Lecture 9 Liquid Properties 10/10/2014

Liquid Properties The density of liquid at reservoir conditions allows for assessment of oil formation factor, leading to production decisions Ideal liquid solutions Liquid w/ known composition 2 methods to compute density (hard & easy) Liquid & gas w/ unknown composition Correlations for formation volume factors Corrections for pressures above bubble point Viscosity of liquids

Definition Recollection Oil Formation Volume Factor Bo = vol. oil + dissolved gas at reservoir conditions volume oil entering stock tank barrel at s.c. Solution gas-oil Ratio Rs= (volume of dissolved gas at r.c.) (volume of oil entering stock tank at s.c.) B0 Reservoir Pressure Pbp PSC 1.0 Rs Reservoir Pressure Pbp PSC

Ideal Liquid Solution V1 V V2 If “ideal”, volume of mixture is: And density is: V V1 V2

Reservoir Conditions Not Ideal C1-C2are not liquids at standard conditions Partial vaporization of oil at standard conditions Consequences: Composition changes as a function of pressure and time Density at SC difficult to determine because no liquid density available for lighter components

Apparent Liquid Density Use an apparent liquid density (ALD) for methane and ethane ALD: density C1 and C2 if they were liquid at standard conditions ALD represents contribution of methane and ethane to density of the liquid mixture ALD is determined by: 1. Measuring densities at elevated p and T for mixtures of methane & heavier, and ethane & heavier 2. Using compressibility and thermal expansion factors to go back to s.c. 3. Subtracting contribution by heavier components

ALD Chart This chart gives the ALD as a function of the density of the complete system at SC The density of the complete system is called the pseudoliquid density of the system McCain Fig. 11-2 Standing and Katz, Trans., AIME, 146, 159.

ALD Chart This chart gives the ALD as a function of the density of the complete system at SC The density of the complete system is called the pseudoliquid density of the system McCain Fig. 11-2 Standing and Katz, Trans., AIME, 146, 159. 1 g/cc = 62.4 lb/cu. ft

ALD Chart This chart gives the ALD as a function of the density of the complete system at SC The density of the complete system is called the pseudoliquid density of the system McCain Fig. 11-2 Standing and Katz, Trans., AIME, 146, 159. 1 g/cc = 62.4 lb/cu. ft Cannot use this chart without having a prior estimate of the density at SC

Isothermal Compressibility Chart This chart gives necessary compressibility corrections McCain Fig. 11-3 Standing, Volumetric and Phase Behavior of Oild Field Hydrocarbons, SPE, Dallas, 1951.

Isothermal Compressibility Chart This chart gives necessary thermal expansion corrections Approx. independent of pressure McCain Fig. 11-4

Procedure If we want liquid density @ RC, then we need: pseudoliquid density @ SC RC Pseudoliquid correction charts

Procedure If we want liquid density @ RC, then we need: pseudoliquid density @ SC BUT If we want pseudoliquid density @ SC, then we need: ALD of methane and ethane RC Pseudoliquid correction charts ALD Chart

Procedure If we want liquid density @ RC, then we need: pseudoliquid density @ SC BUT If we want pseudoliquid density @ SC, then we need: ALD of methane and ethane HOWEVER If we want the ALD of C1 and C2, Then we need: pseudoliquid density @ SC RC Pseudoliquid correction charts ALD Chart

Procedure If we want liquid density @ RC, then we need: pseudoliquid density @ SC BUT If we want pseudoliquid density @ SC, then we need: ALD of methane and ethane HOWEVER If we want the ALD of C1 and C2, Then we need: pseudoliquid density @ SC RC Pseudoliquid correction charts ALD Chart

Iterative Approach 1. Guess the pseudoliquid density at SC 2. Determine corresponding apparent liquid densities 3. Compute corresponding pseudoliquid density. If same as guess, stop. 4. Repeat for a second initial guess 5. Plot guesses and computed pseudoliquid densities 6. Determine point on graph for which y = x

Example Compute the density of a reservoir liquid at its bubble point at 3280 psia and 218 F with the following composition of well stream. Initial Guess: 47 lb/cu ft

Example

Example – Guess 1

Example

Example – Guess 2

Example

Compressibility and Thermal Expansion Compressibility correction = +0.9 Thermal expansion correction = -4.4 Density at reservoir conditions is 50.5 + 0.9 - 4.4 = 47.0 lb/cu ft

Simpler Method 1. Compute weight fraction W1 of methane in the mixture 2. Compute weight fraction W2 of ethane in ethane+ mixture 3. Read density ratio from Fig. 11-6 in McCain 4. Multiply density ratio by density of propane+ which gives pseudoliquid density Then: find density at reservoir conditions using compressibility and thermal expansion charts

Simpler Method The weight fraction of C1 in the mixture is: The weight fraction of C2 in C2+ is: Figure 7-5 gives a density ratio of approx. 0.92 The density of C3+ is: which leads to a pseudoliquid density of 50.0 lb/cu ft (note a slightly different result than before).

