05-Formation Fluid Pressure and Its Application

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Chapter 5

Formation Fluid Pressure

and Its Applicationby

Edward A. Beaumont

and

Forrest Fiedler



Edward A. BeaumontEdward A. (Ted) Beaumont is an independent petroleum geologist from Tulsa, Oklahoma.He holds a BS in geology from the University of New Mexico and an MS in geology fromthe University of Kansas. Currently, he is generating drilling prospects in Texas,Oklahoma, and the Rocky Mountains. His previous professional experience was as a sedi-mentologist in basin analysis with Cities Service Oil Company and as Science Directorfor AAPG. Ted is coeditor of the Treatise of Petroleum Geology. He has lectured on cre-ative exploration techniques in the U.S., China, and Australia and has received theDistinguished Service Award and Award of Special Recognition from AAPG.

Forrest FiedlerForrest Fiedler earned his Bachelor of Arts and Science degree in geology from LehighUniversity in 1957 and his Master of Science in geology from Virginia PolytechnicInstitute in 1967. He worked as a mine geologist in Canada and assistant state highwaygeologist in Virginia before moving to the oil industry. Fiedler’s petroleum experience wasentirely with Amoco (and its predecessors). Throughout his career, he worked on projects

throughout the world in positions ranging from geologist and formation evaluator toresearch supervisor and regional reservoir engineering supervisor. He retired in 1989 asan engineering associate.



Overview • 5-3

Overview

Oil and gas are fluids. Pressure is one the main elements characterizing the physicalbehavior of fluids in the subsurface. Understanding pressure concepts and their applica-tions is critical to effective petroleum exploration.

This chapter discusses the characteristics and behavior of fluids (liquids and gases) andthe pressures manifested by subsurface fluid behavior. It also discusses how an under-standing of fluid pressure can be applied to oil and gas exploration.

Introduction

This chapter contains the following sections.

Section Topic Page

A Pressure Regimes 5 –4

B Using Pressures to Detect Hydrocarbon Presence 5 –11

C Predicting Abnormal Pressures 5 –36

D Pressure Compartments 5 –44

E Capillarity and Buoyancy 5 –53

F Hydrodynamics 5 –57

G Annotated Bibliography 5 –63

In this chapter



5-4 • Formation Fluid Pressure and Its Application

Pressure is a measure of force per unit area. Pressure in the subsurface is a function of the densities of rocks and fluids. This section discusses different pressure regimes, mainlyconcentrating on formation fluid pressures.

Introduction

Section A

Pressure Regimes

This section contains the following topics.

Topic Page

Normal Hydrostatic Pressure 5 –5

Geostatic and Lithostatic Pressure 5 –6

Normal Hydrostatic Pressure Gradients 5 –7

Abnormal Hydrostatic Pressure 5 –8

Causes of Overpressure 5 –9

Causes of Underpressure 5 –10

In this section



Pressure Regimes • 5-5

A fluid is “a substance (as a liquid or gas) tending to flow or conform to the outline of itscontainer ” (Webster, 1991). Thus, the explorationist should think of oil, gas, and water asfluids to understand their behavior in the subsurface. In this chapter, where the fluid

state (liquid or gaseous) is important, the state (or phase) is specified.

Fluids

Normal Hydrostatic Pressure

Fluid pressure is that pressure exerted at a given point in a body of fluid.Fluid pressure

Normal hydrostatic pressure is the sum of the accumulated weight of a column of waterthat rises uninterrupted directly to the surface of the earth. Normally pressured fluidshave a great degree of continuity in the subsurface through interconnected pore systems.

Abnormally pressured fluids can occur where fluids are completely isolated in contain-ers (compartments) that are sealed on all sides.

Hydrostaticpressure

The geological definition of “hydrostatic ” differs from the engineering definition. Engi-neers use “hydrostatic ” to refer to the pressure exerted by the mud column in a boreholeat a given depth. Hydrostatic mud pressures are found on DST (drill-stem test) reportsand on scout ticket reports of DSTs.

Hydrostaticmud pressure

Normal hydrostatic pressure has the following properties (Dahlberg, 1994):• Amount of pressure increases with depth.• Rate of pressure change depends only on water density.• Vector representing the direction of maximum rate of pressure increase is vertical (i.e.,

the fluid is not flowing laterally).• The pressure –depth relationship is completely independent of the shape of the fluid

container.

Properties ofhydrostaticpressure

Fluid pressure is nondirectional if the fluid is static. If a pressure imbalance exists in anydirection, the fluid moves in the direction of lower fluid pressure. The diagrams belowillustrate balanced and unbalanced pressures.

Static vs.dynamic fluids

Figure 5– 1.

Balanced Pressure Unbalanced Pressure




The geostatic pressure at a given depth is the vertical pressure due to the weight of acolumn of rock and the fluids contained in the rock above that depth. Lithostatic pres-sure is the vertical pressure due to the weight of the rock only.

Definitions

Geostatic and Lithostatic Pressure

Three variables determine geostatic pressure:• Densities of formation waters as related to salinities• Net thickness of different lithologies, e.g., sandstone, shale, limestone• Porosities of different lithologies

Geostaticvariables

We can calculate geostatic pressure using the formula below:

P G = [weight of rock column] + [weight of water column]

P G = [ρm ×(1 – φ) ×d ] + [ ρw × φ ×d]

where:PG = geostatic pressure (psi)ρm = weighted average of grain (mineral) density (sandstone and shale = 2.65 g/cm 3,

limestone = 2.71 g/cm 3)ρw = weighted average of pore-water density (g/cm 3)φ = weighted average of rock porosityd = depth (ft)

To calculate weighted averages, use 1000-ft (300-m) increments.

Calculatinggeostaticpressure

Geostatic gradient is the rate of change of geostatic pressure with depth. A geostatic gra-dient of 1 psi/ft results from an average density of 2.3 g/cm 3.

Geostaticgradient

Geostatic gradients vary with depth and location. The gradient increases with depth fortwo reasons:1. Rock bulk density increases with increasing compaction.2. Formation water density increases because the amount of total dissolved solids (TDS)

in the water increases with depth.For example, in the Cenozoic of Louisiana, the geostatic gradient is 0.85 psi/ft at 1000 ftand 0.95 psi/ft at 14,000 ft.

How geostaticgradient varies




The hydrostatic pressure gradient is the rate of change in formation fluid pressure withdepth. Fluid density is the controlling factor in the normal hydrostatic gradient. In theU.S. Rocky Mountains, a formation water gradient of 0.45 psi/ft is common. In the U.S.

Gulf Coast, a gradient of 0.465 psi/ft is common.

Definition

Normal Hydrostatic Pressure Gradients

Fluid density changes with depth as a result of changes in the following factors:• Temperature• Pressure• Fluid composition (including dissolved gases and solids)• Fluid phase —gaseous or liquid

These factors must be taken into account when estimating fluid pressure at depth. Thesmall amount of dissolved gas contributes little to the density and can be ignored in theexploration state.

Factorscontrolling fluiddensity

Oil density varies greatly because of the large variety of oil compositions and quantity of dissolved gases. Also, oil composition is inherently much more variable than formationwater composition.

Factorscontrolling oildensity

Gas density is strongly affected by pressure, temperature, and composition. In the reser-voir, gas may be in the liquid phase; if so, we should treat it as a very light oil.

Predicting gas phase can be complicated. Consult an experienced reservoir engineer whenmaking this prediction.

Factorscontrolling gasdensity

Oil-field liquids and gases occur in a wide range of compositions. The table below showstypical density ranges and gradients for gas, oil, and water. However, because exceptionsoccur, have some idea of the type of fluid(s) expected in the area being studied and useappropriate values.

Fluid Normal density range (g/cm3) Gradient range (psi/ft)

Gas (gaseous*) 0.007– 0.30 0.003– 1.130

Gas (liquid) 0.200– 0.40 0.090– 0.174

Oil 0.400– 1.12 0.174– 0.486

Water 1.000– 1.15 0.433– 0.500

*Varies with pressure, temperature, and composition. The composition used for this table is for an average gas composed of84.3% methane, 14.4% ethane, 0.5% carbon dioxide, and 0.8% nitrogen (GO Log Interpretation Reference Data Handbook,1972).

