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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

PVT    DATA

	Pressure	Oil FVF Bo	Solution GOR Rs	Gas FVF Bg	Oil Viscosity μo	Gas Viscosity μg
#	psi	rbbl/stb	scf/stb	rbbl/scf	cp	cp
1	max.
2
3
4
5
6
7
8
9
10
11
12
13
14
15

RELATIVE  PERMEABILITY   DATA

	Total Liquid Saturation SL	Relative Permeability Ratio (kg/ko)
#
1	min.
2
3
4
5
6
7
8
9
10
11
12
13
14
15

RESERVOIR  &   WELL   DATA

Initial Water Saturation		fraction
Original Oil In Place		bbls
Gas Cap to Oil Pore Vol		ratio
Number of Wells
Average Initial PI of wells		bbl/psi
Well FBH pressure		psi

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OUTPUT   VARIABLES   &   GRAPHS

	Pressure	Cumulative Oil Production	Instantaneous Gas Oil Ratio	Cumulative Gas Production	Krg/kro	Oil Recovery Factor	Oil Production Rate	Time
#	psi	bbl	scf/bbl	scf		%	bbl/day	months
1
2
3
:

Material Balance Equation - Solution Gas Drive/Gas-Cap Drive

The M.B.E. remains an important analytical tool in reservoir engineering, employed mainly in the preliminary design of reservoir development and operations, prelude/complement to fully-fledged reservoir simulation, and in economic/planning studies.

The modified Schilthuis procedure is implemented here to compute oil and gas production from a combination of solution gas drive/gas-cap drive reservoir producing at or below the bubble-point pressure. Direct production/injection of gas fro/to the gas cap is not included here. It is assumed that the gas-oil contact does not move into the oil zone, but gas expansion from the gas cap will diffuse through the oil zone. Also water encroachment is considered negligible.

User Input: The user is expected to enter PVT and Relative-Permeability data, each consisting of 10 to 15 data points. The PVT pressure values should be in descending order and pressure intervals must be constant. The liquid saturation values in the Rel. Perm table, should be in ascending order rising to 1.0. For rate-time prediction, the required data are: number of oil wells, and the wells' average initial productivity index and flowing bottomhole pressure. Not all the wells are considered active in day one. A constant drilling policy is assumed, i.e. a more or less equal number of new wells are brought into production at each new pressure step.

The main MBE equation and three auxillary equations are given below:

where:
     SDI = solution gas drive index
     GDI = gas-cap gas drive index
     N = initial oil in place, bbl
     N_Pn = cumulative oil produced at pressure step n, fraction of N
     G_Pn = cumulative gas produced at pressure step n, fraction of N
     M_i = initial ratio of gas-cap to oil reservoir pore space
     B_t = two-phase formation vol. factor at pressure step n
     B_o = oil formation vol. factor at pressure step n
     B_oi = initial oil formation volume factor, bbl/scf
     B_gn = gas formation vol. factor at pressure step n
     B_gi = initial gas formation volume factor, res.bbl/scf
     R_sn = solution gas-oil ratio at pressure step n
     R_si = initial solution gas-oil ratio, scf/bbl
     R_In = instataneous gas-oil ratio
     S_Ln = total liquid saturation at pressure step n
     S_w = water saturation
     μ = viscosity, cp
     k = permeability, mD

The productivity index (J) decline relative to the initial productivity index (J_i) is approximated by:
          J = J_i[1 - S_wi]³[μ_oB_o]/ [μ_oiB_oi]

The cubic spline interpolation method is used to generate continuous values of relative perm. data from the entered set of discrete values.

BIBLIOGRAPHY

• Dake L.P.; Fundamentals Of Reservoir Engineering; Elsevier Scientific Publ. Co., Amsterdam, The Netherlands, 1979, chap. 3.
• Ahmed T.; Reservoir Engineering Handbook; Gulf Publ. Co., Houston, Texas, 2000, chap. 11.
• Sinha M.K. & Padget L.R.; Reservoir Engineering Techniques Using Fortran; IHRD Corp, Boston, 1985, chap. II.9.
• Mian M.A.; Petroleum Engineering Handbook For the Practicing Engineer; Pennwell Publ Co, Tulsa, 1992, vol I, chap. 4.