Persamaan Umum Material BalanceSehingga

Analisa Garis Lurus Havlena OdehF = N [Eo + m Eg + Ec] + We Maka analisa Havlena odeh adalah :

ANALISA GARIS LURUS HAVLENA ODEHPersamaan 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. Ec =

Eg adalah merupakan ekspansi dari tudung gas awal (initial gas cap)

Eg = Bti [(Bg/Bgi) 1]

KRITERIA METODE HAVLENA ODEHVolumetric Undersaturated-Oil ReservoirsVolumetric Saturated-Oil ReservoirsGas-Cap-Drive ReservoirsWater-Drive Reservoirs

A. Volumetric Undersaturated-Oil ReservoirsWe = 0, m = 0, Rs = Rsi = Rp(1)

Plot F vs (Eo+Ec)Gambar 1

TUGAS 2The Virginia Hills Beaverhill Lake field is a volumetric undersaturated reservoir. Volumetric calculations indicate the reservoir contains 270.6 MMSTB of oil initially in place. The initial reservoir pressure is 3685 psi. The following additional data is available:Swi = 24%, cw = 3.62 x 106 psi1, cf = 4.95 x 106 psi1, Bw = 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.

Data Produksi dan PVT

B. Volumetric Saturated-Oil Reservoirs Assuming that the water and rock expansion term Ec is negligible in comparison with the expansion of solution gas,

F = N Eo(2)

C. Gas-Cap-Drive ReservoirsFor 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), the effect of water and pore compressibilities can be considered negligible.F = N [Eo + m Eg]The practical use of Equation above in determining the three possible unknowns is presented below:(3)

Equation (3) indicates that a plot of F versus (Eo + m Eg) on aCartesian scale would produce a straight line through the origin with a slope of N, as shown in Figure 2. In making the plot, the underground withdrawal F can be calculated at various times as a function of the production terms Np and Rp.Conclusion: N = Slopea. Unknown N, known m:

Gambar 2

b. Unknown m, known N:Equation (3) can be rearranged as an equation of straight line, to give: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. One advantage of this particular arrangement is that the straight line must pass through the origin which, therefore, acts as a control point. Figure 3 shows an illustration of such a plot.Conclusion: m = Slope(4)

Gambar 3

c. N and m are UnknownIf there is uncertainty in both the values of N and m, Equation (3)can be re-expressed as:A plot of F/Eo versus Eg/Eo should then be linear with intercept N and slope mN.Conclusions: N = intercept mN = slope m = slope/intercept(5)

Gambar 4

D. Water-Drive ReservoirsFor a water-drive reservoir with no gas cap, the equation can beexpressed as:Several water influx models including the: Pot-aquifer model Schilthuis steady-state method Van Everdingen-Hurst model(6)

The Pot-Aquifer Model in the MBE

We = (cw + cf) Wi f (pi p)Where, ra = radius of the aquifer, ftre = radius of the reservoir, fth = thickness of the aquifer, ft = porosity of the aquifer = encroachment anglecw = aquifer water compressibility, psi1cf = aquifer rock compressibility, psi1Wi = initial volume of water in the aquifer, bbl(7)

Since the aquifer properties cw, cf, h, ra, and are seldom available, it is convenient to combine these properties and treated as one unknown K. We = K pSehingga Persamaan 6 menjadi :Equation (9) indicates that a plot of the term (F/Eo) as a function of (p/Eo) would yield a straight line with an intercept of N and slope of K, as illustrated in Figure 5.(8)(9)

Gambar 5

The Steady-State Model in the MBEThe steady-state aquifer model as proposed by Schilthuis (1936) is given by:Where,We = cumulative water influx, bblC = water influx constant, bbl/day/psit = time, dayspi = initial reservoir pressure, psip = pressure at the oil-water contact at time t, psi

Plotting (F/Eo) versus results in a straight line 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 Unsteady-State Model in the MBEThe van Everdingen-Hurst unsteady-state model is given by:We = B p WeDVan 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 ( p WeD)/Eo on a Cartesian scale. If theassumed aquifer parameters are correct, the plot will be a straightline with N being the intercept and the water influx constant Bbeing the slope. It should be noted that four other different plotsmight result. These are:

Gambar 7