Ranges of fluiddensity andgradientvariation




Abnormal hydrostatic pressure is a departure from normal fluid pressure that is causedby geologic factors. The term “geopressure ” was introduced originally by Shell OilCompany to refer to overpressured intervals in the U.S. Gulf Coast. “Geopressure ” is

gradually being replaced by the more descriptive terms “overpressure ” and “underpres-sure. ”

Definition

Abnormal Hydrostatic Pressure

Abnormal fluid pressures may be caused by any of the following:• Uplift• Burial• Rock compaction or dilation• Abnormal heat flow

Abnormal pressures develop when fluid is unable to move into or out of the local pore sys-tem fast enough to accommodate to the new environment. Such a pore system must beisolated from the surrounding system by impermeable barriers for abnormal pressure toexist.

The table below shows the generally accepted major causes of abnormal fluid pressure.

Overpressure Underpressure

Uplift Burial

Heat increase Heat decrease

Compaction Dilation of poresGeneration of hydrocarbons

Causes

More than one mechanism may operate simultaneously or sequentially to create abnor-mal pressure. For example, burial of a sealed compartment carries a trapped fluid pres-sure into a deeper environment. The pressure in the compartment compared with the sur-rounding environment would be abnormally low. The higher temperature at depth wouldslowly raise the pressure in the compartment to normal.

It may not be possible to predict the existing condition of the pressure system in exampleslike this because the combined effects of all the variables are often not well known inadvance.

Multiplesimultaneouscauses




When a fluid pressure is higher than estimated from the normal hydrostatic fluid gradi-ent for a given depth, it is called overpressure. For this situation to occur, the fluid mustfirst be trapped within a rock unit (pressure compartment).

Overpressure can be caused by uplift, increased heat, compaction, generation of hydrocar-bons, or a combination of these factors.

Introduction

Causes of Overpressure

A unit can be uplifted into a regime of lower normal pressure. The encapsulated fluidthen is at a pressure higher than that found at the new depth in surrounding formationswhere the fluid is under normal constraints.

The diagrams below illustrate this situation.

Uplift

Perhaps the most common way that pressure is increased is for the encapsulated fluid to

be heated. The trapped fluid, unable to expand into adjacent pore systems, rises in pres-sure. Fluids outside the area of trapping are free to adjust to the heating, so they remainat about normal pressure.

Heat increase

Figure 5– 2.

As an encapsulated rock mass is buried, it tends to compact. Under normal conditions, asthe porosity is reduced, the interstitial fluid is expelled. When the fluid cannot escape, thepressure within the encapsulated rock mass rises. This higher fluid pressure takes onsome of the overburden load, limiting the amount of compaction. In such cases, the fluidis overpressured and the rock matrix is undercompacted.

Compaction




Underpressure exists when a fluid pressure is lower than estimated from the normalhydrostatic fluid gradient for that depth at which it occurs. For this situation to exist, thefluid must be trapped within a rock unit.

Underpressure can be caused by burial or heat decrease.

Introduction

Causes of Underpressure

If the encapsulated unit is buried deeper, its original pressure is carried to a higher pres-sure environment. If the rock cannot compact, the trapped pressure is abnormally low forthe new depth.

As long as a rock unit remains encapsulated by impermeable rocks, it becomes underpres-sured by burial as faulting or as downwarp occurs.

The diagrams below illustrate this phenomenon.

Burial

The major factor causing underpressure is the cooling of pore fluids as they are upliftedand the overburden erodes. For example, drain a bottle filled with hot water and immedi-ately seal the bottle back up by screwing on the cap. The bottle will be underpressured asit cools to room temperature.

This same phenomenon occurs when an encapsulated rock unit is uplifted into a region of lower temperature. However, predicting pressure in uplifted rock units is difficult.Because uplift brings a rock unit from a region of high pressure to a region of low pres-sure, the uplifted unit may be at a higher-than-expected pressure, a lower-than-expectedpressure, or normal pressure, depending on the state of equilibration.

Heat decrease

Figure 5–3.



Using Pressures to Detect Hydrocarbon Presence • 5-11

Buoyancy pressures caused by hydrocarbon columns can be recognized by comparing hydrostatic pressure gradients with formation pressures. Pressures exceeding expectedhydrostatic pressures could be due to the presence of hydrocarbon columns.

Two items are critical for detecting buoyancy pressure in a well:• Accurate static water plot for the well• Reliable formation fluid pressure measurements

This section discusses how to detect the presence of hydrocarbons using formation fluidpressures.

Introduction

Section B

Using Pressures to Detect Hydrocarbon Presence

The table below outlines a procedure for using pressures to detect the presence of a hydro-carbon column in a formation.

Step Action

1 Make a hydrostatic pressure –depth plot through the interval of interest.

2 Plot the pressure(s) measured from the interval of interest.

3 If the measured formation pressures are greater than the hydrostatic pressure,then the formation may contain a hydrocarbon column.

4 Check to see if anomalous pressures make geological sense.Example: Measured fluid pressure is 250 psi over the static water pressure.The formation is believed to contain 30 ° API gravity oil, and the total verticaltrap closure is 500 ft.Solution: If the 250-psi pressure is due to the presence of a hydrocarbon col-umn, then a column of 2500 ft of 30 ° API gravity oil would have to be present inthe trap (assuming a freshwater gradient). Vertical trap closure is only 500 ft;therefore, the measured formation pressure does not match the geology and isprobably wrong.

Procedure

This section contains the following subsections.

Subsection Topic Page

B1 Determining Hydrostatic Pressure Gradient 5 –12

B2 Static Hydrocarbon Pressure Gradients 5 –19

B3 Methods for Obtaining Formation Fluid Pressures 5 –29

In this section




A critical element in detecting the presence of hydrocarbons using formation fluid pres-sures is an accurate hydrostatic pressure gradient for zones of interest. We use the hydro-static pressure gradient to determine the expected pressures for the zone of interest as if it had no hydrocarbons. Pressures exceeding hydrostatic pressures may be due to thepresence of a hydrocarbon column. Most methods for determining hydrostatic pressuresare not very precise. Other petrophysical data can help when the estimated hydrostaticpressure gradient is suspect.

Introduction

Subsection B1

Determining Hydrostatic Pressure Gradient

This subsection contains the following topics.

Topic Page

Constructing a Hydrostatic Pressure –Depth Plot 5 –13Estimating Formation Water Density 5 –16

In thissubsection




The goal of constructing a hydrostatic pressure –depth plot is to identify pressures greaterthan the hydrostatic gradient that may correspond to a hydrocarbon-bearing zone. A hydrostatic pressure –depth plot can be constructed from any of the following:

• Measured pressures• Regional rule-of-thumb pressure gradients• Pressures calculated from water density

Calculated pressures are much less accurate than measured pressures but can be usedwith some effectiveness when they are supplemented with other petrophysical data.

Introduction

Constructing a Hydrostatic Pressure–Depth Plot

The table below outlines a procedure for constructing a hydrostatic pressure –depth plotfor a single well.

Step Action

1 Using graph paper with a linear grid, label the X-axis as pressure and the Y-axisas depth. Use as large a scale as possible. Also, make the Y-axis on at least oneplot the same scale as on the well logs to aid in interpretation.

2 Plot measured pressure from the aquifers (100% S w) in the well. If none is avail-able, go to step 3.

3 Plot measured pressure from the aquifers in nearby wells. If none is available,go to step 4.

4 Calculate and plot hydrostatic pressures for a depth above and a depth below thezone of interest. Use the rule-of-thumb pressure gradient for that zone. If it isnot available, calculate the gradient from the water density using density mea-

sured from the formation water or calculated from R w.For help, see the following sections.

Procedure:Constructing aplot

The formation fluid pressure at any depth in a well is a function of the average formationwater density (ave. ρw) above that depth, not the density of the formation water at anyparticular depth. Formation water generally becomes more dense with increasing depth.

To calculate water pressure gradient (P grad ), use the following formula:

P grad = ave. ρw ×0.433 psi/ft

where:

ave. ρw =ρw = water density

For example, given ave. ρw = 1.13, the equation works as follows:

P grad = 1.13 × 0.433 psi/ft = 0.489 psi/ft

Calculatingpressuregradients fromwater density

∑n

1 ρ

wn




The table below lists hydrostatic pressure gradients, water density, and salinity in weightpercent total dissolved solids (TDS).

