs) Bg (We WpBw) Bg SwiCw Cf ( Bo Boi) ( Rsi Rs ) Bg mBoi 1 Boi (1 m) P Bgi 1 Swi ) Sehingga Np Bo ( Rp Rs ) Bg WpBw Bg SwiCw Cf 1 N (1 m) Boi P 1 Swi Bgi N ( Bo Boi ) ( Rsi Rs) Bg mNBoi Analisa Garis Lurus Havlena Odeh Np Bo ( Rp Rs ) Bg WpBw Bg SwiCw Cf 1 N (1 m) Boi P Bgi 1 Swi N ( Bo Boi ) ( Rsi Rs) Bg mNBoi Maka analisa Havlena odeh adalah : F = N [Eo + m Eg + Ec] + We Ec = SwiCw Cf P 1 Swi (1 m) Boi Eg adalah merupakan ekspansi dari tudung gas awal (initial gas cap) Eg = Bti [(Bg/Bgi) − 1] .ANALISA GARIS LURUS HAVLENA ODEH Persamaan Dalam Metode Havlena Odeh F adalah volume reservoir yaitu jumlah dari minyak. gas dan produksi air. F = Np[Bo + (Rp – Rs) Bg] + WpBw F = Np[Bt + (Rp – Rsi) Bg] + WpBw Eo adalah ekspansi dari volume minyak dan dissolved gas Eo = (Bo – Boi) + (Rsi – Rs)Bg = (Bt – Bti) Ec adalah persamaan kompresi yaitu ekspansi air pada ruang pori batuan. C. B. Volumetric Undersaturated-Oil Reservoirs Volumetric Saturated-Oil Reservoirs Gas-Cap-Drive Reservoirs Water-Drive Reservoirs .KRITERIA METODE HAVLENA ODEH A. D. Volumetric Undersaturated-Oil Reservoirs We = 0. m = 0.A. Rs = Rsi = Rp F N (E o Ec ) 0 y a x b (…1) . Plot F vs (Eo+Ec) Gambar 1 . 95 x 10−6 psi−1. The initial reservoir pressure is 3685 psi.TUGAS 2 The Virginia Hills Beaverhill Lake field is a volumetric undersaturated reservoir. Volumetric calculations indicate the reservoir contains 270.62 x 10−6 psi−1.0 bbl/STB pb = 1500 psi Calculate the initial oil in place by using the MBE and compare with the volumetric estimate of N. cw = 3. cf = 4. . The following additional data is available: Swi = 24%.6 MMSTB of oil initially in place. Bw = 1. 3102 0 0 3680 2 1.330 8.557 0 3664 4 1.3109 215.481 0 3676 2 1.3104 34.3116 364.846 0 3640 19 1.530 2.579 3360 59 1.750 0 3667 3 1.613 0 3567 36 1.3170 2575. of Bo Np Wp Average Pressure producing wells bbl/STB MSTB 3685 1 1.159 3515 48 1.500 3188 61 1.681 0 3605 25 1.3150 1691.3128 841.805 3448 59 1.077 6.3122 542.591 0.3160 2127.3105 78.887 5.3130 1273.Data Produksi dan PVT Volumetric No.3105 101.008 3275 61 1.3104 20.000 MSTB .985 0. B. F = N Eo (…2) . Volumetric Saturated-Oil Reservoirs Assuming that the water and rock expansion term Ec is negligible in comparison with the expansion of solution gas. C. the effect of water and pore compressibilities can be considered negligible. F = N [Eo + m Eg] (…3) The practical use of Equation above in determining the three possible unknowns is presented below: . Gas-Cap-Drive Reservoirs For a reservoir in which the expansion of the gas-cap gas is the predominant driving mechanism and assuming that the natural water influx is negligible (We = 0). In making the plot.a. Unknown N. as shown in Figure 2. known m: Equation (3) indicates that a plot of F versus (Eo + m Eg) on a Cartesian scale would produce a straight line through the origin with a slope of N. the underground withdrawal F can be calculated at various times as a function of the production terms Np and Rp. Conclusion: N = Slope . Gambar 2 . One advantage of this particular arrangement is that the straight line must pass through the origin which. known N: Equation (3) can be rearranged as an equation of straight line. to give: F Eo mEg N (…4) The above relationship shows that a plot of the term (F/N − Eo) versus Eg would produce a straight line with a slope of m.b. acts as a control point. therefore. Conclusion: m = Slope . Figure 3 shows an illustration of such a plot. Unknown m. Gambar 3 . Conclusions: N = intercept mN = slope m = slope/intercept . N and m are Unknown If there is uncertainty in both the values of N and m.c. Equation (3) can be re-expressed as: F Eg N mN Eo Eo (…5) A plot of F/Eo versus Eg/Eo should then be linear with intercept N and slope mN. Gambar 4 . Water-Drive Reservoirs For a water-drive reservoir with no gas cap.D. the equation can be expressed as: F We N Eo Eo (…6) Several water influx models including the: • Pot-aquifer model • Schilthuis steady-state method • Van Everdingen-Hurst model . The Pot-Aquifer Model in the MBE We = (cw + cf) Wi f (pi − p) (Enroachment angle) o f 360 o (ra2 re2 )h Wi 5. bbl . ft φ = porosity of the aquifer θ = encroachment angle cw = aquifer water compressibility. psi−1 cf = aquifer rock compressibility. ft re = radius of the reservoir. psi−1 Wi = initial volume of water in the aquifer. ft h = thickness of the aquifer.615 360 o (…7) Where. ra = radius of the aquifer. it is convenient to combine these properties and treated as one unknown K. as illustrated in Figure 5. We = K Δp (…8) Sehingga Persamaan 6 menjadi : F p N K Eo Eo (…9) Equation (9) indicates that a plot of the term (F/Eo) as a function of (Δp/Eo) would yield a straight line with an intercept of N and slope of K. and θ are seldom available. cf. ra.Since the aquifer properties cw. h. . Gambar 5 . bbl/day/psi t = time. psi p = pressure at the oil-water contact at time t. We = cumulative water influx.The Steady-State Model in the MBE The steady-state aquifer model as proposed by Schilthuis (1936) is given by: 1 We C (( pi p )dt 0 Where. days pi = initial reservoir pressure. bbl C = water influx constant. psi F N C Eo 1 ( pi p )dt Eo 0 . . 1 F N C Eo ( pi p )dt Eo 0 1 Plotting (F/Eo) versus ( pi p)dt / Eo results in a straight line 0 with an intercept that represents the initial oil in place N and a slope that describes the water influx C as shown in Figure 6. Gambar 6 . the plot will be a straight line with N being the intercept and the water influx constant B being the slope. If the assumed aquifer parameters are correct. It should be noted that four other different plots might result.The Unsteady-State Model in the MBE The van Everdingen-Hurst unsteady-state model is given by: We = B Σ Δp WeD B 1. These are: .119C t re2 hf Van Everdingen and Hurst presented the dimensionless water influx WeD as a function of the dimensionless time tD and dimensionless radius rD that are given by: Plot (F/Eo) versus (Σ Δp WeD)/Eo on a Cartesian scale. F Eo pW eD Eo Gambar 7 .