Reservoir MT

Modules 1+2+3+4+5(theory)

Is IGIP stated at reservoir or standard conditions?

Standard

IGIP → the total volume of gas in the reservoir at standard conditions.

• Metric Units: se⁶m³ (million standard cubic metres)

What are the 3 methods of estimating IGIP? Rank them from least accurate to most

1. Volumetrics - least accurate, assumes an average net pay

2. Planimetrics - more accurate than volumetrics because BV and PV is calculated more accurately (using a contour map)

3. Material Balance (P/z method) - most accurate because it is based on the actual production history of the reservoir.

When using Material Balance to estimate IGIP - ie. using P/z vs. Cum. Production - what are the 4 necessary assumptions?

1. Closed tank reservoir

2. No water influx

3. Little or no water production

4. Homogeneous reservoir

What are the units of the P/z slope?

kPaa/se⁶m³

At what conditions is Recoverable Gas stated?

Standard

Recoverable gas → the total volume of gas that can be recovered or produced over the life of the well.

• Metric Units: se⁶m³

• Imperial Units: MMSCF

What is a typical recovery factor range for gas reservoirs?

60% to 95%

Gas condensate reservoir → 60% to 70%

Dry gas reservoir → 90% to 95%

Explain the difference between Recoverable Gas and Marketable Gas

Marketable Gas is the total volume of gas that can be sold to market at market specs.

Therefore, it will always be less than Recoverable Gas, as some processing is required to bring the raw produced gas to sales specs, and all processing facilities have some process loss and require some fuel to operate

What is residue gas?

Residue gas is the volume of gas after processing (and ususally before F&M is taken off - but not always!)

While sales gas or marketable gas is the gas after processing (residue gas) minus any F&M (ie. minus all surface losses). 

In a gas condensate reservoir, gas-cycling is often used to improve recovery, wherein lean gas is injected and wet gas-condensate is produced. The process of injection is continued until most of the gas-condensate is recovered, or the liquid content is too low to economically re-inject the lean gas. At that point, injection is terminated and the reservoir is allowed to produce below the dew point until abandonment. The reservoir would now be stated to be in _____-______ mode.

blow-down

no more injection = reservoir is producing solely off its own pressure = reservoir pressure is depleting = reservoir is “blowing down”

Define

• Condensate Yield Ratio

• NGL Yield Ratio

• Sulphur Yield Ratio

These are all ratios of the inlet, or raw gas rate.

• Condensate yield ratio: ratio of condensate (ie. liquid) produced to the raw inlet gas 

  • Unit sm³/se³m³

• NGL yield ratio: ratio of NGLs (ie. liquids) produced to the raw inlet gas

  • Unit sm³/se³m³

• Sulphur yield ratio: ratio of sulphur produced (solid) to the raw inlet gas

  • Unit mT/se³m³

NOTE: these are all based on the raw inlet gas; they are never based on residue or sales gas.

What is the operating pressure of a gas cycling scheme?

At or slightly above the dew point

• the whole point of re-injection is to keep the reservoir P above the dew point in order to produce more liquids

• Below dew point = blow-down

In calculating SL, PL and F&M should be a fraction of what?

Raw gas

NOTE: F&M is sometimes given as a fraction of residue gas - in which case it must be converted to a fraction of raw gas before being combined with PL to get SL.

F&M as frac of raw = (Residue gas as frac of raw) x (F&M as frac of residue)

• ie. a simple unit cancellation

In a gas cycling scheme, _____ gas is injected and _____ gas is produced.

lean injected and wet produced

From which gas stream is the heating value calculated?

From the residue gas stream only (ie. after processing)

In gas analysis, what is the primary goal of recombination?

To reconstruct the original composition of the gas as it exists in the reservoir

After liquids are extracted, will the the heating value of the residual gas stream be higher or lower?

Lower

more carbons = higher heating value

The gross heating value of a gas is a direct function of what?

