Mark P. WalshPetroleum Recovery Research Institute

Austin, Tex.

Brian F. TowlerUniversity of Wyoming

Laramie, Wyo.

A new simple method computes the black-oil PVT properties of gas condensates. The new algorithm represents a significant improvement over past approaches.

The algorithm is a valuable tool for the reservoir engineer who analyzes gas-condensate reservoirs.

To obtain the so-called black-oil PVT properties (Bo, Bg, Rs, and Rv) of gas condensates, this method requires only data normally available from a standard constant-volume depletion.

The method is rigorous, direct, and simple and is ideally suited for a spreadsheet. Remarkably, no k-value or equation-of-state flash calculations are required as in previous methods. The calculations demand only a fraction of the time required by other methods.

### PVT PROPERTIES

The so-called black-oil PVT properties are routinely used in a wide variety of reservoir engineering calculations, ranging from material-balance calculations to finite-difference numerical simulations.

Differential-vaporization tests are routinely used to determine the fluid properties Bo, Bg, and Rs for black oils. Numerous authors have discussed how the differential-vaporization data are manipulated to derive Bo, Bg, and Rs.1-5 Obtaining the black-oil PVT properties for gas condensates and volatile oils is less straightforward because these reservoir fluids require determination of Rv in addition to Bo, Bg, and Rs.

Rv is the volatile oil-gas ratio and describes the stock-tank-oil content of the reservoir gas phase. Rv is customarily reported in units of stock-tank barrels of lease-condensate per MMscf of gas. Cook, et al.,6 referred to Rv as the "liquid content of the gas." Coats7 referred to it as the "oil vapor in the gas."

Rv is not required for black oils because black-oil reservoirs yield negligible lease-condensate production.

Several authors6-8 have shown how Rv is used in finite-difference, modified-black-oil reservoir simulators, and other references9-12 describe how Rv is used in material-balance calculations.

Several authors have presented methods to determine the black-oil properties for gas condensates.6-8 13 None of these methods are as quick and direct as the new method. The best available methods are probably described by Coats7 and Whitson and Torp.13

In Coats' procedure, a multicomponent equation-of-state (EOS) first matches the results of either a laboratory constant-volume depletion (CVD) or constant-composition expansion (CCE). Then with an optimized EOS description, he predicts the stock-tank-oil and separator-gas yields by flashing the appropriate reservoir-simulated oil and gas mixtures through a hypothetical separator configuration. The black-oil PVT properties are then computed from the predicted separator yields.

Whitson and Torp, on the other hand, start with the high-pressure gas compositions measured from a CVD. They then estimate the corresponding equilibrium oil compositions and flash the compositions through a hypothetical separator configuration to predict the stock-tank-oil and separator-gas yields. The compositions are flashed using Standing's k-values.14 The stock-tank-oil and separator-gas densities are estimated using empirical correlations.16 17 The black-oil PVT properties are then computed from the predicted separator yields.

While both of these approaches appear to yield reasonable results, neither is as direct or simple as our new method.

Our method requires only five measurements which are taken directly from a standard CVD report:

- Oil yield 2. Gas yield
- Gas deviation factor
- Two-phase z-factor
- Retrograde-liquid volume fraction.

These data uniquely determine all black-oil PVT properties of any reservoir fluid, including a gas condensate. The method does not require k-values, equations-of-state, flash routines, or empirical correlations.

Our algorithm is rigorous, direct and simple. It consists of a series of algebraic equations and can be implemented on a spreadsheet in a few minutes. This algorithm is a great improvement over other methods. It also underscores the importance of a CVD to evaluate the phase behavior of gas condensates.

Given the results of a laboratory CVD and limited field production data, this algorithm, together with the generalized material-balance equation9-12 18 gives reservoir engineers a consistent, laboratory-to-field method to estimate oil and gas reserves in gas-condensate reservoirs.

### ALGORITHM

The goal of the algorithm is to compute: Bo, Bg, Rs, and Rv as a function of pressure, given the following CVD data: GP, NP, z, z2, and Vo as a function of pressure, where:

Gp = Cumulative produced gas, Mscf

Np = Cumulative produced oil, st-tk bbl

z = Gas deviation factor

z2 = Two-phase z-factor

Vo = Volume fraction of liquid condensate.

The cumulative produced gas is the sum of the gas produced from all separators. The oil and gas yields Np and GP are customarily reported per MMscf of original reservoir (well stream) fluid. The algorithm requires that these values be input per MMscf of initial separator gas. To covert, simply multiply the values by the scf of original reservoir fluid per scf of initial separator gas.

For example, if 1,000 Mscf of original reservoir fluid contains 885 Mscf of separator gas, then the conversion factor is 1.130.

The "Measured" data in Table 1 (49136 bytes) show the CVD results for Gas Condensate A reported by Core Laboratories.19 The properties are dew point = 3,428 psia, temperature = 200 F., Rvi = 148.06 st-tk bbl/MMscf, and Bgi = 0.7722 res. bbl/Mscf

The algorithm consists of twenty equations. The equations are summarized in the Equation box and the variables are defined in the Nomenclature box. Each of the equations is derived from either a mass balance constraints a manipulation of the real gas law, or a definition. Many of the equations call be combined to yield a fewer number of equations if the user wishes. We have purposely included twenty separate steps for the sake of clarity.

Each intermediate calculation has physical significance. For instance, the intermediate calculations include the total cell volume, oil and gas-phase volumes, fraction of the initial moles remaining, standard cubic feet of gas remaining and stock-tank barrels of oil remaining.

