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HW 13 Gas Compressibility.docx

Petr 3520

HW 13: Gas Compressibility (cg)

Assigned: Thurs, Feb 26, 2015 Name:

Due: Mon, March 2, 2015

cg Equations: Ideal Gas: Real Gas:

1. Derive cg for an ideal gas.

2. Derive cg for a real gas.

3. Calculate cg for an ideal gas at p = 300 psi.

4. Calculate cg for methane (treat as a real gas) at T = 320°F and p = 1500 psi. (Read z’s from pure methane chart, calculate z/p from discrete z and p values.) Compare with cg from Excel for pure methane.

5. Calculate cg for methane (treat as a real gas) at T = 176 °F and p = 3500 psi. (Read z’s from pure methane chart or from get from Excel, calculate z/p from discrete z and p values.) Compare with cg from Excel for pure methane.

Answers: 3. cg = 0.00333 psi-1 ; 4. cg = 646.86*10-6 psi-1 (Excel: 645.8*10-6 psi-1 ); 5. Z values read from chart: cg = 243*10-6 psi-1 ; Z values read from Excel DAK: cg = 242.4*10-6 psi-1 ; (Excel: cg = 232.5*10-6 psi-1 )

201

psi

HW 14 Intro to FVFs and Units(1) (1).docx

Petr 3520

HW 14: Intro to FVF’s and Units

Assigned: Fri, Feb 27, 2015 Name:

Due: Mon, March 2, 2015

1. Unit conversions:

(a) How many ft3 are in one (oil field) barrel?

(b) How many gallons are in one (oil field) barrel?

(d) What is the typical (U.S.) standard temperature (Tsc) and pressure (psc)?

(e) What is a “reservoir barrel” (RVB) of oil?

(f) What is a STB of oil?

(g) What is a RCF of gas? An SCF of gas?

(h) What is an MCF (aka MSCF) of gas?

2. Describe what happens to a unit volume (1 RCF) of gas at TR, pR (reservoir conditions) when it is brought to the surface at Tsc, psc (surface conditions).

3. Describe what happens to a unit volume (1 RVB) of oil at TR, pR (reservoir conditions) when it is brought to the surface at Tsc, psc (surface conditions).

4. Define: (a) Oil formation volume factor, Bo.

(b) Gas formation volume factor, Bg.

5. (a) Draw Bo vs. p curve. (b) Derive the equation (using oil compressibility co) that defines the Bo curve above the bubble point pb; (c) For Bob = 1.3 RVB/STB, co = 8*10-6 psi-1, and pb = 4000 psi, determine Bo at p = 4400 psi.

6. Draw: (a) Bg vs. p curve; (b) Rs vs. p curve; (c) o vs. p curve.

202

lectures.zip

16b Intro to Black Oil Properties and Determination.pdf

Petr 3520: Reservoir Engineering Lecture 16: Intro to Black Oil Properties and Determination

Introduction: Reservoir oil can be “volatile or high shrinkage oil,” “low shrinkage (black) oil,” or a heavy oil. All are complex mixtures of 1000’s of various kinds of hydrocarbon molecules. The complete PVT behavior of these is rarely

completely described or determined. (For example, you will almost never see a complete p-V or p-T diagram for an oil

system.) Petroleum engineers most often use a simplified fluid property description of the system called a “black oil”

model. A “black oil” fluid description of an oil system consists of the following properties:

Commonly Needed Black Oil Properties

Oil: Single Values: Bubble Point Pressure, pb

Oil Stock Tank Gravity, °API or o

(Over a pressure range)

(Esp. at pb)

Oil Formation Volume Factor, Bo vs. p [RVB/STB]

Solution Gas Oil Ratio, Rs vs. p [MCF/STB or SCF/STB]

Oil Viscosity, o vs. p

Oil Compressibility, co (often considered constant above pb)

Gas:

(Associated with the oil)

Single Values: Gas Gravity, g

(Over a pressure range) Gas Formation Volume Factor, Bg vs. p

Gas Viscosity, g vs. p

Two Ways to Obtain Black Oil Properties:

1. Correlations: Easy. Cheap. Require a few basic pieces of data (o or °API, g , TR ). But are they correct for our oil system?

2. Lab test of actual fluid: Most accurate (as long as have representative fluid sample). Expensive.

How obtain fluid sample? Two ways: (a) Downhole sample (at p and T); (b) Recombine surface flows of oil and gas (must do this in proper proportion!).

Determining Black Oil Properties: Think! You Design Experiments or Tests for These!