The molecular weight of the gas

• see formula sheet:

  • GHV (MJ/m³ ) = 1.9892M_g + 5.9916

What are the 2 methods of calculating the GHV of a gas?

Both require you to have the mole fractions of each component

1. mole frac. of comp. x GHV of comp. (given)

   • sum all comp. GHVs to get GHV of gas

2. mole frac. of comp. x MW of comp.

   • sum all comp. MWs to get MW of gas

   • plug into formula for GHV on formula sheet

A question asks you to combine a liquid and a gas stream, while giving the flow rates of each stream as molar flow rates. What conversion has to be done in order to combine the gas & liquid streams? 

No conversion

• molar flow rates can simply be combined because the units are the same

q_total = q_gas(molar) + q_{liquid(molar)}

What is a GEL flowrate?

Gas-equivalent liquid flow rate → allows you to take a liquid flow rate (sm³/d) and convert it into a gas-equivalent flow rate (se⁶m³/d) so that it can be combined with another gas stream. 

We cannot add 120.00 se³m³/d of gas and 3.00 sm³/d of liquid. Why?

a) because the units are different

b) because the streams are in different phases

b) because the streams are in different phases

• volumetric flow rates depend on density, and density differs by phase

Note that molar flow rates are simply moles/unit time and therefore independent of density/phase - and so can be combined

Give the formulas for liquid and gas component recovery

• where n = component (C₁, C₂, C₆, etc.)

n gas recovery = n q_gas / n q_gas + n q_GEL

n liquid recovery = n q_GEL / n q_GEL + n q_gas

Be careful with production units

Example: You’re given values of average annual production in MMSCF/d and then asked to calculate the cumulative production over 10 years in BSCF

• [(sum 10 yr daily averages in MMSCF)*365]/1000 = 10 yr cum. BSCF

A gas well in Alberta produces raw wet and sour gas at a flowrate of 38.26 MMSCF/d. The gas is processed at a nearby gas plant with process loss of 18%, and fuel & metering error of 8% of raw gas.

• Draw the flow schematic for this question

Main thing to recognize is that the F&M comes off of the raw gas because it is stated in the question as a fraction of raw

∴ your residue gas & sales gas values will be off if you don’t clock this

• See HW1 Q2

If you have the molar composition of the raw gas and then calculate the molar compositions of the liquid and gas streams → how can you quickly find the GEL flowrate if you know the raw gas flowrate?

q_GEL = (sum of the moles in the liquid)*(q_{raw gas})

• this works b/c the sum of the liquid moles is essentially the fraction of raw gas that condensed into liquid, assuming your raw gas composition was given for 1 mole of raw gas

What is another term for Expected Ultimate Recoverable (EUR) ?

Total Reserves

What is the GEL ratio?

GEL ratio = GEL rate/liquid rate

What is boundary dominated flow?

Boundary-dominated flow occurs when the pressure disturbance from production has reached the physical limits of the reservoir

• in other words: the reservoir has produced long enough for the initial pressure pulse to reach the outer boundary of the reservoir

• It is one of the assumptions used in Decline Curve Analysis

What is another term for the nominal decline rate, a?

• what is its unit?

Instantaneous decline rate

Unit: 1/time (ie. 1/day 1/month 1/year etc.)

a = nominal decline rate = negative of the instantaneous slope of the exponential decline curve

• ‘instantaneous slope’ meaning the slope of the tangent to the curve at any one point

What are the 2 types of diagnostic plots used in decline curve analysis?

1. Rate-Time

2. Rate-Cum. (Rate vs. Cumulative Production)

What are the assumptions used in Arps’ Equations?

• boundary dominated flow

• tank depletion model

• constant number of wells

• constant permeability and porosity

• constant separator and tubing conditions

Which type of decline model has a constant nominal decline rate?

Exponential

A linear decline curve for rate vs. time on a semi-log plot indicates which type of decline model?

