petroleum reservoir engineering ii lecture 8: material
TRANSCRIPT
Tishk International UniversityEngineering FacultyPetroleum and Mining Engineering Department
Petroleum Reservoir Engineering II
Third Grade- Spring Semester 2020-2021
Lecture 8: Material Balance Equation
Instructor: Sheida Mostafa Sheikheh
Oil Recovery Mechanisms
β The recovery of oil by any of the natural drive mechanisms is called primary
recovery.
β The term refers to the production of hydrocarbons from a reservoir without the use
of any process (such as fluid injection) to supplement the natural energy of the
reservoir.
β In the previous lecture, an introduction of various primary recovery mechanisms and
their effects on the overall performance of oil reservoirs has been given.
β The objective of this lecture is to provide the basic principles of the material balance
equation and other governing relationships that can be used to predict the
volumetric performance of oil reservoirs.
Primary Recovery Mechanisms
β For a proper understanding of reservoir behavior and predicting future performance,
it is necessary to have knowledge of the driving mechanisms that control the
behavior of fluids within reservoirs.
β The overall performance of oil reservoirs is largely determined by the nature of the
energy, i.e., driving mechanism, available for moving the oil to the wellbore.
β There are basically six driving mechanisms that provide the natural energy
necessary for oil recovery:
β’ Rock and liquid expansion drive
β’ Depletion drive
β’ Gas-cap drive
β’ Water drive
β’ Gravity drainage drive
β’ Combination drive
Content: β Material Balance Equation
β Material Balance Derivation:
1. Pore Volume Occupied by the Oil Initially in Place
2. Pore Volume Occupied by the Gas in the Gas Cap
3. Pore Volume Occupied by the Remaining Oil
4. Pore Volume Occupied by the Gas Cap at Reservoir Pressure
5. Pore Volume Occupied by the Evolved Solution Gas
6. Pore Volume Occupied by the Net Water Influx
7. Change in Pore Volume due to Initial Water and Rock Expansion
8. Pore Volume Occupied by the Injection Gas and Water
β Example of Material Balance Equation Application
The Material Balance Equation
β The material balance equation (MBE) has long been recognized as one of the basic
tools of reservoir engineers for interpreting and predicting reservoir performance.
β The MBE can be used to:
β’ Estimate initial hydrocarbon volumes in place
β’ Predict future reservoir performance
β’ Predict ultimate hydrocarbon recovery under various types of primary driving
mechanisms.
The Material Balance Equation
β The equation is structured to simply keep inventory of all materials entering, leaving,
and accumulating in the reservoir.
β In its simplest form, the equation can be written on a volumetric basis as:
Initial volume= Volume remaining + Volume removed
β Since oil, gas, and water are present in petroleum reservoirs, the material balance
equation can be expressed for the total fluids or for any one of the fluids present.
The Material Balance Equation
β Before deriving the material
balance, it is convenient to
denote certain terms by
symbols for brevity.
The Material Balance Equation Derivation
β Several of the material balance calculations require the total pore volume (P.V) as
expressed in terms of the initial oil volume N and the volume of the gas cap.
β The expression for the total pore volume can be derived by conveniently introducing
the parameter m into the relationship as follows.
β Defining the ratio m as:
π =πΌπππ‘πππ π£πππ’ππ ππ πππ πππ
ππππ’ππ ππ πππ ππππ‘πππππ¦ ππ πππππ=πΊ π΅ππ
π π΅ππ
The Material Balance Equation Derivation
β Solving for the volume of the gas cap gives:
πΌπππ‘πππ π£πππ’ππ ππ π‘βπ πππ πππ = πΊ π΅ππ = π π π΅ππ
β The total volume of the hydrocarbon system is then given by:
πΌπππ‘πππ πππ π£πππ’ππ + πΌπππ‘πππ πππ πππ π£πππ’ππ = (π. π)(1 β ππ€π)
π π΅ππ +π π π΅ππ = (π. π)(1 β ππ€π)
Or π. π =π π΅ππ(1+π)
(1βππ€π)βββ(1)
The Material Balance Equation Derivation
π. π =π π΅ππ(1 + π)
(1 β ππ€π)βββ(1)
Where ππ€π= initial water saturation
π= initial oil-in-place, STB
π. π= total pore volume, bbl
m= ratio of initial gas-cap gas reservoir volume to initial reservoir oil volume, bbl/bbl
The Material Balance Equation Derivation
β Treating the reservoir pore as an
idealized container as illustrated
below, volumetric balance expressions
can be derived to account for all
volumetric changes which occur
during the natural productive life of
the reservoir.
