3 3 Cubic packing = 47.6 % Rombic packing = 26 % Cubic packing, different grain size = 12.5 % 1) Porosity Porosity: V p = pore volume V matrix = grain volume V tot = bulk volume Ideal Porous sandstone Sand grain water oie Pore size: 10 - 50 m
4 4 Effective porosity eff is the porosity of interconneceted pores Residual porosity res is the porosity of the remaining pores Typical effective porosity: Sandstone: = 10 - 40 % depending on grain shape Limestone and dolomite: = 5 - 25 % depending on fractures Total porosity: tot = eff + res How do we measure the porosity eff ? 1. In situ measurements in the reservoir (well logging) 2. Core analysis: drilling cores from the reservoir followed by laboratory analysis Drilled cores (d = 2,5 - 5´´) Drilling sylindrical core plugs (d = 1,5´´, h = 3 ´´) Clean and dry plugs
5 5 2) Saturation A porous medium (reservoir or core plug) usually contains several fluids: water, oil, gas Saturation = the fraction of the total pore volume V p which contains the actual fluid Water saturation:Oil saturation: Gas saturation: Normally, the entire pore volum will be filled be fluids, hence: The porosity determines the amount of oil in the reservoir V = the totale pore volume (PV) S o = the oil saturation S wc = “connate water” – the original water saturation Stock Tank Oil Originally In Place (STOOIP): B o = “oil formation volum factor” = the ratio between the oil volume in the reservoir and the oil volume in the stock tank at the surface (Rm 3 /Sm 3 ). Often B o > 1 because gas is released from the oil when brought to the surface. Oil In Place (OIP): OIP = V S o = V (1 - S wc ) unit Rm 3 STOOIP = OIP /B o =V (1 - S wc )/B o unit Sm 3
6 6 3) Miscible and immiscible fluids a) water and oil are immiscible The van der Waals force is larger between like molecules. The molecules in a liquid is held together by electrostatical forces (van der Waals forces) acting between the molecules b) water and alcohol (ethanol) are miscible The van der Waals force is larger between unlike molecules.
7 7 4) Wettability = 0 - 30 o strongly water-wet = 30 o - 90 o preferably water-wet = 90 o – neutrally wet = 90 o - 150 o preferably oil-wet = 150 o - 180 o strongly oil-wet Most oil reservoirs are water wet: Wettability is the ability of one fluid to spread on a solid surface in the presence of other fluids The wettability is defined by the wetting angle Sand grain water oil Wettability may also be quantified by capillary pressure properties. We will return to this later. solid water oil = 0 Water wet Vann oil solid water = 90 o Neutrally wet solid water oil 180 o oil wet Pipette with water Oil Water drop
88 5) Viscosity Viscosity is internal fluid friction Shear forces act between different fluid layers and between the fluid and container walls y F v Shear tension: The velocity gradient in the y-direction: Empirical studies shows that for most fluids: = the viscosity coefficient or simply the viscosity Unit: 1 Pa s = 1 Ns/m 2 = 10 P (poise) This is a Newtonian fluid
9 9 6) Darcy’s law og permeability A pressure difference p is needed for a fluid to flow through a porous medium. Henri Darcy (1856) discovered that the volume flow rate Q through a filter of cross section A: where the proportional constant a depends on both the fluid and the filter The modern version av Darcy’s law for fluid flow in a porous medium (e.g a core plug): L pBpB pApA Q A core plug Q = volume per unit time (volume flow rate) K = the absolute permeability of the medium = the fluid viscosity Permeability unit This is a rather large unit. Therefore we define a new unit der:1 darcy (D) 1 millidarcy (mD) = 10 -3 D = 0.98692·10 -15 m 2
10 7) Relative permeability The flow possibility for one fluid may then depend on the saturation of the fluids present Oil may flow more easily in this case: than here: Sand grain olje water along the pore walls (water wet) Sand grain oil Water will flow more easily than the oil A sentral question arises: Does Darcy’s law and the permeability concept also apply when there are more than one fluid flowing in the porous medium? Single phase flow: The absolute pemeabilitty K i Darcy’s equation is independent of the fluid, and depends only on the properties of the porous medium. Multiphase flow: Several immiscible fluid phases (water, oil, gas) flow simultaneously through the porous medium We see that the oil will flow more easily when more oil is present (large S o ) oil
11 Capillary pressure curves in capillary tubes oil water One simple capillary tube oil water 1.0 S iw water oil Fre water level (FWL) Water/oil contact (OWC) Height; Cap. press Water sat. (S w ) 0 Tube radius (R ) smalllarge A battery of tubes with varying radius and therefore varying capillary pressure: There is a linear relation between capillary pressure p c and height h. The total water saturation S w below h in all tubes decrease when the tubes get thinner
12 Darcy’s equations Equations of state Viscosity Continuity of equation Saturation The capillary pressure Total 14 equations
13 From the continuity equations we have: Hence Introduce Finally we get: This is called the saturation equation 2. order partiell differential equation for S w (x,t); non-linear with coeffisients which are functions of the independent variable S w. The equation must be solved numerically. When S w has been found, we may calculate f w and u w og u o, and finally p w the p o, all as functions og x and t.