Exponential 

• can be seen from formula sheet: the rate vs. time equations with log/ln in them for exponential decline are both equations of a straight line (ie. in the form y=mx+b):

  • log(q) = -at/2.303 + log(q_i) 

  • ln(q) = -at + ln(q_i)

For an exponential decline, plotting Rate vs. Cumulative Production on a Cartesian plot will result in what type of trend?

Linear (ie. straight line)

• can be seen from formula sheet

Of the 3 decline models, which estimates the most pessimistic (minimum) value of the total reserve (EUR)?

Exponential

The cumulative production corresponding to the flow rate at abandonment, is know as what?

Expected Ultimate Recoverable (EUR)

• N_p @ q_a

• G_p @ q_a

The percentage in change in the flow rate over a period of time (usually 1 year)

Effective decline rate, d

• Unit: %/year

What is the bubble point?

2500 psia 

• max live oil volume

What is the bubble point?

2000 psia

• max B_o

If the decline exponent, b, is greater than 1, what does this indicate about the reservoir?

b > 1 → reservoir is likely unconventional (assuming boundary dominated flow)

A family of curves as “pre-solutions” that are plotted for different values of b & a_i

Type curves

What are the assumptions for IGIP and IOIP formulas?

IGIP 

• only gas + water (ie. no oil)

IOIP

• only oil + water (no gas)

Which decline model is the most general form of decline analysis?

Hyperbolic

• exponential and harmonic are considered ‘special cases’ of hyperbolic where b = 0 and b = 1 respectively.

What is the unit of a_i in this hyperbolic DCA equation?

1/day

• b/c the q (rate) value is always in volume/day

In the Cullender & Smith method, which will always be larger?

a) the P_b estimated using the Trapezoid Rule

b) the P_b calculated using Simpson’s Rule

a) the P_b estimated using the Trapezoid Rule

• This will always be an overestimation of P_b, given that, mathematically, the trapezoid method will always over estimate the area under a curve

  • Simpson’s rule then corrects this overestimation

For the majority of conventional reservoirs with boundary dominated flow, what range will the decline exponent “b” fall into?

0 to 1 

Name 3 possible reasons for observing an “unusual” (ie. outside the 0 to 1 range) decline exponent “b” 

1) Error in the analysis of the data where a b<1 can also be applied to match the historical production data.

2) The flow has not reached the boundary dominated condition yet and it is still transient flow.

3) Unconventional oil and gas reservoirs (such as tight oil, tight gas, shale oil, shale gas reservoirs) often exhibit b>1.

TorF: Decline analysis of unconventional reservoirs is different than traditional methods and requires its own set of modifications of the equations

True

Of the 3 decline models (exponential, hyperbolic, harmonic), which one has no straight line relationship?

Hyperbolic

• evident from equations on formula sheet

In a gas material balance question, you are asked to calculate the recoverable raw gas at abandonment conditions - what are the 4 steps to this calculation?

a) Calculate the P_i/z_i

b) Calculate the slope, m (rearrange the IGIP formula)

c) Calculate P_a/z_a

d) Calculate the RG @ abandonment

See Tutorial 1 Q1

(Ali mentioned that on a test, the Q may not be broken down into steps like the tutorial - so you should know how to get to RG w/o it being spelled out)

Convert 1 month to days

365/12 = 30.43 days/mo

Harmonic decline is a special case of ________ decline.

hyperbolic

(so is exponential)

You plot rate vs. cum. on a semi-log plot and obtain a straight line - which decline model is it?

Harmonic

• look at the equations

The equation of the trend line (in exponential format) for Rate (sm³/d) vs. Cum. on a semi-log plot is y = 160e^-0.0433x , what is the initial rate?