Gradient (psi/ft) Density (g/cc) TDS (ppm) TDS (wt %)

Table of waterpressuregradients

Constructing a Hydrostatic Pressure –Depth Plot, continued

04.330.4370.441

1.0001.0101.020

<7,00013,50027,500

013.527.5

0.4440.4450.451

1.0291.0301.040

37,00041,40055,400

37.041.455.4

0.4540.4590.463

1.0501.0601.070

69,40083,70098,400

69.483.798.4

0.4650.4670.471

1.0751.0801.090

100,000113,200128,300

100.0113.2128.3

0.4760.4800.485

1.1001.1101.120

143,500159,500175,800

143.5159.5175.8

0.4890.4910.493

1.1301.1351.137

192,400200,000210,000

192.4200.0210.0

0.5000.510

1.1531.176

230,000260,000

230.0260.0

Most sedimentary basins have a rule of thumb for average hydrostatic water pressuregradients. For the Gulf Coast basin, it is 0.465 psi/ft. For Rocky Mountain basins, it is0.45 psi/ft. For fresh water, it is 0.433 psi/ft. If measured hydrostatic pressure is not avail-able for a well, find out the accepted rule-of-thumb average hydrostatic pressure gradientfor the depth of the zone of interest where the well is located.

Rules of thumb




Water density is a function of its TDS concentration. The hydrostatic pressure at anydepth is a function of TDS concentration from the surface to that point. The plot below of TDS vs. depth is from southern Arkansas. It shows a gradual increase in TDS from the

surface to about 2000 ft, probably due to meteoric effects, and then a linear, more rapidincrease in TDS from 2000 to 10,000 ft. Generally, below the depth of meteoric waterinfluence, the increase in TDS in connate brines is linear and ranges from 25,000 to100,000 mg/l per 1000 ft (80 to 300 mg/l per m) (Dickey, 1969). There are exceptions tothis general case.

Such consistent salinity increase with depth is not unique to the East Texas basin but ischaracteristic of most basins.

Example of TDSvs. depth

Constructing a Hydrostatic Pressure –Depth Plot, continued

Figure 5– 4. From Dickey, 1969; courtesy Chemical Geology.

( f t )




Formation water density is a function of three variables:• Temperature• Pressure• Total dissolved solids (TDS)

It is the mass of the formation water per unit volume of the formation water and is givenin metric units (g/cm 3). For reservoir engineering calculations, it is considered equivalentto specific gravity.

Introduction

Estimating Formation Water Density

If TDS is known from a chemical analysis of formation water, then the formula below canbe used to estimate formation water density ( ρw) (Collins, 1987):

ρw = 1 + TDS ×0.695 ×10–6 g/cm 3

Estimatingdensity fromTDS

Use the procedure outlined in the table below to estimate formation water density atreservoir conditions using R w. The approximate error is ±10% (after Collins, 1987).

Step Action

1 Gather data: formation temperature (T f ), water resistivity (R w), and formationpressure. Estimate pressure by multiplying depth by 0.433 psi/ft or otherappropriate gradient. Check for T f errors.

2 Estimate sodium chloride (NaCl) concentration from R w using Figure 5 –5.

3 Estimate density from wt % NaCl and temperature using Figure 5 –6.

Procedure:Estimatingdensity from Rw

To estimate formation water density, collect estimates of the following:• Formation temperature• Formation pressure• Formation water resistivity

Step 1:Gather data




Step Action

1 Estimate formation temperature (Tf ) using the following formula:

where:Ts = average surface temperature ( ˚F)Df = depth to the formation (ft)BHT = bottom-hole temperature (found on log header) ( ˚F)TD = total depth (BHT and TD must be from the same log run) (ft)

2 Estimate formation pressure (psi) by multiplying 0.433 (freshwater gradient)by formation depth.

3 Obtain formation water resistivity (Rw) (ohm-m) in one of three ways:

• From a sample of water from the formation of interest measured for R w• Using a water catalog • Calculating it from an SP log

Step 1:Gather data(continued)

Estimating Formation Water Density, continued

The predominant solute in most formation water is sodium chloride (NaCl). Its concentra-tion determines formation water density and R w. When only R w is available, we can useNaCl concentration to determine density.

Use Figure 5 –5 below to determine NaCl concentration. At the intersection of formationtemperature (from Y-axis) and R w (from X-axis), find the NaCl concentration (in ppm) byreading diagonal line labels and interpolating.

Step 2:Determine NaClconcentrationfrom Rw

Figure 5– 5. Courtesy Schlumberger.

Example:

1. Formation temperature = 142 °F

2. Rw = 0.13

3. NaCl concentration = 28,000 ppm

T E M P

E R A T U R E ° F

RESISTIVITY OF SOLUTION OHM – METERS




Estimate formation water density from ppm NaCl and temperature using the chartbelow. The following table describes the procedure to use with the chart.

Steps 3 & 4:Estimate density

Estimating Formation Water Density, continued

Figure 5– 6. Courtesy Gearhart-Owens (1972).

Step Action

1 Enter the chart along the X-axis using formation temperature.

2 Proceed vertically to the appropriate salt concentration expected in the zone.

3 Proceed horizontally to read the liquid density at atmospheric pressure.

4 Using the “Effects of Pressure ” segment of the chart, add a density incre-ment to the above-computed density to correct for pressure effects.




We can determine the downdip hydrocarbon column length by plotting a reservoir ’s statichydrocarbon pressure gradient vs. its hydrostatic pressure gradient. Hydrocarbon densi-ties determine static hydrocarbon pressure gradients. The gradient is easily calculatedwhen the density is measured. When density is not measured, charts are available to helpestimate density.

This subsection shows how to determine oil and gas pressure gradients, make a plot of hydrocarbon pressure gradient, and determine hydrocarbon column length.

Introduction

Subsection B2

Static Hydrocarbon Pressure Gradients


Topic Page

Estimating Static Oil Pressure Gradients 5 –20

Estimating Static Gas Pressure Gradients 5 –21

Plotting the Hydrocarbon Pressure Gradient 5 –26

Finding Free-Water Level Using Pressure 5 –27

In thissubsection




The static oil pressure gradient is dependent on oil density. Subsurface density of oil orcondensate depends on composition, amount of dissolved gases, temperature, and pres-sure. Oil or condensate density can be estimated to useful accuracy if stock tank API grav-

ity and solution gas –oil ratio (GOR) are known (Schowalter, 1979).

Introduction

Estimating Static Oil Pressure Gradients

Follow the steps listed below to estimate static oil pressure gradient.

Step Action

1 Estimate oil density using Figure 5 –7 below.

2 Estimate oil pressure gradient using the following formula:

P oil grad = ρoil

× 0.433 psi/ftwhere:

P oil grad = oil pressure gradient

ρoil = oil density

Estimating oilpressuregradients

Figure 5– 7. From Schowalter, 1979; courtesy AAPG.

Determining oildensity

Use the figure below to determine oil density. If the GOR is unknown or if there is nodissolved gas in the oil, use the 0 line.




The static gas pressure of a gas reservoir is a function of gas density. Static gas pressuregradients can be estimated if subsurface gas density is known or has been estimated.

Subsurface gas density is dependent on the ratio of its mass to its volume. Mass is relatedto the apparent molecular weight of the gas. Volume is related to pressure, temperature,and the apparent molecular weight of the gas.

At atmospheric pressures and temperatures, gas density can be estimated using the IdealGas Law. At subsurface temperatures and pressures, gas molecules are so close to oneanother that they interact enough to change ideal gas behavior. A compressibility factor, z,is added to the Ideal Gas Law to correct for subsurface gas behavioral changes.

Introduction

Estimating Static Gas Pressure Gradients

Follow this procedure to estimate the gas pressure gradient of a gas reservoir or potentialgas reservoir.

Step Action

1 • If data are available on gas composition and formation temperature go tostep 2.

• If no data on gas composition or formation temperature are available,estimate gas density from the average gas chart (Figure 5 –11) and go toStep 6.

2 Determine the apparent molecular weight of the gas mixture.

3 Read pseudoreduced temperature and pressure from Figure 5 –8.

4 If not already known, estimate compressibility factor, z, from Figure 5 –9.

5 Using information obtained from steps 2, 3, and 4, estimate gas density fromFigure 5 –10.

6 Estimate gas pressure gradient using the following formula:

P gas grad = ρgas × 0.433 psi/ftwhere:

P gas grad = gas pressure gradientρgas = gas density

Procedure:Estimating gaspressuregradient

The apparent molecular weight of a gas mixture is equal to

MWapp = MF 1(MW1) + MF 2(MW2) + ... MF x(MWx)where:

MWapp = apparent molecular weight of the gas mixtureMF x = mole fraction of a component of the mixtureMWx = molecular weight of a component of the mixture

Determiningmolecularweight




To practice, use these values for a gas mixture:• Composition = 50% methane, 25% ethane, 25% propane• Molecular weight of carbon (C) = 12• Molecular weight of hydrogen (H) = 1• Molecular weight of methane (CH 4) = 12 + 4 = 16• Molecular weight of ethane (C 2H6) = 24 + 6 = 30• Molecular weight of propane (C 3H 8) = 36 + 8 = 44

MWapp = 0.5(16) + 0.25(30) + 0.25(44) = 8 + 7.5 + 11 = 26.5

Determiningmolecularweight

(continued)

Estimating Static Gas Pressure Gradients, continued


We can determine the pseudoreduced temperature and pressure from the figure below. Inthe example, apparent molecular weight is 23, reservoir temperature is 200 ˚F, and reser-voir pressure is 2500 lb.

