Reservoir Final

Modules 9-12

What are the P and T conditions for the Ideal Gas Law?

Low P

High T

What are the assumptions of the Ideal Gas Law?

• No interactions between gas molecules (low P)

• No volume occupied by gas molecules

An instrument that uses the Ideal Gas Law to measure effective porosity of core plug samples

Helium Porosimeter

What does a Helium Porosimeter measure?

Grain Volume

• Effective pore volume can then be calculated from:

  • PV_e = BV - GV

What is the Real Gas Law?

A modified EOS (ie. relates V to P&T) that can be used for gases at any T & P.

• Z (Compressibility Factor) corrects for volume changes due to changes in T & P

Why is the Z-factor different for different gases?

Due to the varying T_c & P_c of the different gases

The Law of Corresponding States says that the Z-Factor of all pure gases depends only on the gas' ___________ and ___________.

Reduced Temperature (T_r)

Reduced Pressure (P_r)

A gas mixture that is assumed as one component

Pseudo Gas

Because of Avogadro’s Law, what can be assumed about the Volume Fraction of a given component of a gas mixture and its Mole Fraction?

That they are equal.

ie. Volume Fraction of component i = Mole Fraction of component i

Avogadro’s Law: equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules.

What are Pseudo-Critical Properties?

Used to treat a gas mixture as if it is a single component gas

• Essentially a weighted sum of each component’s T_c and P_c

For a pure gas, Z-Factor is a function of ___ and ___.

Similarly, for a gas mixture, the Z-Factor is a function of ___ and ____.

Pure gas → T_r and P_r

Gas mixture → T_pr and P_pr

When calculating pseudo-critical P and T, what units must be used for all T & P values?

T → K

P → kPaa

What are the most common non-hydrocarbon reservoir gases?

N₂

CO₂

H₂S

What is acid gas?

A gas mixture containing significant amounts of acidic gases:

• N₂

• CO₂

• H₂S

Which gases cause a deviation of pseudo-critical properties in a mixture, and hence must be adjusted for?

• H₂S

• CO₂

Use chart or ε formula

What are Corrected Pseudo-Critical Properties?

Used when treating a mixture containing H₂S and/or CO₂ as a single component gas

• T’_pc

• P’_pc

What is the Gas Formation Volume Factor ?

B_g

The ratio of the volume of a given mass of gas at reservoir conditions to its volume at standard conditions

What is the Gas Formation Expansion Factor (E_g) ?

The reciprocal of B_g

What are the units for B_g and E_g ?

B_g → rm³/sm³

E_g → sm³/rm³

What are the assumptions made for Closed Tank Gas Reservoirs?

1. Reservoir contains only Gas Phase + Water Phase

   • Water phase is at S_wirr

2. Zero gas dissolved in formation water

3. Reservoir Pressure is not maintained during production lifetime

4. Reservoir is isolated from aquifers/other formations

5. Reservoir gas composition remains constant during production

6. Reservoir Temperature stays constant during production

7. Compressibility of Reservoir Rock is negligible

8. Compressibility of Formation Water is negligible

If the volume of gas at surface conditions is known, how would you calculate the volume of gas at reservoir conditions?

Multiply it by B_g

∴ IGIP or G (initial resource @ STP) can be multiplied by B_gi to get the IGIP @ initial reservoir T & P

From the Gas Material Balance Equation, define:

• G_p

• P

• B_g

• G-G_p

• (G-G_p)B_g

• G_p → Volume of Cumulative Gas Production @ STP

  • (se⁶m³ or MMSCF)

• P → Current Reservoir Pressure

  • ie. the P that is declined from P_i after producing Gp

• B_g → Gas FVF @ reservoir P & T

• G-G_p → Remaining gas Volume in reservoir @ STP

  • (se⁶m³ or MMSCF) (ie. after producing G_p)

• (G-G_p)B_g → Remaining gas Volume in reservoir @ reservoir P & T

  • (se⁶m³ or MMSCF) (ie. after producing G_p)

What are the 2 methods of determining IGIP, using material balance?

1. Using P/Z vs. Cumulative Gas Production (G_p) Graph

   • y-intercept = (P/Z)_i

   • x-intercept = IGIP = G (ie. G_p @ P/Z = 0)

2. Using P/Z Equation

   • IGIP = G = (-1/slope)(P/Z)_i

   • In other words you are solving for the x-intercept ie. the x-coordinate (G_p) when the y-coordinate (P/Z) equals 0.

   • ∴ you’re using y = mx+b to find x when y = 0

   • ie. finding G_p in (P/Z)i = mG_p + (P/Z) when (P/Z) = 0

When is a gas reservoir at its economic limit?