160 sm³/d

• from formula sheet

The pressure profile plot (pressure vs. depth) is usually:

a) linear

b) non-linear

b) non-linear

The temperature profile plot (temperature vs. depth) is usually:

a) linear

b) non-linear

a) linear

TorF: The gas pressure gradient in a gas well is usually constant

False 

• gas is compressible

  • Gas density decreases with decreasing pressure → less weight per unit height → smaller incremental pressure change at shallower depth → non-linear curve

If T > T_c , what type of reservoir is it?

Gas

If T < T_c , what type of reservoir is it?

Oil

If T_c > T < T_{cr ,} what type of reservoir is it?

Gas-Condensate

If T > T_cr , what type of reservoir is it?

Dry Gas

The maximum temperature at which liquid and vapor phases can coexist in equilibrium for a given hydrocarbon mixture

Cricondenterm

• ∴ at temps above the cricondentherm, only single phase dry gas is present

As gas pressure increases, density _____________.

increases

When temperature increases, gas density ____________.

decreases

A dramatic shift to the right on a pressure gradient plot for an oil or gas well typically indicates what?

A gas/oil contact, gas/water contact, or oil/water contact 

• because of the large density variance b/w fluids

  • fluid pressure gradients being a function of fluid density

If the slope of a gas pressure gradient is m = 7.9425m/kPaa, what is the gas gradient? 

G = 1/m = 1/7.9425 = 0.1259 kPaa/m

• obvious from the slope units 

Outline the iterative process of calculating P_m (or P_b) used in the Cullender & Smith method

Which cell has the lowest pressure

D

Cells D and E are at the same pressure. Explain the difference in volumes observed.

Cell E must have a lower temperature. 

• When you cool down oil and gas, both will slightly decrease in volume

The ratio of the volume of oil at reservoir conditions to the volume of oil at standard conditions

Oil Formation Volume Factor, B_o

Metric Unit: rm³/sm³

Imperial Unit: bbl/STB

B_o = (Live Oil Volume)/(Dead Oil Volume)

The ratio of the volume of gas at reservoir conditions to the volume of gas at standard conditions

Gas Formation Volume Factor, B_g

Metric Unit: rm³/sm³

Imperial Unit: ft³/scf

The ratio of the volume of the dissolved gas to the oil volume

Solution gas-oil ratio, R_s

Metric Unit: sm³/sm³

Imperial Unit: SCF/STB

R_s = (Solution Gas Volume @ STP)/(Dead Oil Volume @ STP)

R_s = (Volume of dissolved gas @ STP)/(Volume of oil @ STP)

Can be tricky because the dissolved gas is the volume of gas dissolved in the oil in the reservoir, yet it is stated at standard conditions

Explain this graph.

• Why does B_o rise gradually with increasing pressure?

• Why does it drop off slightly at the end?

• What is the bubble point pressure?

• As reservoir pressure increases, more gas dissolves into the oil, causing the oil to expand, increasing B_o

• At the bubble point pressure (the peak on the graph), all of the available free gas has dissolved in the oil (oil is saturated)

  • Increasing pressure beyond this point will not dissolve additional gas (there is no more free gas)

• At pressures above the bubble point, the oil behaves as a slightly compressible liquid. Further increases in pressure cause a small reduction in oil volume, resulting in the slight decrease in B_o observed at the end of the curve

Given that:

• Cell E is at standard conditions

• In cell C, the B_g = 0.01300 ft³/SCF

What is the solution gas-oil ratio (R_s) for cell C?

R_s = (Solution Gas Volume @ STP)/(Dead Oil Volume @ STP) [formula sheet]

From the image:

• Free gas volume for E (STP) = 432 ft³

• Dead oil volume @ STP (cell E) = 0.7634 bbl

• Free gas volume for C = 2.28 ft³

• The remainder of the gas in C is in solution

  • we need this volume at STP

• Convert 2.28 ft³ to STP using B_g

  • 2.28 ft³ / 0.01300 ft³/SCF = 175.38 SCF

• Therefore, solution gas volume @ STP in cell C = 432 - 175.38 = 256.62 SCF

• So R_s = 256.62 / 0.7634 = 337 SCF/STB

What principle is the material balance equation based on?