Simpler Method 1. Compute weight fraction W1 of methane in the mixture 2. Compute weight fraction W2 of ethane in ethane+ mixture 3. Read density ratio from Fig. 11-6 in McCain 4. Multiply density ratio by density of propane+ which gives pseudoliquid density Then: find density at reservoir conditions using compressibility and thermal expansion charts 0.915

Simpler Method The weight fraction of C1 in the mixture is: The weight fraction of C2 in C2+ is: Figure 7-5 gives a density ratio of approx. 0.92 The density of C3+ is: which leads to a pseudoliquid density of 49.7 lb/cu ft (note a slightly different result than before).

Compressibility and Thermal Expansion Compressibility correction = +0.9 Thermal expansion correction = -4.4 Density at reservoir conditions is 50.0 + 0.9 - 4.4 = 46.5 lb/cu ft

Unknown Compositions Reservoir liquid composition is commonly unknown Typical knowns are: solution gas-oil ratio, Rs specific gravity of gas at SC API of crude at SC(related to specific gravity) (Fig. 11-8 in McCain) gives apparent liquid density of gas as function of gas specific gravity and °API of crude Results usually within 5% of measured values

Apparent Liquid Densities of Natural Gas

Class Example Sep. 1 Sep. 2 Tank Total Produced Rs in scf/STB 414.0 90.0 25.0 529.0 Specific gravity of gas 0.640 0.897 1.54 The tank oil has a gravity of 27.4 °API (or a specific gravity of 0.891). The reservoir is at 3280 psia (bubble point pressure) and 218 °F Compute the density of the oil in the reservoir. Also, compute the formation volume factor of the oil. 5.615 cubic feet in 1 STB, 62.4 lb of water in 1 cu ft of water @ SC 1lb mole of gas occupies a volume of 379 scf @ SC

Steps Calculate the specific gravity of the overall gas Calculate the apparent liquid density of gas Calculate the mass of the gas Calculate the mass of the stock tank oil Calculate the pseudoliquid volume of gas Calculate the pseudoliquid density of reservoir oil @ SC Calculate the density of the reservoir oil @ RC Calculate the volume of the reservoir oil @ RC Calculate the formation volume factor

Solution Calculate the specific gravity of the overall gas

Solution Calculate the specific gravity of the overall gas 414.0 × 0.640 + 90.0 × 0.897 + 25.0 × 1.54 (414.0 + 90.0 + 25.0) = 0.726

Solution Calculate the specific gravity of the overall gas 414.0 × 0.640 + 90.0 × 0.897 + 25.0 × 1.54 (414.0 + 90.0 + 25.0) = 0.726 Calculate the apparent liquid density of gas 0.726 and API of 27.4 gives reading of 24.9 lb/cu ft at s.c.

Solution Calculate the mass of the gas MW: 0.726 × 28.97 lb/lb mole = 21.0 lb/lb mole. Vol. in scf: 414.0 + 90.0 + 25.0 = 529.0 scf. Mass: 529.0 scf/STB / 379 scf/lb mol × 21.0= 29.3 lb/STB

Solution Calculate the mass of the gas MW: 0.726 × 28.97 lb/lb mole = 21.0 lb/lb mole. Vol. in scf: 414.0 + 90.0 + 25.0 = 529.0 scf. Mass: 529.0 scf/STB / 379 scf/lb mol × 21.0= 29.3 lb/STB Calculate the mass of the stock tank oil 0.891 × 62.4 lb/cu ft × 5.615 cu ft/STB = 312 lb/STB STB).

Solution Calculate the pseudoliquid volume of gas 29.3 lb/STB / 24.9 lb/cu ft = 1.18 cu ft/STB

Solution Calculate the pseudoliquid volume of gas 29.3 lb/STB / 24.9 lb/cu ft = 1.18 cu ft/STB Calculate the pseudoliquid density of reservoir oil @ SC Total volume: 1.18 + 5.615 = 6.79 cu ft/STB Total mass: 29.3 + 312 = 341 lb/STB Density: 341 / 6.79 = 50.2 lb/cu ft

Solution Calculate the density of the reservoir oil @ RC Compressibility = +0.90 lb/cu ft Thermal expansion = -4.8 lb/cu ft 50.2 + 0.9 - 4.8 = 45.9 lb/cu ft

Solution Calculate the volume of the reservoir oil @ RC 341 lb/STB / 45.9 lb/cu ft = 7.42 cu ft/STB Calculate the formation volume factor 7.42 cu ft/STB / 5.615 cu ft/bbl = 1.28 bbl/STB.

Example Compute the density of a reservoir liquid at its bubble point at 3280 psia and 218 F with the following composition of well stream. Initial Guess: 49 lb/cu. ft. OR 0.785 g/cc

Example

Example – Guess 1

Example 2nd Guess = 53 lb//cu ft

Example – Guess 2

Example

Compressibility and Thermal Expansion Compressibility correction = +0.9 Thermal expansion correction = -4.4 Density at reservoir conditions is 50.5 + 0.9 - 4.4 = 47.0 lb/cu ft