The Material Balance Equation Derivation
β The MBE can be written in a generalized form as follows:
Pore volume occupied by the oil initially in place at ππ + Pore volume occupied by the
gas in the gas cap at ππ=
Pore volume occupied by the remaining oil at p + Pore volume occupied by the gas in
the gas cap at p + Pore volume occupied by the evolved solution gas at p + Pore volume
occupied by the net water influx at p + Change in pore volume due to connate-water
expansion and pore volume reduction due to rock expansion + Pore volume occupied by
the injected gas at p + Pore volume occupied by the injected water at p _ _ _ _ (2)
The Material Balance Equation Derivation
β The above nine terms composing the MBE can be separately determined from the
hydrocarbon PVT and rock properties, as follows:
1. Pore Volume Occupied by the Oil Initially in Place:
ππππ’ππ ππππ’ππππ ππ¦ ππππ‘πππ πππ β ππ β πππππ = π π΅ππ βββ 3
Where π= oil initially in place, STB
π΅ππ= oil formation volume factor at initial reservoir pressure ππ, bbl/STB
The Material Balance Equation Derivation
β The above nine terms composing the MBE can be separately determined from the
hydrocarbon PVT and rock properties, as follows:
2. Pore Volume Occupied by the Gas in the Gas Cap:
ππππ’ππ ππ πππ πππ = π π π΅ππ βββ 4
Where m is a dimensionless parameter and defined as the ratio of gas-cap volume to
the oil zone volume.
The Material Balance Equation Derivation
β The above nine terms composing the MBE can be separately determined from the
hydrocarbon PVT and rock properties, as follows:
3. Pore Volume Occupied by the Remaining Oil:
ππππ’ππ ππ π‘βπ πππππππππ πππ = (π β ππ) π΅π βββ 5
Where ππ= cumulative oil production, STB
π΅π= oil formation volume factor at reservoir pressure p, bbl/STB
The Material Balance Equation Derivation
β The above nine terms composing the MBE can be separately determined from the
hydrocarbon PVT and rock properties, as follows:
4. Pore Volume Occupied by the Gas Cap at Reservoir Pressure p:
βͺ As the reservoir pressure drops to a new level p, the gas in the gas cap expands and
occupies a larger volume. Assuming no gas is produced from the gas cap during the
pressure decline, the new volume of the gas cap can be determined as:
ππππ’ππ ππ π‘βπ πππ πππ ππ‘ π =ππ π΅πππ΅ππ
π΅π βββ 6
Whereπ΅ππ= gas formation volume factor at initial reservoir pressure, bbl/scf
π΅π= current gas formation volume factor, bbl/scf
The Material Balance Equation Derivation
β The above nine terms composing the MBE can be separately determined from the
hydrocarbon PVT and rock properties, as follows:
5. Pore Volume Occupied by the Evolved Solution Gas:
βͺ This volumetric term can be determined by applying the following material balance
on the gas solution:
π£πππ’ππ ππ π‘βπππ£ππππ£ππ
π πππ’π‘πππ πππ =
π£πππ’ππ ππ πππ ππππ‘πππππ¦ ππ π πππ’π‘πππ
βπ£πππ’ππ ππ
πππ πππππ’πππβ
π£πππ’ππ πππππ πππππππππππ π πππ’π‘πππ
The Material Balance Equation Derivationβ The above nine terms composing the MBE can be separately determined from the
hydrocarbon PVT and rock properties, as follows:
5. Pore Volume Occupied by the Evolved Solution Gas:
βͺ This volumetric term can be determined by applying the following material balance on the gas solution:
ππππ’ππ ππ π‘βπ ππ£πππ£πππ πππ’π‘πππ πππ
= π π π π β πππ π β π β ππ π π π΅π ββ β(7)
Where ππ= cumulative oil produced, STB
π π= net cumulative produced gas-oil ratio, scf/STB
π π = current gas solubility factor, scf/STB
π΅π= current gas formation volume factor, bbl/scf
π π π= gas solubility at initial reservoir pressure, scf/STB
The Material Balance Equation Derivation
β The above nine terms composing the MBE can be separately determined from the
hydrocarbon PVT and rock properties, as follows:
6. Pore Volume Occupied by the Net Water Influx:
πππ‘ π€ππ‘ππ πππππ’π₯ = ππ βπππ΅π€ βββ(8)
Where ππ= cumulative water influx, bbl
ππ= cumulative water produced, STB
π΅π€= water formation volume factor, bbl/STB
The Material Balance Equation Derivation
β The above nine terms composing the MBE can be separately determined from the
hydrocarbon PVT and rock properties, as follows:
7. Change in Pore Volume Due to Initial Water and Rock Expansion:
βͺ The compressibility coefficient c, which describes the changes in the volume
(expansion) of the fluid or material with changing pressure, is given by:
π =β1
π
ππ
ππ
Or
βπ = π π βπ
Where βπ represents the net changes or expansion of the material as a result of
changes in the pressure.