Determiningpseudoreducedtemperatureand pressure




The gas compressibility factor, z, for the gas reservoir of interest may already be knownbecause it was measured. In this case, use that value. If z is not known, use the figurebelow to determine it from the pseudoreduced temperature and pressure determined from

Figure 5 –8. Figure 5 –9 uses values determined for Figure 5 –8.

Determining z



C O M P R E S S I B I L I T Y F A C T O R

, Z

C O M P R E

S S I B I L I T Y F A C T O R

, Z




We can determine gas density from the figure below, knowing reservoir pressure, reser-voir temperature, gas compressibility factor, and apparent molecular weight.

Determiningsubsurface gasdensity



According to Gerhardt-Owens (1970), average natural gas estimated by Stephens andSpencer is considered to be 84.3% methane, 14.4% ethane, 0.5% carbon dioxide, and 0.8%nitrogen. However, many natural gas wells have produced almost pure methane (99%).Others have produced up to 88% ethane, 42% propane, 99% nitrogen, and 91% carbondioxide. Using the accompanying average gas chart (Figure 5 –11) is completely satisfac-tory is most cases.

Averagenatural gas

We can estimate gas density from Figure 5 –11. The chart assumes an average gas compo-sition and was made using the following:• Formation temperature = 80 ˚F plus 0.8 ˚ per 100 ft of depth• Formation fluid pressure gradient = 0.465 psi per ft of depth• Supercompressibility factors used from George G. Brown, University of Michigan

Estimatingsubsurface gasdensity




The formula used to determine reduction in volume and the accompanying increase indensity of a given gas (because of changes in temperature and pressure) is

V = V 1 ×P a1 /P a ×T a /T a1 × z/z 1

where:

Estimatingsubsurface gasdensity

(continued)

V = volume, ft 3

V = original volume ft 3

P a = pressure, psiaP a1 = original pressure, psia

DEPTH IN FEET X 10 3

D E N

S I T Y

OF

GA

S —

gm

/ c c

Figure 5– 11. Courtesy Gearhart-Owens, 1970.


0 10 20 30

0 10 20 30

.4

.3

.2

.1

0

.4

.3

.2

.1

0

Ta = absolute temperature, ˚RTa1 = original absolute temperature, ˚Rz = supercompressibility factorz1 = original supercompressibility factor




We can estimate the downdip free-water level from a valid fluid pressure measured with-in a reservoir.

The table below outlines the procedure for plotting a hydrocarbon pressure gradient on ahydrostatic pressure plot when a measured pressure is available from the reservoir.

Step Action

1 Plot measured fluid pressure on a hydrostatic pressure –depth plot.

2 Determine the hydrocarbon pressure gradient from one of two ways:• Measured hydrocarbon density• Estimates of hydrocarbon density

3 Determine the buoyancy pressure gradient: static water pressure gradient

minus hydrocarbon pressure gradient.4 Determine a pressure above or below the measured depth point. The table

below lists the steps for determining this number.

Step Action

1 Pick a depth above or below the measured point.

2 Multiply the difference in depth by the buoyancy pressure gradient.

3 Add the number from step 2 to the measured pressure if the depthis deeper; subtract if shallower.

Example:Measured pressure at 7607 ft is 3530 psi and buoyancy pressure gradient is0.076 psi/ft. What is the hydrocarbon pressure at 7507 ft?Solution:7607 – 7507 = 100 ft100 ft × 0.076 psi/ft = 7.6 psiHydrocarbon pressure at 7507 ft = 3530 psi – 7.6 psi = 3522.4 psi

5 Plot the pressure number from step 4 on the pressure –depth plot and draw aline between this point and the measured pressure point. This line is the hydro-carbon pressure gradient.

Introduction

Plotting gradient

Plotting the Hydrocarbon Pressure Gradient



The table below outlines the procedure for determining the free-water level using a singlepressure buildup point in the reservoir.

Step Action

1 Determine buoyancy pressure (P b) at the depth of the measured pressure(Pm) from the measured pressure:

P b = P m – P hydrostatic

2 Determine buoyancy pressure gradient (P bg ):P bg = P hydrostatic pressure gradient – P hydrocarbon pressure gradient

3 Calculate downdip length of hydrocarbon column (h):

Procedure usinga singlemeasurement

The free-water level occurs where buoyancy pressure is zero in the reservoir –aquifer sys-tem. It defines the downdip limits of an accumulation. Pressure data reliability affects theresolution; however, resolution improves when it is supplemented with other petrophysi-

cal information.

Introduction

Finding Free-Water Level Using Pressure

An easy method for determining free-water level (FWL) is projecting RFT pressure datadownward from a reservoir to the aquifer. The figure below illustrates the procedure.

Procedure:Using RFT data

Figure 5– 12.





Finding Free-Water Level Using Pressure, continued

As an example, let ’s determine the downdip length of a 30 ° API oil column with the follow-ing givens:

Pm = 3555 psi at 7611 ft

P hydrostatic = 3525 psiP hydrostatic pressure gradient = 0.465 psi/ftP hydrocarbon pressure gradient = 0.38 psi/ft

Answer (tied back to steps above):Step 1:

P b = P m – P hydrostatic = 3555 – 3525 = 30 psiStep 2:

P hydrostatic pressure gradient – P hydrocarbon pressure gradient = 0.465 – 0.38 = 0.085 psi/ftStep 3:

= 556 ft

Therefore, the free-water level is at 8167 ft.

Procedure usinga singlemeasurement

(continued)



Methods for obtaining formation fluid pressures can be divided into two groups: mea-sured and estimated. The table below lists the methods by these two categories.

Measured Estimated

Methods

Subsection B3

Methods for Obtaining Formation Fluid Pressures

• Using RFT (repeat formation tester) data• Using reservoir bottom-hole pressure buildup

tests• Using DST shut-in pressures

• Calculating hydrostatic pressures from mea-sured water density or salinity

• Estimating hydrostatic pressures from fluiddensity using Rw (formation water resistivity)

• Using the weight of drilling mud• Using the rule-of-thumb pressure gradient,

0.465 psi/ft

RFTs, DSTs, and bottom-hole pressure buildup tests measure formation fluid pressures.Pressure gauge accuracy is a critical factor in all three tests, but the BHP measurement isgenerally more precise due to the greater time taken for the test. Generally, two types of gauges measure pressures: strain and quartz. The table below shows the accuracy andprecision of both types.

Gauge Type Accuracy (% Full Scale) Precision

Strain Gauge 0.18 < 1 psi

Quartz Gauge 0.025 0.01 psi

Accuracy ofmeasuredpressures


Topic Page

Determining Formation Fluid Pressure from DSTs 5 –30

Determining Formation Fluid Pressure from RFTs 5 –33

In thissubsection





A drill-stem test, or DST, is the most common method to measure reservoir pressure.DSTs are the most reliable reservoir pressure measurement method if sufficient timeelapses during the test for the higher formation pressure to equilibrate with the lower

borehole pressure. Pressures often must be extrapolated. Irregular boreholes cause toolproblems, and assessing the reliability of a DST is often more of an art than a science.

Introduction

Determining Formation Fluid Pressure from DSTs

There are three major types of periods during a typical DST:• During run-in or run-out periods , drilling fluid flows through ports in the tool wall

and pressure gauges respond to the weight of the drilling fluid column. The testervalve is closed.

• During flowing periods, an interval of the borehole is sealed off from the rest of theborehole by one (bottom hole) or two (straddle) inflatable packers. The tester valve isopened, creating a pressure drop in the tool which sucks fluids into the tool anddrillpipe string. Recovered volumes of oil, gas, water, or drilling mud are recorded.

• During shut-in periods, the packer(s) is still inflated and the tester valve is closed.Ideally, pressure in the closed tool gradually builds up until it reaches equilibrium withthe pressure of the isolated formation.