When:

• Cost of Producing Gas = Total Income

What is the Abandonment Production Rate (GR_a) ?

The rate of gas production at the economic limit

• se³m³/day

What is the relationship between the abandonment rate and the cost of production?

What is the relationship between then abandonment rate and the gas price?

• Gas Price ↑ , Abandonment Rate ↓

  • ie. if gas prices are high, you can produce less to break even

• Cost ↑ , Abandonment Rate ↑

  • ie. if your costs of production are high, you need a high production rate to break even

NOTE: these relationships can be derived from the formula for calculating GR_a on the formula sheet

What is another way of defining Initial Reserves?

Initial Reserve = G_pa = Recoverable Gas

ie: The initial reserve is equal to the cumulative production at abandonment conditions (se⁶m³)

• this is because reserves are defined as the volume of gas that can be produced economically

Define these various gas volumes:

• G_pa

• G_ps

• G_r

• G_par

• G_u

• G_pa → Cum gas prod. @ abandonment = recoverable gas = initial reserve (se⁶m³)

• G_ps → cum gas production to date (se⁶m³)

• G_r → Remaining gas in place = remaining resource (se⁶m³)

• G_par → Remaining cum gas production = remaining reserve (se⁶m³)

• G_u → Unrecoverable gas (se⁶m³)

What are the assumptions for the Oil Material Balance (Stock Tank Oil Reservoirs) ?

The Oil Reservoir:

• is @ initial conditions (not yet in production)

• contains only oil phase + water phase (@S_wirr)

• pressure is not maintained during production lifetime

• is not connected to any water aquifer

• no gas/water injection

• temperature remains constant during production

• compressibility of reservoir rock is negligible

• compressibility of formation water is negligible

• no gas dissolved in reservoir water

When is an oil reservoir considered to be undersaturated?

When P_res ≥ P_b

• ie: when the reservoir pressure is greater than or equal to the bubble point pressure

• all available gas is dissolved in the oil (ie. no free gas)

For Oil Reservoir Material Balance, define:

• N

• B_oi

• NB_oi

• N_p

• P_i

• P

• B_o

• N-N_p

• (N-Np)B_o

• N → IOIP = Initial Resource @ STP (sm³)

• B_oi → Initial Oil Formation Volume Factor (rm³/sm³)

• NB_oi → IOIP @ initial reservoir T&P (ie. T_i & P_i) (rm³)

• N_p → Cumulative oil production @ STP (sm³)

• P_i → Initial reservoir pressure (kPaa)

• P → Current reservoir pressure (ie. after producing N_p) (kPaa)

• B_o → Oil FVF @ current reservoir P&T (rm³/sm³)

• N-N_p → Remaining oil volume in reservoir = remaining resource @ STP (sm³)

• (N-Np)B_o → Remaining oil volume in reservoir = remaining resource @ reservoir P&T (rm³)

If the volume of oil at surface conditions is known, how would you calculate the volume of oil at reservoir conditions?

Or in other words, how would you calculate the Live Oil Volume if the Dead Oil Volume is known?

Multiply it by B_o

∴ IOIP or N (initial resource @ STP) can be multiplied by B_oi to get the IOIP @ initial reservoir T & P

For Oil Reservoir Material Balance, when P_res< P_b, define:

• R_p

• RF

• R_so

• R_soi

• B_g

• R_p → Production GOR (sm³/sm³)

• RF → Recovery factor = N_p/N

• R_so → Dissolved (solution) GOR @ current reservoir P&T (sm³/sm³)

• R_soi → Initial dissolved (solution) GOR (sm³/sm³)

• B_g → Gas FVF @ current reservoir P&T (rm³/sm³)

Recall: R_so stands for Ratio Solution Oil (ie. Solution GOR)

What is the difference between FVFs (ie. B_o and B_g) and the various GORs (ie. R_so, R_p, R_soi) ?

• Formation volume factors (FVF) are used to adjust for the difference in volume of a single phase of oil (B_o) or gas (B_g) when at reservoir conditions and at surface conditions.

• Gas to oil ratios are used to define the ratio of a gas volume to an oil volume at various conditions. ie:

  • At surface: R_p (production GOR)

  • At reservoir: R_so (dissolved GOR)

  • At reservoir initially: R_soi (initial dissolved GOR)

For GORs, under which conditions (surface or reservoir) are they all measured in?

Surface conditions (all will have units sm³/sm³)

ie:

• Production GOR (R_p) → The actual measured GOR at the surface (sm³/sm³)

• Dissolved (solution) GOR (R_so) → the amount of gas that would come out of solution if the oil is brought to surface over the amount of oil at surface (sm³/sm³)

∴ GORs will always have surface units

Under what conditions does R_p = R_so ?