The Material Balance Equation Derivation
β The above nine terms composing the MBE can be separately determined from the
hydrocarbon PVT and rock properties, as follows:
7. Change in Pore Volume Due to Initial Water and Rock Expansion:
βͺ Therefore, the reduction in the pre volume due to the expansion of the connate-
water in the oil zone and the gas cap is given by:
ππππππ‘π β π€ππ‘ππ ππ₯ππππ πππ = ππππ π£πππ’ππ ππ€π ππ€ βπ
The Material Balance Equation Derivation
β The above nine terms composing the MBE can be separately determined from the
hydrocarbon PVT and rock properties, as follows:
7. Change in Pore Volume Due to Initial Water and Rock Expansion:
βͺ Substituting for the pore volume (P.V) with equation (1) gives:
πΈπ₯ππππ πππ ππ ππππππ‘π π€ππ‘ππ =π π΅ππ(1 + π)
1 β ππ€πππ€π ππ€ βπ ββ β(9)
Where βπ= change in reservoir pressure, (ππ β π)
ππ€= water compressibility coefficient, ππ πβ1
π= ratio of the volume of the gas-cap gas to the reservoir oil volume, bbl/bbl
The Material Balance Equation Derivation
β The above nine terms composing the MBE can be separately determined from the
hydrocarbon PVT and rock properties, as follows:
7. Change in Pore Volume Due to Initial Water and Rock Expansion:
βͺ Similarly, the reduction in the pore volume due to the expansion of the reservoir rock
is given by:
πΆβππππ ππ ππππ π£πππ’ππ =π π΅ππ(1 + π)
1 β ππ€πππ‘ βπ ββ β(10)
The Material Balance Equation Derivation
β The above nine terms composing the MBE can be separately determined from the
hydrocarbon PVT and rock properties, as follows:
7. Change in Pore Volume Due to Initial Water and Rock Expansion:
βͺ Combining the expansions of the connate-water and formation as represented by
equations (9) and (10) gives:
πππ‘ππ πβπππππ ππ ππππ π£πππ’ππ = π π΅ππ 1 +πππ€π ππ€+ ππ
1 β ππ€πβπ ββ β 11
The Material Balance Equation Derivation
β The above nine terms composing the MBE can be separately determined from the
hydrocarbon PVT and rock properties, as follows:
8. Pore Volume Occupied by the Injection Gas and Water:
βͺ Assuming that πΊπππ volumes of gas and ππππ volumes of water have been injected
for pressure maintenance, the total pore volume occupied by the two injected fluids is given by:
πππ‘ππ π£πππ’ππ = πΊππππ΅ππππ +πππππ΅π€ βββ(12)
Where πΊπππ= cumulative gas injected, scf
π΅ππππ= injected formation volume factor, bbl/scf
ππππ= cumulative water injected, STB
π΅π€= water formation volume factor, bbl/STB
The Material Balance Equation Derivation
β Combining equations (3) through (12) with equation (2) and rearranging gives:
π =πππ΅π + πΊπ β πππ π π΅π β ππ βπππ΅π€ β πΊππππ΅ππππ βπππππ΅π€
π΅π β π΅ππ + π π π β π π π΅π +ππ΅πππ΅ππ΅ππ
β 1 + π΅ππ(1 + π)ππ€πππ€ + ππ1 β ππ€π
βπ
ββ β 13
Where π= initial oil-in-place, STB
πΊπ= cumulative gas produced, scf
ππ= cumulative oil produced, STB
π π π= gas solubility at initial pressure, scf/STB
π= ratio of gas-cap gas volume to oil volume, bbl/bbl