The figure below shows a typical DST tool, the configurations of the tool during a DST,and the periods of a DST.

Types ofperiods duringa DST

Figure 5– 13. Modified from Dalhberg, 1994; courtesy Springer-Verlag.



During a DST, pressure is continuously recorded against time. The record begins as theDST tool is lowered down the borehole and ends when the tool returns to the surface. Thefigure below is a DST plot, showing the various pressures recorded during the different

DST periods.

Point A is the initial hydrostatic pressure (IHP), the pressure exerted by the mud column

in the borehole at the depth where the recorder is located.Points B to B ′ are the pressures recorded when the tool is opened up to the formationand fluids flow up the drillpipe. B is the initial flowing pressure; B ′ is the final flowing pressure.

Point C is the initial shut-in pressure (ISIP). It is measured while the tool is closed. Therapid expulsion of fluid from the reservoir during the preceding flow period causes reser-voir pressure to drop near the wellbore. ISIP is the pressure in the reservoir after the firstshut-in period. The duration of this shut-in time is determined by the operator and shouldbe planned in advance of the test.

Points D to D ′ are the pressures recorded during the next flow period. This flow period

(and subsequent flow periods, in some cases) usually lasts longer than the first in order totest the productivity of the reservoir.

Point E is the final shut-in period (FSIP). It records the pressure in the reservoir afterthe last shut-in period.

Point F is the final hydrostatic pressure (FHP), the pressure of the mud column at thetest depth after the test was performed. It should match the IHP within 5 psi as a check of the tool ’s accuracy (assuming the packers did not leak).

A DST plot

Determining Formation Fluid Pressure from DSTs, continued

Figure 5– 14.


Runningin

ToolOpen

Shutin

ToolOpen

Shutin

Runningout

Initial and FinalHydrostatic(Mud) Pressure

Initial Shut-inPressureFinal Shut-inPressure

Final FlowFinal FlowInitial FlowInitial Flow

P r e s s u r e

Initial PressureBuild-up Period

Final PressureBuild-up Period

Time

B

B'D'

D

A (IHP)

C (ISIP)

F (FHP)

E (FSIP)




DST pressures may not be reliable because the tool is not shut in long enough for pres-sure to stabilize at final reservoir pressure. Agraphical procedure devised by Horner(1951) infers the true reservoir pressure by extrapolating the shut-in periods to infinity.

Below is an example showing how pressure is extrapolated from ISIP and FSIP on aHorner plot (pressure vs. psuedo or Horner time, or (T + ∆T)/ ∆T.

Extrapolatingtrue pressures

Determining Formation Fluid Pressure from DSTs, continued

Scout tickets are a common source of fluid pressure data. They list the duration of variousepisodes, the pressures measured during the episode, and the amount and types of fluidsrecovered. How reliable are scout ticket data and which pressure should one use for for-mation fluid pressure? As an example, Dahlberg (1994) studies 27 DSTs for formationpressure reliability. He extrapolates the reported pressures to true formation pressureusing a Horner plot and finds that pressures must be increased an average of 10 psi.

During a DST, two pressures measure the fluid pressure of the formation being tested:the ISIP and the FSIP. The higher is usually closest to true formation fluid pressure. Inmany cases, it is the ISIP.

DST pressuresfrom scouttickets

Figure 5– 15. From Dahlberg, 1994; courtesy Springer-Verlag.

RECORDER CHART

PRESSUREBUILDUP GRAPH

P R E

S S U R E

P R E

S S U R E

TIME IN MINUTES

F I N A L

I N I T I A

L

P L O T

T E D P O

I N T S

(Ratio of period durationto elapsed time)

LOG (LOG 1.0)

ExtrapolatedPmax



The repeat formation tester (RFT) tool was designed to measure formation pressurequickly and accurately. It measures pressure at specific points on the borehole wall. Thediagram below shows a typical RFT tool. Formation pressure is measured by the forma-

tion sampler (see diagram) when it is extended from the tool to contact the formation.Fluid samples from the formation can also be taken with the tool.

RFT tool

Determining Formation Fluid Pressure from RFTs

An RFT has several important advantages for formation pressure measurement over aDST. The table below lists some considerations.

Consideration RFTs DSTs

Time to take one Less than 5 minutes for More than 90 minutesmeasurement permeable formations

Drilling delay to run About one logging run About equal to two trips with drillstringtest (wireline conveyed)

Sampling interval Small, < 1 in. (< 2 cm); Several feet or more; generally tests multiple flow unitscan test a single flow unit

Samples per run Many Few

Expense per test Small Large

Purpose of tool Pressure measurement Fluid recovery and pressure

Survey problems • Getting good seat to • Packer failuremeasure pressure • Depth determination

• Screen plugging withmaterial in drilling mud

Fractured reservoir May be unreliable Good if fractures intersect wellbore

Layered reservoir Not representative Good if many layers are included in tested interval

Skin damage Can be major error Can be measured and corrected for

Differencesbetween RFTsand DSTs

Figure 5– 16. Fom Dahlberg, 1994; courtesy Springer-Verlag.





Below is a plot of reservoir pressure vs. depth from a low-permeability chalk reservoir.The RFT data clearly show the hydrostatic gradient, the gas gradient, and the gas –watercontact. Making the same interpretation from the DST data in this example is very diffi-

cult because data are from a low-permeability chalk reservoir. Reliable pressures are diffi-cult to obtain in low-permeability reservoirs with DSTs. Extrapolated DST shut-in pres-sures from a partial buildup may not reflect actual fluid pressures. As rock qualityincreases, extrapolated pore pressure from DST buildup falls more and more closely toactual fluid pressure.

Example:Comparing RFTto DST

Determining Formation Fluid Pressure from RFTs, continued

Below is a typical RFT pressure –time profile. Points are similar to points on a DST pres-sure profile.

RFT pressureprofile

Figure 5– 17. From Gunter and Moore, 1987; courtesy JPT.

Figure 5– 18.



The table below explains how to operate an RFT survey (see Gunter and Moore, 1987).

Step Action

1 Use well logs to pick permeable zones for formation pressure measurements.Look for an invasion profile.

2 Plot mud hydrostatic and formation pressure at the well site to recognize anom-alies or tool errors and to optimize station coverage.

3 Occasionally repeat formation pressure measurements at the same depth tocheck for consistency.

4 Repeat at some of the same depths for multiple surveys to help normalize thedifferent surveys.

5 Sample both water- and hydrocarbon-bearing intervals to establish both thewater and hydrocarbon pressure gradients.

6 Plot pressures at the same scale as well logs to aid in interpretation.

Operating anRFT survey

Determining Formation Fluid Pressure from RFTs, continued

The table below describes how to control RFT quality. For details, see Gunter and Moore,1987.

Step Action

1 Inspect the tool and check calibration before going in the hole.

2 Run quartz and strain gauges simultaneously. Record both readings indepen-dently. Normalize to one another after completing the survey.

3 Maintain a slight overflow of mud to keep the level in the borehole constant dur-ing the survey and to prevent mud hydrostatic pressure errors.

4 Take mud hydrostatic pressures while descending into the hole to give the in-struments time to equilibrate to changing temperature and pressure and toprovide a mud hydrostatic pressure profile.

5 Check for tool errors by calculating mud hydrostatic pressures at differentdepths from mud weight; check them against measured mud hydrostatic pres-sures at the same depths.

Controlling RFTquality





Knowledge of expected subsurface pressure regimes helps us predict the presence of porosity and hydrocarbon charging and promotes safe drilling conditions. When making those predictions, consider the zone of interest in the prospective exploration area in thecontext of the depositional and tectonic history of the basin where it was deposited. Is thezone of interest in the target area part of a normal progression of deposition, seal forma-tion, and burial? Or were there conditions such as high heat flow, large translations of blocks, and major fault displacements that could produce abnormal pressures?

Besides unraveling the geological history, we can observe the weight of the drilling mudused, cuttings, and well logs to predict formation fluid pressures. This section discussesmethods for predicting the presence of abnormal pressures.

Introduction

Section C

Predicting Abnormal Pressures


Topic Page

Reconstructing Burial History 5 –37

Analysis of Mud Weights 5 –38

Analysis of Cuttings 5 –39

Analysis of Well-Log and Seismic Data 5 –41

In this section



Reconstructing the burial history of a play area gives an estimate of vertical displacementby either burial or faulting of at least an order of magnitude of measurement. Apres-sure –depth plot, using the estimate of vertical displacement and normal fluid gradients,

helps reveal the magnitude of the pressure abnormality that might be present if sealswere in place at the appropriate time to trap the abnormal pressure.

