Reservoir engineering

Wiki Write-Off Entry
Student Chapter	University of Brawijaya
Competition	June 2015

Reservoir rock have many lithologies like sandstones, limestones, granitic, tuff, and shale. Reservoir filled by hydrocarbon on fracture or pores. All reservoir hydrocarbon content connate water . some reservoir content connate water in the micropore that content 10-60% from the pores volume.

Information about scale factor needed to conceptualized reservoir. Scale factor can differences by microscopic; relates to pores and sand grains, macroscopic; relates to conventional core-plug scale, megascopic relates to the scale of grid-blocks in simulation models, and gigascopic relates to regional scale.

Physical Properties of Reservoir

Homogeneity and Heterogeneity

Homogeneity factor consist uniform material. Homogeneity factor is similar depositional environment, grain distribution is relatively similar, and similar kind of intensity diagenesa. While the heterogeneity factors is changes in depositional environment, sedimentary material, grain size distribution, and facies, also different type and intensity of diagenesis processes.

Pore Structure and Geometry

Pore structure varies with the size, shape, and composition of natural grains, as well as fractures. Geometry ranging from <1 micron to 100 micron . Pore characteristic will determine oil recovery method.

Reservoir Pressure

Fluid in reservoir have hydrostatic pressure that associated reservoir system. Pressure from overburden rock also press the pore and increase the fluid pressure.

Temperature Reservoir

Temperature at some depth comes from gradient geothermal and it is directly proportional to the depth.

Reservoir Boundary

Reservoir bounded by impermeable layers and fluid contacts. Field boundaries is ensured through the well but based on well data; electric logs, well flow testing, and repeat formation tester (RFT). Boundary of water and hydrocarbon zones is reduced gradually. This saturation interval resulted in the transition zone. This zone is used as perforation zone in production well.

Physical Properties of Rocks

Porosity (Phi) 5, permeability (k) mD, fluid saturation (S) %, capiler pressure (Pc) Psi, compressibility (C) Psi^-1, resistivity (R) ohm.

Porosity

Porosity is the amount of free space compared to the bulk volume of rock. Porosity affects the ability of the rock to keep the fluid inside the pores of the rock. The pores can be interconnected and isolated. The pores are interconnected referred to as the effective porosity. Total porosity of rock is a combination of pore volume and pore volume isolated interconnected. While porosity very small called microporosity. Connate water is stored in this microporosity.

1. Formula for absolute porosity
   • $\phi _{\text{ab}}={\frac {\text{Volume of total pores}}{\text{Total rocks volume}}}$
2. Formula for effective porosity
   • $\phi _{\text{eff}}={\frac {\text{Volume of interconnected pores}}{\text{Total volume of rocks}}}$

Figure 1.Pore distribution inside the reservoir rocks

Permeability

Permeability is the ability of the rock to drain fluid (hydraulic conductivity) through the pores of the rock. The bigger the pore throat more easily drain the fluid. Unit permeability is miliDarcy.

Absolute permeability (Ka)

Absolute permeability retrieved from conventional core analysis or by the approach through equations based on log analysis. Empirical equation that can be used is :

• Timur equation:

$k_{a}=0.136{\frac {\phi ^{4.4}}{Swi^{2}}}$

• Coates equation

$k_{a}^{1/2}=100\phi ^{2}{\frac {[1-Swi]}{Swi^{2}}}$

Effective permeability (Kef)

Measurements can be made directly at the reservoir scale well test analysis. Direct measurement is only valid on the condition that a constant fluid saturation. In the analysis of special core analysis laboratory with a known value of relative permeability. Relative permeability equation for Corey Model is:

$k_{rw}=(S_{w}^{*})^{4}$

$k_{ro}=(1-S_{w}^{*})^{3}(1+S_{w}^{*})$

With effective permeability is

${\text{K}}_{\text{ef}}={{\text{K}}_{\text{r}}\times {\text{K}}_{\text{a}}}$

Fluid Saturation (S)

A fraction of the level of pore space is filled by a fluid.

${\text{S}}_{\text{f}}{\text{(fraksi)}}={\frac {{\text{V}}_{\text{v}}}{{\text{V}}_{\text{p}}}}$

Capillarity and Wettability

Capillarity is the power of pressure between the two types of fluid immissicible. Based on capillarity power will be able to determine the level of the fluid content wettability of rock. Wettability is the ability of fluid to wetting the rocks, that the value is represented by contact angel (θ). The cut off limit wettability is θ = 90°. If θ<60°, then the rock are water wet, and if θ>120° the rock has oil/gas wet. Intermediate wet has gotten if the θ around 90° (between 60° and 120°).

Figure 2. Capilarity and wettability of fluids that fills the reservoir

Capillary Reservoir Pressure

Surface pressure of two different types of fluid known as capillary pressure. Capillary pressure is influenced by the pore size and wettability.

$P_{c}={\frac {2\sigma \cos {\theta }}{r}}$

With θ wettability contact, σ is surface tension, and r pore size or curvature of the fluid surface. Capillary pressure data known as wetting phase function. Conversion of laboratory data required to determine the reservoir to reservoir capillarity.

