Reservoir Thermodynamics KNW

hydrocarbon reservoir

an accumulation of hydrocarbon (in gas, liquid, solid or combo state) in porous permeable sedimentary or fractured rock formations.

HC at STP formula

STHIIP = Vø(1-Swi)/B_Hi

V = gross/ bulk rock volume

ø = porosity

Swi = initial water saturation

B_Hi = initial HC formation volume

STP

T = 15°C = 60°F

P = 101325 Pa = 14.7 psia

principles of EOR

• improve mobility ratio

• increase capillary number

Why do we need to know about reservoir fluids?

• multiphase flow

• suitability for surface facilities

• environmental & health issues

• compatibility

What do we need to know about reservoir fluids?

• composition

• solution gas oil ratio, Rs

• formation volume factor, Bo Bg

• density

• viscosity

• IFT, surface tension

• PT

compositional analysis

the measurement of the distribution of HC and other components present in oil and gas samples using modern chromatography techniques

HC grouping criteria

• molecular configuration: straight chin, branched, cyclic or aromatic

• number of carbon bonds: single, double & triple

HC groups

• aliphatic compounds: alkanes (C_nH_2n+2), alkenes (C_nH_2n), alkynes (C_nH_2n-2)

  • saturated → single bonds

  • unsaturated → at least one double/ triple bond

• aromatic compounds: arenes

  • contain unsaturated cyclic compounds

  • react readily bc of C=C bond

  • formula: C₆H₆(CH₂)_n

compounds present in the reservoir

• HC

• inorganic compounds: He, N2, CO2, H2S, water

• sulfur/ sour compounds: H2S, RSH, RSR, RSSR

• non-HC elements: Hg, Ni, V, radioactive elements

• solid like compounds: waxes, resins, asphaltenes, diamondoids, hydrates

intensive property

a property which is independent of the system mass (quantity) = bulk property e.g.

• activity/ fugacity

• them potential

• density/ hardness/ roughness

• specific/ molar enthalpy/ entropy/ Helmholtz free energy/ internal energy/ gibs free energy/ heat capacity/ volume

• isothermal compressibility

• pT

• thermal conductivity/ diffusivity

• volumetric thermal expansion

extensive property

a property which is dependent of the system mass (quantity) = additive property e.g.

• Helmholtz free energy

• enthalpy

• internal energy

• entropy

• gibs free energy

• heat capacity

• mass

• volume/ length

• charge

thermodynamic state

the macroscopic condition of a thermodynamic system at a particular time determined when all intensive properties are fixed.

• steady → a system has numerous properties that are unchanging in time (time-invariant or equilibrium), but the system is either open or closed.

• unsteady → a process variable (property) has been changed, and the system has not yet reached a steady state (i.e., local equilibrium or partial equilibrium).

homogeneous system

a thermodynamic system whose intensive properties change continuously and uniformly (smoothly). i.e., chemical composition and physical properties are the same in all parts of the system or change continuously from one point to another

heterogeneous systems

a thermodynamic system consisting of two or more homogeneous bodies (phases). Each phase is separated from other phases by interfaces or boundaries, and in passing over such a boundary, the chemical composition of the substance or its physical properties abruptly changes.

phase

a restricted part of a system with distinct physical and chemical properties.

state functions/ variables

a system property that depends only on the system’s current (equilibrium) state → allow quantifying any change of a system e.g. enthalpy, entropy & internal energy

path function

a system property that depends on the specific transition (or path) between two equilibrium states. e.g. mechanical work & heat

process

any change that a system undergoes from one equilibrium state to another.

• reversible → a process that can be reversed without leaving any trace on the surroundings

  • carried out infinitesimally slowly

  • idealisation of processes

• irreversible → a process in that change is brought about rapidly, and the system does not attain equilibrium.

equilibrium = state of rest

no further change or - more precisely - no net-flux will take place unless one or more properties of the system are altered.

(dG)_T,p = 0

concentration

the amount of solute in a solution mixture

mass concentration

the mass of a solute dissolved in a unit volume of a solution

𝜌_solute = m_solute/ V_solution [kg/m3]

molar concentration = molarity

the number of moles of a solute dissolved in a unit volume of a solution

M = c_solute = n_solute/ V_solution [mol/lit]

1 mol/lit = 1000 mol/m3

volume concentration = volume fraction

the volume of a solute dissolved in a unit volume of a solution

ø_solute = V_solute/ V_solution [m3/m3]

molality

the number of moles of a solute dissolved in a unit mass of a solvent

m = n_solute/ m_solvent [mol/kg of volvent]

internal energy, U

energy of a system, i.e., the energy associated with the random motion of the molecules within a system = Associated with the temperature of the system.

U = Q + W [J]

• kinetic = translational, rotational & vibrational

• potential = static energy of atoms & chemical bonds

1.law of thermodynamics

change in the total macroscopic energy of a system is equal to the difference between the total amount of heat supplied to the system and the amount of work done by the system on its surroundings.

dE = 𝛿Q - 𝛿W

d(E_kin) + d(E_pot) + dU = 𝛿Q - 𝛿W

dU = 𝛿Q - 𝛿W

∆U = Q - W

enthalpy, H

a measure of the total heat content of a thermodynamic system at constant pressure conditions.

H = U + pV [J]

∆H = ∆U + ∆(pV)

∆H = Q - W + ∆(pV). & W = p∆V => ∆H = Q at KE, PE = 0

entropy, S

the measure of the tendency to change and the direction in which change can occur = Potential of an macroscopic system to be described by different microscopic states.

dS ≥ 𝛿Q/T [J/K]

2.law of thermodynamics

the entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process.