1. Bubble Point?

2. Oil FVF, Bo? Solution GOR, Rs?

3. Gas FVF, Bg?

4. Viscosity (of oil or gas)?

16c Black Oil Correlations Example Probs.pdf

16d Black Oil Property Distributions for Correlations.pdf

Petr 3520: Black Oil Properties (Typical Ranges)

Definitions:

Oil Gravity = API Gravity (°API): 141.5

API 131.5 o 

  o = Spec Gravity of Oil

Gas Gravity =  = MW/28.96 Temperature = Reservoir Temperature ( °F)

Bubble Point = pb (psi) FVF = Oil Formation Volume Factor (Bo) = RVB/STB

Solution Gas Oil Ratio (GOR) = Rs = SCF/STB or MCF/STB

17a PVT Black Oil Property Correlations Intro 1.pdf

Sample Black Oil Property Correlations (for pb, Bo, Rs, co) There are 20+ different black oil correlations. These two (Standing; Vasquez and Beggs) are provided to introduce the idea of black oil correlations and sample calculations with them.

Unless otherwise stated, units for these correlations are as follows:

Basic three input variables:

Gas Gravity [g]

Oil Gravity [o] or [°API]

Reservoir Temperature, TR [°F]

Additional input variables (depends on case): Pressure, p [psi] (if at bubble point, pb)

Solution Gas Oil Ratio, Rs [SCF/STB]

Calculated values: Bubble point pressure, pb [psi]

Solution Gas Oil Ratio, Rs [SCF/STB]

Oil FVF, Bo [RVB/STB]

Oil Compressibility, co [1/psi]

Viscosities (o, g, w), [cp]

A. Bubble Point Correlations

If know gas gravity, oil API gravity, reservoir temperature, and Rsb, can find bubble point pressure (pb):

1. Standing (1942, based on 105 California crude oils). (The first, still often used…)

APITA R

 0125.000091.0

 





 





  





 



 

 





 



  4.1102.18

83.0

sb b

R p



2. Vasquez and Beggs (1980, based on 5,008 data points) (Many consider this the best overall…)

Constants for Vasquez and Beggs Bubble Point Correlation

Constant ≤ 30 °API ≥ 30 °API

C1 0.0362 0.0178

C2 1.0937 1.187

C3 25.724 23.9310

    

 2/1

31 460/exp

sb b

TAPICC

R p

  



  



 



B. Solution Gas Oil Ratio (Rs) Correlations

If know gas gravity, oil API gravity, reservoir temperature, and pressure p, can find solution GOR (Rs).

1. Standing (1942) (algebraically rearranged bubble point correlation)

APITA R

 0125.000091.0

  205.1

102.18

48.25  

  





 

Ags

p R 

2. Vasquez and Beggs (1980) (algebraically rearranged bubble point correlation)

Constants for Vasquez and Beggs Rs Correlation (same as for Bubble Point Correlation)

Constant ≤ 30 °API ≥ 30 °API

C1 0.0362 0.0178

C2 1.0937 1.187

C3 25.724 23.9310

  

   





 

460 exp 3

1 2

s T

APIC CpR 

C. Oil Formation Volume Factor (Bo) Correlations

If know gas gravity, oil gravity, reservoir temperature, and solution GOR (Rs), can find oil FVF (Bo).

(It’s interesting that these are in terms of Rs instead of pressure. But since Rs is a function of pressure, expressing in

terms of Rs accomplishes the same result.)

1. Standing (1942)

s TRX 

 

   

  25.1

5.0



(note in terms of oil specific gravity, not API)

175.1 000147.0972.0 XB

o 

2. Vasquez and Beggs (1980)

Constants for Vasquez and Beggs Bo Correlation

Constant ≤ 30 °API ≥ 30 °API

C4 4.677∙10 -4 4.670∙10

-4

C5 1.751∙10 -5 1.100∙10

-5

C6 -1.8106∙10 -8 1.337∙10

-9

    s

Rso RCC

API TRCB 

 





 



 

654 601



C. Oil Compressibility (co) Correlation

If know gas gravity, oil gravity, reservoir temperature, bubble point solution GOR (Rsb), and bubble point pressure

(pb), can find oil compressibility (co).

Vasquez and Beggs (1980) (for co at the bubble point)

 

  





 

5 10

143361.1211802.175

gRsb

o p

APITR c

 [1/psi]

Note: Rsb has units of [SCF/STB]

(Some versions of this correlation have a 5000*Rsb term where Rs is in [MCF/STB])

D. Bo above Bubble Point

Once have oil compressibility co (assume constant above pb), can calculate Bo at any pressure above pb.

oobo

oboo

BBB

Finally

pBcB

B c

V c







 



 

negative) be (will