15 Well logging Goal: Petrophysics as function of depth in reservoir A tool with instruments lowered into the borehole. The instruments in the probe measures the properties of formation and transmits data via mud to the surface lithological (rock type) porosity saturation Reservoir tool
17 Øvre transmitter Mottaker antenne Øvre transmitter Gamma- sensor Logge- sonde Kraft- kilde Bore- krone Slam- motor Resisitivitets- sensor a) Measurement While Drilling (MWD) Logging While Drilling (LWD) Tool at the bottom of the drill string. Signals transmitted as pressure waves through mud. b) Wireline Logging Drill string is pulled up and the probe is sent down with a wire that transfer data to / from the logging instruments. Expensive, less common Two methods
18 Log tools must withstand: high reservoir pressure, 1000 atm high reservoir temperatures, 120 ° C large mechanical stresses For time-efficient electronics The tools measure into the formation outside invasion zone for drilling fluids Drilling Fluids (mudfiltratet) penetrates the formation (invasion). This may give false results.
19 1. Neutron-log Atom nuclei consist of positively charged protons and neutrons without charge Protons and neutrons have roughly the same mass. Neutrons with energy 3-4 MeV sent into the formation from a source in the tool (1 MeV = 1.6 ° 10-13 Joules) Neutrons lose energy when colliding with atomic nuclei, hydrogen, in the formation When the energy is reduced to a they may be “captured” by nuclei This excited nuclei emit gamma rays This radiation can be detected in a gamma- detector in the tool n Neutron source Gamma- detector Sonde Formation Clamp Si kjerne n n n n
20 Much hydrogen ….. Increased gamma radiation. Most effective if the neutrons collide with protons (p), ie hydrogen nuclei If the detector detects gamma radiation we have a neutron-gamma log Most probes simultaneously measure the epithermal neutrons (En> 1 eV). It is called the neutron-neutron log The response from nøytronloggen is a measure of hydrogen-containing fluid (oil, water, gas) in the formation ie, hydrogen index (HI) Since these fluids are located in the pores, it is a measure of porosity. Problem 1: Response from all hydrogen. Also from water bound to clay.. Problem 2: The gas has a low HI, - underestimation of porosity. - Detect gas layer. n Neutron- source Gamma- detector Sonde Formation Clamp Si kjerne n n p n n p p p
21 Radioactive isotopes: Occur in the earth (crust) Type and rate of radioactivity depends on the mineral type Depends on rock type, occurs particularly in shale Radioactivity is a "finger print" of great interest to the lithologic and stratigraphic description of the reservoir 2. Gamma-log It measures naturally occurring radioactivity in the formation. Only gamma-rays have sufficient penetration ability in the formation of reaching the detector in the logging tool Gamma- detector Sonde Formatjon 40 K nuclei 238 U nuclei
22 Important isotopes 1) 40 K ; T 1/2 = 1.3·10 10 year 40 K 40 Ar 40 Ca E =1.46 MeV ++ -- 2) 232 Th ; T 1/2 = 1.4·10 10 year 232 Th + 228 Ra 208 Pb Thorium-series: 3) 238 U ; T 1/2 = 4.5·10 9 year Uranium-series: 238 U + 234 Th 8 6 206 Pb
23 The most important minerals that may contain radioactivity are: 1) Quartz [SiO 2 ] (sandstone) – Clean regular lattice – little room to accommodate radioactive isotopes 2) Carbonates (chalk) [ CaCO 3 ] – Deposits of living organisms - clean 3) Dolomitt [ CaMg(CO 3 ) 2 ] – Traces of Uranium 4) Feltspat [KAlSi 3 O 8 ] and mica clay and shale - Crystalline, containing Al, K, Na, Ca, Ba – silicates poor crystal structure, ie foreign atoms (eg. radioactive) can take place: thus much radioactivity
24 Petrophysics from gamma-log: 1) Lithology (rock type) – Identify shale and clean sand (in addition to mud log) 2) Clay content. Gamma-index: GRmin = intensity of the clean zone (without clay / shale) GRmax = intensity of the assumed pure clay zone GRlog = intensity of the current zone 3) The turning points in the IGR-curve defines the transition between the layers. 4) Depth Reference. Can be used to determine casing need. 0 < I GR < 1
25 3. Density log (gamma-gamma log) A radioactive source ( 60 Co, 137 Cs) - gamma radiation. Principal: mud clamp Radioactiv source Gamma- detectors Bore- hole Formation tool led Gamma radiation (photons) scattered from electrons of atoms in the formation. Photons lose energy. Those who lose the most energy are those scattered back the probe. This decreases the number of electrons with the original energy recorded in the detectors. Absoprbsjonskoeffisienten is proportional to the number electrons in the Z atom (molecule) which in turn depends mass density b. Gamma-gamma log measures density in formation
26 Bulk Mass of formation is the sum mass of pore volume (liquid) and matrix (rock) : Porosity: The matrix density m and the fluid density f til reservoir fluids is known, porosity may be found vi by measuring b with the density log. We must expect that the density-log records: High density of shale and cemented layers Greater density in the oil-bearing sandstone layers than the layer of gas Greater density in lower porosity layers Slightly greater density in the water zones than in the oil zones
27 Gas Oil Vann Neutron-log Shale Sand- stone Semented Sand- stone Sand- stone Sand- stone Coal Shale Tak- berg- art High Low Gamma-log Density-log Shale: high radio activity, A lot of water (bound in clay), high density Sandstone: low natural gamma Low neutron pga gas (low HI) Cemented sandstone: high density Sandstone with oil: HI high, high neutron-log, high density Cemented sandstone: high density Shale: high gamma, much water Sandstone with oil: density log and neutron log depends on porosity Increasing effect on the density log the transition to the water zone Cementert sandstone: high density Coal: high water content, inc. neutron Sandstones with low porosity, Increased density, less water gamma-log: high for shale fingerprint for minerals identify layers Neutronlog: high for oil/water low for gas high for shale Density-log (gamma-gamma log): high in shale and cemented layers higher in oil/water compared to gas