$P_{c_{res}}=P_{c_{lab}}{\frac {\sigma _{res}(\cos {\theta })_{res}}{\sigma _{lab}(\cos {\theta })_{lab}}}$

If the hydrocarbon pressure equal to the water capillary pressure equal with zero. This point is called as a free water level (FWL).

${\text{P}}_{\text{c}}={\text{P}}_{\text{hc}}-{\text{P}}_{\text{w}}$

Changes in capillary pressure against the reference position below the hydrocarbon zone can be seen as a function of:

$h={\frac {P_{c}}{0.433(\rho _{w}-\rho _{hc})}}$

To determine fluid contacts must be known threshold value of pressure (Pct) is known from the curve Pc against Sw.

${\displaystyle {\text{Depth WOC or Depth GWC}}=D_{$FWL}-{\frac {P_{c}t}{0.433(\rho _{w}-\rho _{hc})}}}

Compressibility

Isothermal compressibility is defined as the relative volume changes due to changes in system pressure at fixed temperature.

$C={\frac {1}{V}}\left({\frac {\Delta V}{\Delta P}}\right)_{T}(psi^{-1})$

Calculate compressibility rock cores in data analysis, it can be used Newman empirical equation:

Compressibility Sandstone:

$C_{f}={\frac {97.32(10^{-6})}{(1+55.8721\phi )^{1.42859}}}$

Compressibility Carbonate:

$C_{f}={\frac {0.853531}{(1+2.47664\times \phi )^{0.92990}}}$

For hydrocarbon reservoir compressibility can be express by:

${\text{C}}_{\text{t}}={\text{S}}_{\text{o}}{\text{C}}_{\text{o}}+{\text{S}}_{\text{g}}{\text{C}}_{\text{g}}+{\text{S}}_{\text{w}}{\text{C}}_{\text{w}}+{\text{C}}_{\text{f}}$

Physical Properties of Gas

Equation of state for gas can be express by

${\text{PV = nRT}}$

Where P is a pressure in psia, V is volume, mole content is n, R is universal constant with gas is 10.73, and T is temperature in reamur. In a atmosphere condition gas have compressible characteristic than ideal gas. The amount of gas deviations stated in deviation factor z (supercompressibility factor), so :

${\text{PV = znRT}}$

Specific Gravity

Specific gravity defined by the rate of gas density in a pressure and temperature sub surface by gas density in equal temperature and pressure (usually in surface). </ref>

${\displaystyle \gamma _{g}={\frac {$MW}{28.97}}}

Gas Formation Volume Factor

Formation Volume Factor is ratio between gas volume in reservoir condition by standard condition. For gas volume formation is:

$B_{g}=0.02829{\frac {zT}{P}}$

in cuft/scf

$B_{g}=0.00504{\frac {zT}{P}}$

in bbl/scf

Compressibility Isothermal Gas

Compressibility isothermal gas can be calculated by :

$C_{g}={\frac {1}{P}}-{\frac {1}{z}}{\frac {dz}{dP}}(psi^{-1})$

Where

${\frac {dz}{dP}}\times {\frac {1}{z}}$

is the slope of the line versus P at the point of the review.

Viscosity Gas

Viscosity gas in P and T identified can be expressed by :

$\mu _{P,T}=\mu _{1}\left({\frac {\mu }{\mu _{1}}}\right)$

μ1 is the viscosity for 1 atm

Physical Properties of Oil

Gas Saturation in Oil

Gas saturation in oil calculated by

$R_{s}=\gamma _{g}\left({\frac {P}{18\times 10^{\gamma _{g}}}}\right)^{1.204}$

Where

${\displaystyle \gamma _{g}=0.00091T-0.0125(^{\circ }{\text{$API}})}

Oil Formation Volume Factor

Formation volume factor is the ratio of the volume of oil in the reservoir (include saturated gas) and the volume of oil on the surface. Oil in reservoir volume VR (include saturated gas) will changes into 2 phase fluid, it is oil stock tank volume VST and gas stock tank volume VGST. Ratio formation volume factor oil Bo expressed by:

$B_{o}={\frac {V_{R}}{V_{ST}}}$

Where

• V_R = oil volume in reservoir condition
• V_ST = stock tank oil volume

The unit of Bo is barrel reservoir (rb) per stock tank barrel (STB). For reservoir pressure bigger than bubble point (limit phase changes) pressure (P>Pb), Bo equation is :

$B_{o}=B_{o_{b}}\exp(C_{o}(P_{b}-P))$

For P ≤ P_b, use Standing correlation:

$B_{o}=0.972+0.000147F^{1.175}$

Where

$F=R_{s}\left({\frac {\gamma _{g}}{\gamma _{o}}}\right)^{0.5}+1.25T$

with T in Fahrenheit (°F)

Compressibility Oil

If there is no PVT analysis data, compressibility oil can be calculated by this equation

For P > P_b:

${\displaystyle C_{o}={\frac {5Rsb+1.72T-1180\gamma _{g}+12.62^{\circ }{\text{$API}}-1433}{P\times 10^{5}}}}

For P < P_b:

${\displaystyle \ln {C_{o}}=-0.644-1.430\ln {P}-0.395\ln {P_{b}}+0.390\ln {T}+0.455\ln {Rsb}+0.262\ln(^{\circ }{\text{$API}})}

Where T in Fahrenheit (°F)

Formation Volume Factor of two Phase

Above bubble point pressure, gas and oil combined in one phase. For this case, fluid volume in reservoir have different value in surface volume, and it is called two-phase formation volume factor (B_t), expressed by:

$B_{t}=B_{o}+B_{g}(R_{s_{i}}+R_{s})$

Where,

• R_si = saturated gas in oil,
• B_g = formation volume factor gas, and
• R_s = gas saturated under bubble point

Oil Viscosity

Oil reservoir with pressure above the bubble point, the viscosity decreases as a result of a pressure drop. If otherwise (P <Pb), viscosity enlarged in line with declining reservoir pressure as a result of dissolved gas liberated.

For P ≤ P_b:

Dead oil calculated by Egbogah correlation:

${\displaystyle \log[\log(\mu _{$OD}+1)]=1.8653-0.025086(^{\circ }{\text{API}})-0.5644\log {T}}

Live oil calculated by Beggs-Robinson correlation:

${\displaystyle \mu _{o}=10.715(R_{s}+100)^{0.515}\mu _{$OD}^{B}}

where,

$B=5.44(R_{s}+150)^{-0.388}$

For P > P_b:

Live oil calculated by Vasquez-Beggs Corelation:

$\mu _{o}=\mu _{ob}\left({\frac {P}{P_{b}}}\right)^{m}$

Where μ_ob = viscosity live oil in Pb

$m=2.6P^{1.187}\exp[-11.513-8.98\times 10^{-5}\times P]$

Physical Properties Water Formation

Water Formation Volume Factor

Water formation volume factor (B_w) estimated by McCain correlation:

${\displaystyle B_{w}=(1+\Delta V_{WT})(1+\Delta V_{$WP})}

Where,

$\Delta V_{WT}=-1.0001\times 10^{-2}+1.33391\times 10^{-4T}+50.50654\times 10^{-7}T^{2}$

${\displaystyle \Delta V_{$WP}=-1.95301\;\times \;10^{-9}PT\;-\;1.72834\;\times \;10^{-13}P^{2}T\;-\;3.58922\;\times \;10^{-7}P\;-\;2.25341\;\times \;10^{-10}P^{2}}

Saturated Gas in Water

The gas can be dissolved in water formation, the factors that influence it is salinity. Estimated solubility is calculated by correlation McCain:

$Rsw=Rswp\times 10^{-0.0840655S\times T^{-0.285854}}$

Rswp is saturated gas in pure water:

${\displaystyle {\text{R}}_{\text{swp}}={\text{A}}+{\text{$BP}}+{{\text{CP}}^{2}}}

Where,

${\text{A}}=8.15839-6.12265\times 10^{-2}{\text{T }}+1.91663\times 10^{-4}{\text{T}}^{2}-2.1654{\text{T}}^{3}$

${\text{B}}=1.01011\;\times \;10^{-2}\;-\;7.44241\;\times \;10^{-5}{\text{T }}+\;3.05553\;\times \;10^{-7}{\text{T}}^{2}\;-\;2.94883\;\times \;10^{-10}{\text{T}}^{3}$

${\text{C}}=10^{-7}(9.02505\;-\;0.130237{\text{T }}+\;8.53425\;\times \;10^{-4}{\text{T}}^{2}\;-\;2.34122\;\times \;10^{-6}{\text{T}}^{3}\;+\;2.37049\;\times \;10^{-9}{\text{T}}^{4})$

Water Compressibility

Compressibility can be calculated by Osif correlation at pressure above the pressure Pb in water and gas systems.

$C_{w}=-{\frac {1}{Bw}}\left({\frac {\partial Bw}{\partial P}}\right)_{T}$

$C_{w}=(7.033P+541C_{NaCl}-537.0T+403.300)^{-1}$

Where CNaCl is water salinity

Water Viscosity

Greater reservoir pressure affect the viscosity is getting smaller, the higher the salinity increase water viscosity. The higher temperature causes the viscosity decreases. to determine the viscosity of water McCain correlation can be used.

At atmosphere pressure and reservoir temperature:

$\mu _{w1}=(109.574-8.40564S+0.313314S^{2}+8.72213\times 10^{-5}S^{3})\times T^{A}$

where

$A=-1.2166\;+\;2.63951\;\times \;10^{-2}S\;-\;6.79461\;\times \;10^{-4}S^{2}\;-\;5.47119\;\times \;10^{-5}S^{3}\;+\;1.55586\;\times \;10^{-6}S^{4}$

At reservoir pressure and temperature:

$\mu _{w}=(0.9994+4.0295\times 10^{-5}P+3.1062\times 10^{-9}P^{2})\times \mu _{w1}$

Other Source

• Koesoemadinata. 1980. Geologi Minyak dan Gas Bumi. Bandung: ITB

feet from west line

muddy water

barrels

American Petroleum Institute

stock tank barrels

outside diameter

wash pipe

bridge plug

casing pressure