Introduction

Reconstructing Burial History

To predict the fluid pressure of a sealed container using burial history analysis, use theprocedure outlined in the table below.

Step Action

1 Plot the normal pressure gradient that existed when the container wassealed.

2 Plot the present gradient, adding the new depth of burial.

Procedure:Predicting fluidpressure

In the case of a sand body carried deeper by a growth fault, first plot the normal gradientsthat would have existed prior to burial; then replot the gradients at the existing depth.

The diagrams below illustrate burial stages 1, 2, and 3 and the corresponding pressure –depth relationships.

Example

Figure 5– 19.

Use of normal pressure gradients only gives an approximation for estimating pressure ina burial history analysis. It is difficult, if not impossible, to be more precise because thereare so many other unknowns, such as pressure and temperature at the charging stage,molecular composition of the fluids, effectiveness of seals, and original and current tem-peratures.

Using normalpressuregradient

Predicting Abnormal Pressures • 5-37




The mud weight needed to control a well reflects pore pressure of any permeable forma-tions drilled. To control a well, operators generally use a mud weight that will exert apressure close to the expected pore pressure. When drilling mud kicks or blows out, the

pressure from the mud is less than, but usually close to, pore pressure.

Mud weight andpore pressure

Analysis of Mud Weights

When the drilling mud kicks or blows out, pore pressure can be calculated by using thefollowing formula:

Pore pressure = 0.052 ×mud weight ×depth

For example, if a 7500-ft-deep hole contains mud with a weight of 10.5 ppg, then the porepressure at the bottom of the hole is 4095 psi or more.

Calculatingpressure frommud weight

This method ’s accuracy mainly depends on estimates of mud weight. The accuracy of mudweight estimates, measured periodically from the mud pits at the well site, is affected bythree factors:• Formation water and gas cutting of the mud• Entrapment of air at the surface• Long circulation periods of the mud

A difference of 0.1 ppg in mud weight can cause an error of 500 psi at 10,000 ft in the esti-mate of pore pressure.

Accuracy

Different operators have different policies about how much margin to allow between for-mation pressure and mud pressure; the range in margin is quite large. Also, the well borecan penetrate a pressure seal for many hundreds of feet without penetrating a permeablezone, in which case mud weight may not reflect the presence of abnormal pressure belowthe seal. In general, mud weight should be a clue to be confirmed by other evidence.

Problems withinterpretingpressure frommud weight

In overpressured formations, normal mud weight will not offset formation pressure. If mud weight is increased, however, it can break down (fracture) the normally pressuredformations higher in the hole. High pressure requires higher-than-normal mud weight,but the actual weight used might have been more than necessary (i.e., the formation pres-sure might not be as high as the mud weight implies).

Mud weight inoverpressuredformations

If significant underpressure is found, such that the formation breaks down (fractures andtakes mud), the condition is noted in the drilling record. In underpressured formations,normal mud weight can fracture the formation. If the weight is decreased, however, fluidcan flow into the well bore from uphole formations.

Mud weight inunderpressuredformations




Pore Pressure Intergranular Stress Rock Matrix Appearance Porosity

Abnormally high Abnormally low Evidence of undercompaction Higher than normalfor depth of burial

Abnormally low Abnormally high Evidence of overcom- Lower than normalpaction, i.e., grains may for depth of burialbe broken and/or sutured

The physical appearance of drill cuttings may be a clue to subsurface pressure conditionsas reflected in the state of compaction or induration of the rock. This applies to cuttingsfrom permeable as well as impermeable rocks.

Introduction

Analysis of Cuttings

When the formation fluid pressure is greater than the mud pressure, the cuttings tend toexplode into the well bore. Cuttings are liberated promptly into the mud with a minimumof abrasion by the bit. Consequently, the cuttings have sharp edges and look fresh; theymay even be somewhat larger than normal. This case also applies to shale, so we don ’thave to wait for a mud kick from a permeable zone to anticipate significant overpressure.Cuttings tend to be large and fresh looking when they are from overpressured, low-per-meability rocks because the pore pressure cannot readily bleed out of the pore systemwhen permeability is low.

Evidence ofoverpressure

When mud pressure exceeds formation fluid pressure, the mud tends to plaster the hole

(one of the things mud is designed to do). An undesirable byproduct of this attribute isthat cuttings are held in place by the pressure differential between the well bore and theformation. Such cuttings, even if broken away from the host rock, are likely to be struckseveral times by the bit teeth before being carried away in the mud. The cuttings will befurther broken (smaller than normal) and may look worn or abraded. This process is morelikely to take place in permeable zones where there is a finite flow of mud filtrate into theformation.

Evidence of

underpressure

Any discussion about cuttings must be tempered with a consideration of the type of mudused. Consult an experienced drilling and mud engineer to determine the specific proper-ties of a given mud system and its effects on cuttings.

Mud propertiescaveat

Abnormal fluid pressure causes abnormal pressure within the rock matrix; this directlyaffects compaction. Fluid carries some of the overburden stress. When fluid pressure isabnormally high, the intergranular stress is lower than normal, resulting in undercom-paction. Abnormally low fluid pressure increases intergranular stress, allowing overcom-paction (unless the framework is exceptionally rigid, as with a coral reef or well-cementedsandstone).

Compactionand fluidpressure

The table below summarizes the relationships of fluid pressure, intergranular stress, androck matrix appearance.




Analysis of Cuttings, continued

Rocks in overpressured sections have lower bulk densities than rocks in normally pres-sured sections; rocks from underpressured sections have higher bulk densities. Only dif-ferences in shale densities, however, can be detected in cuttings for the following reasons.

When cuttings enter the mud column, the fluids in the pore space try to equilibrate withthe new pressure environment. If the cuttings are permeable, the equilibration takesplace continually as the cutting rises in the mud column. If the cuttings are impermeable,however, equilibration is impeded —very strongly, in the case of shale.

Density ofshale cuttings

Shale cuttings densities are measured at the well site by dropping chips into a glass cylin-der containing a stratified sequence of liquids whose density increases downward. Beadsof known density are dropped into the cylinder. The level at which the beads settle indi-cates the density of the liquid at that level, and the different liquid densities are labeledon the cylinder. The level at which the shale chips settle indicates their density.

Measuringshale cuttingsdensity

Side pressure seals, in particular, are thought to be caused by mineralization adjacent tofaults. Top seals form by mineralization that cuts across stratigraphic units. Top seals of major overpressured compartments are usually cemented by calcite. When unexpectedpore-filling calcite is seen, a pressure seal should be considered a possibility. Any unusualpore-filling minerals seen in cutting samples should alert the geologist to the potential of a pressure seal.

Unusualauthigenicminerals




Resistivity, sonic, and density logs (as well as some others) can give clues to the presenceof over- or underpressure. Shale sections are best for analysis of logs for abnormal porepressure. Because of their low permeabilities, shales do not equilibrate pressure with the

mud column in the well bore. Selecting only the purest shales minimizes the effects of mineral variation, multiple phases, fluid composition, and fluid distribution. That leavesonly porosity as the major variable within shale sections. Because porosity is related tocompaction, porosity measurements from well logs can be calibrated to fluid pressure inthe pore systems.

Introduction

Analysis of Well-Log and Seismic Data

Drilling time is useful for detecting abnormal pressure. If the variables are limited(weight on bit, rotary speed, mud properties, pump pressure, and bit type), the majorremaining variable that affects rate of penetration in shale is porosity.

Drilling time is kept in real time on every drilling rig. It is often the very first indicator of changing downhole conditions.

Log of drillingrate

To locate intervals with potentially abnormal fluid pressure, use the following procedure.

Step Action

1 Find the purest shale intervals on the GR or SP base line. They must be reason-ably thick to allow valid responses of the other logs and free of sand or limestringers. (See points a –e, Figure 5 –20.)

2 At the same depth, mark the value of resistivity, conductivity, sonic travel time,or density.

3 Note any series of these best shale values vs. depth. These define a normalshale trend (NST) line for each of the log curves to be used.

Note: Departure from the NST line indicates abnormal microporosity due toabnormal pore pressure.

Procedure:Analyzing welllogs




The figure below illustrates how overpressures are interpreted from different types of well logs, as explained in the previous table.

Diagram of logresponse tooverpressure

Analysis of Well-Log and Seismic Data, continued

Figure 5– 20.

In some places, an empirical relation can be established to predict pore pressure from welllogs. The figure below shows sonic travel time varying with measured pressure.