Conservation of Mass

TorF: When fluid (oil, gas, water) is produced from the reservoir, that volume of fluid leaves the formation pore space, resulting in a partial void in the original pore space

False

Fluids expand to fill the original pore space

V_e = V_w [formula sheet]

At the bubble point, P_b, what is the volume of free gas in the reservoir?

0

At P > P_b, an oil reservoir is said to be _______________.

undersaturated

• all gas is dissolved in solution (no free gas)

In cell A, what is the volume of gas dissolved in the oil?

What is the R_s @ A?

What is the R_s @ B?

R_s @ B = R_s @ A

• because all gas is still in solution

What are the assumptions used in Simple Oil Material Balance?

• Initially undersaturated oil

• Water expansion & production is ignored

  • ie. water is incompressible

Define all of these Simple Oil Material Balance parameters:

• N

• N_p

• G

• G_p

• B_o

• B_g

• R_s

• R_p

• V_e

• V_w

Using Simple Oil MB parameters, and assuming that the reservoir is initially at the bubble point, how would you calculate the total hydrocarbon volume at initial conditions? 

N x B_oi

• At the bubble point all gas is in solution (ie. inside the volume N)

  • therefore N = total hydrocarbon volume

• Recall that N is stated @ standard conditions, so must be adjusted to initial conditions using B_oi

Flow in a reservoir that has not yet reached boundary dominated flow is called ________ flow.

transient

In the Slider Method (hyperbolic) equations shown (for calculating cumulative production), what must the unit of a_i be?

1/day

• because your rates are all per day

Of the following 4 Oil FVFs, which one represents a heavy oil?

a) B_o = 1.75 (bbl/STB)

b) B_o = 1.25 (bbl/STB)

c) B_o = 1.05 (bbl/STB)

d) B_o = 1.45 (bbl/STB)

c) B_o = 1.05

• heaviest oil will always have the lowest B_o (closest to 1)

  • Heavy oils (dense, low gas solubility) expand very little → smaller B_o

• lightest oil will always have the highest B_o

  • light oils (low density, high gas solubility) expand more due to dissolved gas → larger B_o

You are given the following gas FVFs for different natural gases at reservoir conditions. Which one most likely corresponds to a high pressure, high temperature gas reservoir?

a) B_g = 0.005 (ft³/scf)

b) B_g = 0.02 (ft³/scf)

c) B_g = 0.01 (ft³/scf)

d) B_g = 0.03 (ft³/scf)

a) B_g = 0.005

• B_g​ decreases with increasing pressure and temperature

• High P high T gas reservoirs are highly compressed → smaller B_g

Four crude oil samples were analyzed for solution gas–oil ratio at their respective bubble point pressures.
Which sample most likely represents a heavy oil?

a) R_s = 800 (scf/STB)

b) R_s = 50 (scf/STB)

c) R_s = 1500 (scf/STB)

d) R_s = 300 (scf/STB)

b) R_s = 50 (scf/STB)

Heavy oils dissolve very little gas → low R_s

A formation that contains water

Aquifer

The unique combination of temperature and pressure at which the liquid and vapor phases become indistinguishable

Critical Point

How do you calculate the slope on on a semi-log plot?

m = Δln(y)/Δx

A reservoir in which P_i < P_b is referred to as ___________.

Initially saturated

• oil with a gas cap (ie. free gas)

What is the R_so @ standard conditions?

R_so = (total gas - free gas)/(dead oil) = 432/0.7634 = 566 SCF/STB

What is the minimum R_so @ STP?

0

• ie. the oil contains no dissolved gas

Does the R_so increase above the bubble point?

No

• above the bubble point, all gas is in solution. There is no more available free gas, hence R_so cannot increase