Only in an undersaturated reservoir.

• This would mean that no free gas is present, and hence no free gas is produced, so therefore R_p must equal R_so.

Under what conditions is R_p > R_so ?

When P_res < P_b

• this would indicate the presence of free gas in the reservoir, which will be produced along with the gas dissolved in the oil, leading to an R_p that is greater than the R_so.

When P_res < P_b, what happens to the live oil viscosity as the reservoir pressure declines?

It increases

• as pressure declines while below the P_b, dissolved gas comes out of solution, and the oil loses it’s “lightening agent”, hence the viscosity of the oil increases.

When P_res > P_b, what happens to the live oil viscosity as the reservoir pressure increases?

It increases slightly

• All of the available gas remains dissolved in the oil above the P_b, but as the pressure increases, the oil itself will compress slightly, leading to a slight increase in the oil’s viscosity

What are the assumptions used in Darcy’s Law?

1. Oil/Water are incompressible

2. Single phase

   • pores contain 100% oil or water - no gas

3. Horizontal flow (no gravity effect)

4. Laminar flow

5. Steady-state flow (doesn’t change over time)

6. Fluid doesn’t react with the rock

A medium with a permeability of 1 darcy permits a flow of ____ cm³/s of a fluid with viscosity of ____cp under a pressure gradient of ____ atm/cm acting across an area of ____cm².

A medium with a permeability of 1 darcy permits a flow of 1 cm³/s of a fluid with viscosity of 1 cp under a pressure gradient of 1 atm/cm acting across an area of 1 cm²

Under what conditions is k equal to the absolute permeability?

When only a single phase fluid is present

Under what conditions is k equal to the effective permeability (k_e)

When two or more fluids are present

TorF: The absolute permeability of a rock is constant and independent of fluid type flowing through it

True

TorF: Absolute permeability is independent of the pressure gradient

True

An ideal reservoir wherein the reservoir properties (e.g. k) are assumed to be the same everywhere

Homogeneous Reservoir

An actual reservoir with variation of reservoir properties laterally and aerially (vertically)

Heterogeneous Reservoir

In a vertically fractured rock, which would be greater: k_v or k_h ?

k_v > k_h

What is k₉₀?

The horizontal permeability at a 90° angle from the maximum permeability direction

Which logs are used to measure porosity?

Neutron density log

Acoustic log

How is permeability typically measured empirically?

In a lab using a core sample

The relationship between porosity and permeability

log(k) = b+ (mΦ)

is most likely to be accurate in which of the following:

A) carbonate formations

B) fractured reservoirs

C) sandstone formations

C) sandstone formations

What are the 2 horizontal flow patterns in reservoirs?

1. Linear

2. Radial

The boundary of the region where fluid flows to a well

Drainage radius (or external radius or effective radius) r_e

The area inside the drainage radius

Drainage area

How is the drainage radius (r_e) calculated?

½ of the distance between 2 consecutive wells

• ie. r_e = ½ x (distance to nearest well)

The ratio of the total area of the field to the number of producing wells

Well Spacing (A_w)

• normally reported in acres or hectares per well

What are the 2 methods that can be used to calculate the drainage radius when the well spacing is known?

1. Circle inside square model (on formula sheet)

2. π Model

   • can be derived from A_w = πr_e²

Which will be larger: the r_e calculated using the π Model or the r_e calculated using the ‘circle inside square model’ ?

The r_e from the π Model

Label each type of multi-layer flow

Which equations would you use to calculate the average porosity and the zonal flow rates in a stratified formation?

Stratified = parallel

The point at which a gas and its liquid phase become indistinguishable

Critical point

The temperature above which a gas cannot be liquefied by pressure alone

Critical Temperature T_c

The minimum pressure required to liquefy a gas at its critical temperature

Critical Pressure P_c

What is another name for the gas compressibility factor (Z)?

Gas deviation factor

How would you calculate the volume of intial dissolved gas?

N x R_soi

How would you calculate the volume of gas produced at surface?

N_p x R_p

What must the units always be of a FVF, whether for oil or gas?

reservoir unit/surface unit

ie:

rm³/sm³

bbl/STB

What must the units always be of a GOR, whether it’s a solution/dissolved GOR (R_so) or a production GOR (R_p) ?

surface units/surface units

ie:

sm³/sm³

SCF/STB

What is the unit for permeability (k) ?

mD

Is the relationship between permeability and porosity defined as log(k) = b+ (mΦ) valid for fractured reservoirs?

No