π΅ππ= gas formation volume factor at ππ, bbl/scf
π΅ππππ= gas formation volume factor of the injected gas, bbl/scf
The Material Balance Equation Derivation
β The cumulative gas produced πΊπ can be expressed in terms of the cumulative gas-oil ratio π π
and cumulative oil produced ππ by:
πΊπ = π πππ βββ 14
βͺ Combining equation (14) with equation (13) gives:
π =ππ [π΅π+ π π β π π π΅π] β ππ βπππ΅π€ β πΊππππ΅ππππ βπππππ΅π€
π΅π β π΅ππ + π π π β π π π΅π +ππ΅πππ΅ππ΅ππ
β 1 + π΅ππ(1 + π)ππ€πππ€ + ππ1 β ππ€π
βπ
ββ β 15
βͺ The above relationship is referred to as the material balance equation (MBE).
The Material Balance Equation Derivation
β A more convenient form of the MBE can be determined by introducing the concept of the total
(two-phase) formation volume factor π΅π‘ into the equation.
β This oil PVT property is defined as:
π΅π‘ = π΅π + π π π β π π π΅π βββ(16)
The Material Balance Equation Derivation
β Introducing π΅π‘ into equation (15) and assuming, for the sake of simplicity, no water or gas
injection gives:
π =ππ [π΅π‘+ π π β π π π π΅π] β ππ βπππ΅π€
π΅π‘ β π΅π‘π +ππ΅π‘ππ΅ππ΅ππ
β 1 + π΅π‘π(1 + π)ππ€πππ€ + ππ1 β ππ€π
βπ
ββ β 17
Where ππ€π= initial water saturation
π π= cumulative produced gas-oil ratio, scf/STB
βπ= change in the volumetric average reservoir pressure, psi
The Material Balance Equation Derivation
β In a combination-drive reservoir where all the driving mechanisms are simultaneously present, it is of
practical interest to determine the relative magnitude of each of the driving mechanisms and its
contribution to the production.
β Rearranging equation (17) gives:
π π΅π‘ β π΅π‘ππ΄
+ππ π΅π β π΅ππ /π΅ππ
π΄+ππ βπππ΅π€
π΄+ππ΅ππ(1 + π)
ππ€πππ€ + ππ1 β ππ€π
(ππ β π)
π΄= 1 ββ β 18
With the parameter A as defined by:
π΄ = ππ π΅π‘ + (π π β π π π)π΅π βββ(19)
The Material Balance Equation Derivation
β Equation (18) can be abbreviated and expressed as:
π·π·πΌ + ππ·πΌ +ππ·πΌ + πΈπ·πΌ = 1.0 ββ β(20)
Where π·π·πΌ= depletion-drive index
ππ·πΌ= segregation (gas-cap)- drive index
ππ·πΌ= water-drive index
πΈπ·πΌ= expansion (rock and liquid)- drive index
The Material Balance Equation
Example: The big butte field is a
combination-drive reservoir. The current
reservoir pressure is estimated at 2,500
psi. The reservoir production data and
PVT information are given below:
The following additional information is
available:
Volume of bulk oil zone= 100,000 ac-ft
Volume of bulk gas zone= 20,000 ac-ft
Calculate the initial oil-in-place.
The Material Balance Equation
Solution:
Step1. Assuming the same porosity and connate-water for the oil and gas zones, calculate m:
π =20,000
100,000= 0.2
Step 2. Calculate the cumulative gas-oil ratio π π:
π π =5.5 β 109
5 β 106= 1100
π ππ
πππ΅
Step 3. Solve for the initial oil-in-place by applying equation (15):
π =5β106 1.33+ 1100β500 0.0015 β(3β106β0.2β106
1.35β1.33 + 600β500 0.0015+(0.2)(1.35)0.0015
0.0011β1
= 31.14 πππππ΅