Travel timefrom sonic logs

Figure 5– 21. From Powley, 1990; courtesy Earth Science Reviews.

Depth

Top of seal

Base of seal

Overpressured zone




Resistivity, sonic, and density logs can be used to construct synthetic seismograms which,in turn, can be used to calibrate and refine seismic profiles. Hence, there is a tie-in withgeophysical modeling (directly in the case of sonic –density transforms, indirectly in the

case of resistivity transforms).

Syntheticseismograms

Analysis of Well-Log and Seismic Data, continued

Seismic velocity is a function of the density and strength modulus of the rocks throughwhich the energy passes. Both density and strength are affected by abnormal pore pres-sure. Seismic profiles that show unusually slow interval velocity may indicate an under-compacted (overpressured) interval. Unusually fast interval velocity, conversely, may indi-cate overcompaction (underpressure).

Seismicvelocity

The table below summarizes typical responses in “pure ” shales when encountering zonesof abnormal pressure, relative to normal responses.

Log Type Overpressure UnderpressureDrilling rate Faster Slower

SP May shift to negative May shift to positive

Gamma ray May decrease slightly May increase slightly

Resistivity Lower Higher

Conductivity Higher Lower

Density Lower Higher

Travel time Slower Faster

Seismic interval velocity Low High

Summary of logand seismicresponses




Pressure compartments are found in basins worldwide. A pressure compartment is a vol-ume of rock, all sides of which are sealed such that the fluid within the compartment isisolated from the surrounding normal pressure regime. Pressure compartments affect themovement of fluids that control the migration and accumulation of petroleum and the dia-genesis of reservoirs and seals. This section discusses pressure compartments, methodsfor predicting their presence, and their importance for petroleum exploration.

Introduction

Section D

Pressure Compartments


Topic Page

Regional Pressure Compartments 5 –45

Subregional and Local Pressure Compartments 5 –48

Pressure Compartment Seals 5 –49

Applying Pressure Compartment Concepts to Exploration 5 –51

In this section



Pressure Compartments • 5-45

Most deep sedimentary basins of the world contain a shallow, normally pressuredhydraulic system overlying one or more hydraulic compartments whose pressures areabove or below the normal static water pressure (Powley, 1990). In this discussion these

hydraulic compartments are called pressure compartments . They are defined within abasin from pressure measurements.

Definition

Regional Pressure Compartments

Seals isolate fluids within compartments from fluids that are in pressure communicationwith the surface (normally pressured hydraulic system). The top seal is more or less hor-izontal and usually cuts across stratigraphic units. It forms where authigenic minerals(usually calcite) fill the pore spaces. The bottom seal of regional compartments is usuallya well defined lithostratigraphic unit. Commonly, the side seals are thin, mineralizedzones paralleling vertical faults.

Seals

Pressure compartments develop after the compartment has been sealed, isolating the flu-

ids inside the compartment. Pressure in the compartment can be over, under, or normal.We can map a compartment ’s top, bottom, and sides from pressure measurements. Sincepressure measurements are the main identifying criteria, the normally pressured com-partments are usually not recognized.

Pressure

compartmentrecognition

The following schematic cross section and pressure –depth plot shows how changes in thefluid pressure gradient correlate with the top and bottom seals of a regional pressurecompartment in a foreland basin.

Schematic ofpressurecompartment

Figure 5– 22.




Many sedimentary basins contain two or more pressure compartments. The cross sectionbelow illustrates the multiple pressure compartments of the Anadarko basin.

Multiplepressurecompartments

Regional Pressure Compartments, continued

The cross section below illustrates a regional pressure compartment from the Anadarkobasin of Oklahoma.

Regionalpressurecompartment

Figure 5– 23. From Bradley and Powley, 1995; courtesy AAPG.

Figure 5– 24. From Al-Shaieb et al., 1995a; courtesy AAPG.




Following is a pressure –depth plot of a well through the Anadarko regional pressure com-partment. Fluid pressure goes from normal above the top seal to overpressured within thepressure compartment, then back to normal below the bottom seal. Many regional pres-

sure compartments contain smaller subregional and local pressure compartments. Al-Shaieb et al. (1995b) use the following terms:• Regional pressure compartments —first-order or mega-compartments• Subregional compartments —second-order compartments• Local compartments —third-order compartments

The fluid pressure gradient variations within the pressure compartment on the plot belowrepresent the smaller second- and third-order compartments.

Example:Gradient profile

Regional Pressure Compartments, continued

Figure 5– 25. Modified from Al-Shaieb et al., 1995a; courtesy AAPG.




Subregional or local (second- and third-order) pressure compartments can be found withinnormal pressure regimes or regional pressure compartments.

Introduction

Subregional and Local Pressure Compartments

Below is an example of a subregional compartment contained within the regional pres-sure compartment of the Anadarko basin of Figure 5 –25.

Subregionalpressurecompartments

The fluids in a porous bioherm completely encased in shale (as shown in the figure below)are virtually isolated from the nearby fluid systems outside the bioherm. The bioherm,then, is a pressure compartment that may or may not be abnormally pressured. Othergeological features that may form local pressure compartments are fault blocks, sandlenses, and sand wedges developed in growth faults.

Local pressurecompartments

Figure 5– 26. From Al-Shaieb et al., 1995b; courtesy AAPG.

Figure 5–27.




A seal can be either a pressure seal, a capillary seal, or both. They are defined as follows:• Pressure seals define pressure compartment boundaries. They can also act as capil-

lary seals and define trap boundaries. Pressure seals impede the flow of hydrocarbonsand water. They form where pore throats are effectively closed and absolute permeabil-ity is near zero.

• Capillary seals define trap boundaries. Capillary seals impede the flow of hydrocar-bons. They form where capillary pressure across the pore throats of a rock is greater orequal to the buoyancy pressure from a hydrocarbon column. Water can move throughan interconnected pore system in a capillary seal.

Pressure vs.capillary seals

Pressure Compartment Seals

Commonly, the top seal is at depths where formation temperature is about 200 °F (90 °C).Evidently, this temperature influences the development of authigenic materials. Quitepossibly the zone of mineralization stays near the 200 °F isotherm, migrating as the basinsubsides or rebounds. Once a seal forms, however, fluid migration through the seal is

restricted, so it is more difficult for a seal to dissolve than to form. If so, there may befossil seals that reflect previous isotherms in the basin.

Pressurecompartmenttop-sealgenesis

Bottom seals of regional compartments are usually well-defined lithostratigraphic units.Side or lateral seals can be a lateral convergence of the top and bottom seals; side sealscan also be thin, mineralized zones paralleling vertical faults.

Side andbottom seals

Pressure compartment seals do not usually seal perfectly. If the pressure generation ratewithin the compartment is greater than the rate of leakage, then pressure will build up inthe compartment.

Leaky seals

Regional pressure compartment pressures build as a result of hydrocarbon generationand other mechanisms. Intermittent release of hydrocarbons and other fluids occurswhen hydrostatic pressure exceeds the fracture gradient of the top seal. Hydrocarbonsreleased from regional pressure compartments charge formations overlying the top seal of the compartment. Subsequent bleed-down of pressure allows temporary rehealing of thefractures. This cycle undoubtedly repeats many times. (David Powley, personal communi-cation).

Episodicleakage ofhydrocarbons




The pressure –depth plot below is from Ernie Dome, Central Transylvania basin,Romania. It shows how pressure and fluids are released from a compartment when pres-sure in the compartment reaches the top-seal fracture pressure.

Episodicleakage ofhydrocarbons

(continued)

Pressure Compartment Seals, continued

Below is a plot of rate of pressure generation vs. rate of pressure leakage for a pressurecompartment in the Central North Sea graben. It correlates tectonic activity with pres-sure leakage caused by fault reactivation and hydraulic fracturing of the top seal.

Example ofepisodicleakage

Figure 5–28. After Leonard, 1993; courtesy The Geological Society.

Figure 5–29. After Gaarenstroom et al., 1993; courtesy The Geological Society.




Pressure compartments have a significant impact on the distribution of oil and gas withina basin. Leonard (1993) lists ways pressure compartments affect elements of petroleumgeology:

• Porosity loss due to compaction is less in overpressured and more in underpressuredrocks than in normally pressured rocks.

• Lack of fluid movement in pressure compartments reduces the supply of free ions asso-ciated with cementation and secondary porosity formation.

• Temperature increase associated with overpressured compartments decreases thedepth of burial for hydrocarbon generation.