Columns 1-20 in Table 1 (49136 bytes) show the results of Equations 1-20 for Gas Condensate A. Columns 17-20 yield Bo, Bg, Rs, and Rv. Fig. 1 (39318 bytes) plots the black-oil PVT properties as a function of pressure.

All the entries in Row 1, Columns 1-20, follow from their definitions, For example, Row 1, Column 11 requires the initial Mscf of gas in the cell, G1. If the CVD results are based on 1 MMscf of separator gas, then G1 = 1,000 Mscf.

The following equations may be helpful to evaluate the initial entries in some of the other columns. The initial entry in Column 12, N1, is given by:

N1 = G1Rvi (21)

The initial entries in Columns 14 and 12 are equal. The initial entry in Column 4, VTg,1, is given by:

VTg,1 = G1Bgi (22)

The initial entries in Columns 3 and 4 are equal. The quantities Rvi and Bgi are routinely furnished in the CVD report.

The algorithm computes the black-oil PVT properties at each pressure in the CVD except the initial pressure. To find the black-oil PVT properties at my arbitrary pressure between the initial and final pressures in the CVD, one can apply interpolation or extrapolatiOn techniques, To obtain the black oil PVT properties at pressures greater than the initial pressure in the CVD, one should extrapolate data using the standard techniques based on the PVT data from the accompanying constant composition expansion.1

Table 3 (32389 bytes) summarizes the results for a second gas condensate, Gas Condensate B. Gas Condensate B is from the Overthrust Belt.11 12 For the sake of brevity, only the measured CVD data and the black-oil PVT properties are shown. No intermediate calculations are included.

The properties of Gas Condensate B are as follows:

- Dew point pressure 5,450 psia
- Temperature = 215 F.
- Initial volatile oil-gas ratio (Rvi) = 165.5 st-tk bbl/MMscf
- Initial gas formation volume factor (Bgi) = 0.739 reservoir bbl/Mscf.

Fig. 2 (41804 bytes) plots the black-oil properties as a function of pressure.

### REFERENCES

- Amyx, J.W., Bass, D.M. and Whiting, R.J., Petroleum Reservoir Engineering-Physical Properties, McGraw-Hill Book Co., 1960.
- Dodson, C.R., Goodwill, D., and Mayer, E.H., "Application of Laboratory PVT Data to Reservoir Engineering Problems," Trans. AIME, Vol. 198, 1953, pp. 287-98.
- Craft, B.C., and Hawkins, M.F. Jr., Applied Petroleum Reservoir Engineering, Prentice-Hall Inc., 1959.
- Katz, D.L., et. al., Handbook of Natural Gas Engineering, McGraw-Hill Book Co., 1959.
- Standing, M.B., Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems, Society of Petroleum Engineers, 1951.
- Cook, R.E., Jacoby, R.H., and Ramesh, A.B., "A Beta-Type Reservoir Simulator for Approximating Compositional Effects During Gas Injection," SPE Journal, July 1974, pp. 471-81.
- Coats, K.H., "Simulation of Gas Condensate Reservoir Performance," JPT, October 1986, pp. 235-17.
- Spivak, A., and Dixon, T.N., "Simulation of Gas Condensate Reservoirs," Paper No. SPE 4271, SPE Symposium of Reservoir Simulation, Houston, Jan. 10-12, 1973.
- Walsh, M.P., "A Generalized Approach to Reservoir Material Balance Calculations," International Technical Conference of Petroleum Society of CIM, Calgary, May 9-13, 1993, J. Can. Pet. Tech., January 1995, pp. 55-63,
- Walsh, M.P., "New, improved equation solves for volatile oil and condensate reserves," OGJ, Aug. 72, 1994, pp. 72-76.
- Walsh, M.P., Ansah, J., and Raghavan, R., "The New, Generalized Material Balance as an Equation of a Straight Line, Part 1-Applications to Undersaturated, Volumetric Reservoirs," Paper No. SEE 27684, SPE Permian Basin Oil and Gas Conference, Midland, Tex., Mar. 16-18, 1994.
- Walsh, M.P., Ansah, J., and Raghavan, R., "The New Generalized Material Balance As an Equation of a Straight-Line, Part 2 Applications to Saturated and Non-Volumetric Reservoirs," Paper No. SEE 27728, SPE Permian Basin Oil and Gas Recovery Conference, Midland, Tex., Mar. 16-18, 1994.
- Whitson, C.H., and Torp, S.B., "Evaluating Constant-Volume Depletion Data," JET, March 1983, pp. 610-20.
- Standing, M.B., "A Set of Equations for Computing Equilibrium Ratios of a Crude Oil/Natural Gas System at Pressures Below 1,000 psia," JPT, September 1979, pp. 1193-95.
- Alani, G.H., and Kennedy, H.T., "Volumes of Liquid Hydrocarbons at High Temperatures and Pressures," Trans. AIME, 1960, pp. 219, 288-92.
- Standing, M.B., and Katz, D.L., "Vapor/Liquid Equilibria of Natural Gas-Crude Oil Systems," Trans. AIME, 1944, pp, 155, 232-45.
- Walsh, M.P., A Generalized Approach to Petroleum Reservoir Engineering, Petroleum Recovery Research Institute Press, Austin, 1995.
- Kenyon, D.E., and Behie, A., "Third SPE Comparative Solution Project, Gas Cycling of Retrograde Condensate Reservoirs," Paper No. SPE 12278, Reservoir Simulation Symposium, San Francisco, 1983, JPT, August 1987 pp. 981-97.

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