• ∆𝑆_universe> 0 spontaneous process

• ∆𝑆_universe= 0 reversible (equilibrium) process

• ∆𝑆_universe= ∆𝑆_system + ∆𝑆_surrondings

Gibbs free energy, G

a thermodynamic property that predicts whether a process will occur spontaneously at constant temperature and pressure. → reactions move in the direction of decreasing dG

𝐺= 𝐻 − 𝑇𝑆 [J]

• ∆𝐺 < 0 spontaneous processes

• ∆𝐺 > 0 nonspontaneous processes

Helmholtz free energy, A

a thermodynamic property that predicts whether a process will occur spontaneously at constant temperature and volume.

A = U - TS [J]

• ∆𝐴 < 0 spontaneous processes

• ∆𝐴 > 0 nonspontaneous processes

thermodynamic processes

• adiabatic → adiabatic (no heat added to or removed from the system),

• isothermal → constant temperature

• isobaric → constant pressure

• isochoric → constant volume

thermodynamic systems

a portion of the universe defined by appropriate boundaries (physical or virtual)

• open → allowing exchange of mass, heat, and work energy with the surroundings

• closed → allowing exchange of heat or work energy with the surroundings but not mass

• isolated → allowing neither exchange of mass nor energy in any form with the surroundings

• adiabatic/ insulated → allowing exchange of mass and work energy with the surroundings but not heat

sour gas

any gas that specifically contains hydrogen sulfide in significant amounts (>5.7 mg of H2S per cubic meter of natural gas).

acid gas

any gas that contains significant amounts of acidic gases such as carbon dioxide (CO2) or hydrogen sulfide.

natural gas composition

C1-7 (HC) + CO2/H2S/N2 (non HC)

component

a chemically independent constituent of a system

→ the minimum number of such chemical units or species (ions/molecules) required to describe the composition of all the phases present in the system.

gas viscosity characteristics

directly proportional

• at low p = increases as T increases

• at high p = decreases as T increases

general oil viscosity characteristics

• decrease w/ increasing T

• increase w/ increasing p

saturated oil viscosity characteristics

• decreases w/ increasing p due to the increasing fraction of dissolved light components

• decreases w/ increasing T

typical oil viscosities

• crude: 0.5 -10 cP

• heavy oils: » 100 cP

IFT properties

• decreases w/ increasing T

• effected by pH

• typical range: 20-150 mN/m

IFT influence

• capillary pressure

• residual saturation

• shape of relative permeability curves

degree of freedom, F

the number of variables that may be varied independently without changing the number of phases present at equilibrium.

• F = 0 → invariant: change the no. of present phases (points)

• F = 1 → univariat: the value of one property may be adjusted without changing the number of phases (lines)

• F = 2: bivariant: the values of two properties may be adjusted independently without a change in the number of phases present (areas)

Gibbs’ phase rules

determine the variance (degrees of freedom) of any system at equilibrium.

𝐹 = 𝐶 − 𝑃 + 2

• If the substance is present as only one phase, e.g., a solid, then P = 1

• If the system exists as two phases in equilibrium (e.g., vapor and liquid), then P = 2

• If the system exists as three phases in equilibrium (solid, liquid, and vapor), then P = 3

vapour quality

the ratio of the mass of vapor to the total mass of the saturated mixture

Characteristics of Two Component Systems

• p_crit > p_{crit, pure comp}

• T_crit between T_crit pure components

• BP_temp > BP_{temp, pure light}

• DP_temp < DP_{temp, pure heavy}

phase envelope diagram components

• BP curve

• DP curve

• critical point

• quality lines

• cricondentherm (Tct)

• cricondenbar (Pcb)

reservoir fluids classification

large to small molecules

• black oil

• volatile oil

• gas condensate

• wet gas

• dry gas

reservoir fluids classification parameters

• initial producing gas oil ratio, GOR

• gravity of the stock tank liquid, API

• composition

black oil reservoir

• GORi < 2000 [scf/stb] → increases during production, below pb

• 15 < °API < 40

• brown to dark green

• low vs high shrinkage oil

volatile oil reservoir

• 2000 < GORi < 3300 [scf/stb]→ increases during production

• 40 < °API < 50

• Larger fraction of light and intermediate components

• Greenish to orange

gas condensate reservoir

• Tc < Tres < Tct

• 3300 < GORi < 50000 [scf/stb]

• 50 < °API < 70

• Translucent or slightly colored

dry gas reservoir

• The hydrocarbon mixture exists as a gas both in the reservoir and in the surface

• Tres > Tct

• GORi > 100000 [scf/stb] → no surface liquids

• C1 and smaller fraction of intermediates components (C2-C6) and non-HC components (N2, CO2, etc.)

wet gas reservoir

• The hydrocarbon mixture exists as a gas in the reservoir and two-phase in the surface

• Tres > Tct

• 50000 < GORi < 100000 [scf/stb] → will remain constant

• 60 < °API < 70

• C1 and larger fraction of intermediate components (C2- C6)

• translucent

retrograde condensation

the pressure is reduced below the dew point, the volume of liquid in the two-phase mixture initially increases

condensate banking

When liquid condensate builds up (or 'banks') near the wellbore or in low spots in a pipeline.

• This can happen in gas condensate reservoirs when the pressure drops below a certain level (called the dew point), causing the gas to turn into liquid.