• Fracturing of the top seal could be a key to primary and secondary hydrocarbon migra-tion and location of traps.

• Mapping well-to-well pressure variation could identify sealing faults.

Impact onpetroleumgeology

Applying Pressure Compartment Concepts to Exploration

Overpressured compartments impede porosity loss due to compaction. For example,chalks worldwide begin with porosities greater than 50%. During burial in normally pres-sured sections, chalk porosities decrease to less than 10% at depths of 1500 m or more. Inoverpressured compartments of the North Sea, chalks have porosities of 40% or more atdepths of 2500 m and 25% or more at depths of 3000 m or more (Leonard, 1993). Theseporosities are those that would be expected at 700 –1200 m in normally pressured rocksections.

The figure below is a porosity –depth plot for chalks worldwide.

Porositypreservation

Figure 5– 30. After Leonard, 1993; courtesy The Geological Society.

Pore fluid movement within pressure compartments is quite limited because compart-ments are sealed from surrounding beds. Sediments in a pressure compartment mayescape both reservoir-destroying cementation and reservoir-enhancing grain dissolution.

Diagenesis incompartments




Applying Pressure Compartment Concepts to Exploration, continued

The temperature gradi-ent usually increasesbelow the top seal of

pressure compartmentsbecause the top seal pro-vides a thermal blanketfor underlying sedi-ments. This increase intemperature increasesthe rate of hydrocarbonmaturation within thecompartment. The fig-ure to the right showstemperature gradientincrease below the top

seal.

Effect onhydrocarbonmaturation

Figure 5–31. From Leonard, 1993; courtesy The Geological Society.

In many regional pressure compartments, hydrocarbon generation creates pressuresgreat enough to fracture the top seal. Top-seal fracturing episodically releases pressureand fluids, including oil and gas, from the pressure compartment. Oil and gas tend to betrapped in the first reservoir-quality rock over leak points (Leonard, 1993). Leak pointsform where the top seal is shallowest because fracture pressure is lowest in the top seal atthat point. Leak points also can occur where faults are reactivated during tectonic events(Gaarenstroom et al., 1993).

Concentrationof traps

The diagram tothe right is aschematic crosssection of trapsassociated withpressure com-partments.

Compartment-associated traps

Figure 5–32; after Powley, 1995; courtesy Earth Science Reviews.



Capillarity and Buoyancy • 5-53

Capillarity and buoyancy are the forces that determine the distribution of oil and gas inthe subsurface. This section contains discussions of the concepts of capillarity and buoy-ancy, and their effect on the amount and distribution of hydrocarbons in a trap.

Introduction

Section E

Capillarity and Buoyancy


Topic Page

Capillary Pressure 5 –54

Buoyancy Pressure 5 –56

In this section




The 1987 American Geological Institute ’s Glossary of Geology defines capillarity as “theaction by which a fluid, such as water, is drawn up (or depressed) in small interstices ortubes as a result of surface tension. ”

The same glossary defines capillary pressure as “the difference in pressure across theinterface between two immiscible fluid phases jointly occupying the interstices of a rock.It is due to the tension of the interfacial surface and its value depends on the curvature of that surface. ” Capillary pressure is represented by P c.

Definitions

Capillary Pressure

Capillary pressure arises from three phenomena:1. Interfacial tension (molecular attraction at the boundary of each fluid that causes the

fluids to occur as separate phases)2. Wettability (affinity of fluid to solid)3. Small pore throats (capillaries)

Discussion

Interfacial tension is a force that exists because the molecules of a liquid attract oneanother. This attraction causes a drop of liquid to form a spherical shape outside theinfluence of gravity. Gases have no interfacial tension, so they diffuse instead of formdrops. When the difference in interfacial tension between fluids is high (between oil andwater, and especially between gas and water), they do not combine; so they are said to beimmiscible. Interfacial tension is represented by the Greek letter σ.

Interfacialtension

When two or more immiscible fluids coexist in the pores of a rock, one fluid is likely tohave a greater affinity to wet the solid phase (rock surface). This effect causes one fluid topreferentially coat the pore walls and to be drawn into the smallest pores.

Wettability

In oil-field laboratory testing, the degree of wettability is measured by the contact angle(θ), measured through the more dense phase. In this test, a small drop of oil is inserted inan aqueous bath and is allowed to float up to a polished plate of calcite or quartz. The con-tact angle is measured several times over a period of several days until it stabilizes.

The diagrams below show how the contact angle is measured for water-wet (left) and oil-wet (right) reservoirs.

Contact angles

Figure 5– 33.



Capillarity and Buoyancy • 5-55

Capillary Pressure, continued

The capillary effect is most pronounced when the effects of wettability and interfacial ten-sion are combined in very small tubes (capillaries), which are analogous to small porethroats. Pores and pore throats all have some similarities with capillary tubes, but a pore

system is far more complicated because the pore throats are continuously interrupted inthree dimensions by larger pores.

The example below shows how ideal capillary pressure draws a wetting fluid into capil-lary tubes of different diameters. Note that the direction of movement depends on whichfluid is the wetting fluid.

Capillary effectin small tubes

Figure 5– 34.

A water-wet gas reservoir A strongly oil-wet reservoir

Capillary pressure (P c) is related to interfacial tension ( σ), wetting angle ( θ), and radius of capillarity (r) by the following formula:

P c =

Capillary pressure is measured in dynes/cc, interfacial tension in dynes/centimeter, wet-ting angle in degrees, and radius of capillarity in centimeters.

Capillarypressureequation 2 σ cos θ

r




Buoyancy is the tendency for a body (or a drop of immiscible fluid) to float or rise whensubmerged in a fluid of greater density. Where two immiscible fluids (oil and water) occurtogether, they create a buoyancy pressure that is a function of the density difference

between the two fluids and the length of the less-dense fluid column.

Definition

Buoyancy Pressure

If immiscible fluids occur together, they segregate according to their densities: the lightest(least dense) fluid floats to the top, and the heaviest (most dense) sinks to the bottom of the container (or compartment). When they occur in a container free of capillary effects —such as a bottle, lake, or cave —the different fluids exhibit a sharp, flat interface.

Discussion

Virtually every reservoir holds its fluids in a porous network. The pores are normally wellwithin the size range where capillary forces are strong. To fill a reservoir with oil or gas,the buoyancy force driving the oil or gas into the pores of the reservoir must overcome thecapillary force developed between the original fluid and the displacing fluid. The smaller

the pore throats, the greater the capillary pressure associated with them.Following the path of least capillary resistance, nonwetting fluids (gas or nonwetting oil)first move into the pore system that has the largest pore throats. Later, as the columnheight of the oil or gas grows and the buoyancy pressure increases, the hydrocarbonsbegin migrating into pores with smaller and smaller pore throats (in a water-wet system).

Interactionbetweencapillarity andbuoyancy



Hydrodynamics • 5-57

This section discusses the concept of dynamic fluid systems and how hydrodynamicaquifers affect the distribution and accumulation of hydrocarbons.

Introduction

Section F

Hydrodynamics


Topic Page

Basic Hydrodynamics 5 –58

Hydrodynamic Influence on Trapping 5 –60

Mapping Hydrodynamic Traps 5 –61

In this section




Hydrodynamics describes lateral fluid movement through aquifers that have generallylow dip. The fluids can have a vertical component to their movement but, on a basinwidescale, the lateral flow component is of major concern.

Introduction

Basic Hydrodynamics

Hydraulic head (H w) is the height or elevation above a given subsurface point at which acolumn connected to a body of water will equilibrate. It reflects the level of the potentialenergy possessed by the water (Dahlberg, 1994).

The equation for hydraulic head is

where:Hw = height above P (ft or m)Z = height (elevation) of P above a datum (ft or m)P = measured pressure (lb/ft 2 or kg/cm 2)ρ = density of fluid (lb/ft 3 or g/cm 3)g = coefficient of gravity (lb force/lb mass or kg force/kg mass)

The figure below illustrates the relationship of the variables H w and Z used in the aboveequation.

Hydraulic head

Figure 5– 35. From Hubbert, 1953; courtesy AAPG.

Potential energy ( Φ) is the driving force of fluid movement. Its magnitude depends on thehydraulic head (H w) with respect to sea level and is expressed as

According to Dahlberg (1994), hydraulic head serves as a practical approximation of fluidpotential, since the only difference is the coefficient of gravity (g), which is fairly constant.

Potentialenergy of fluids




The potentiometric surface is the surface defined by the hydraulic head (elevation) from arock unit from several different wells. If the potentiometric surface for a given subsurfacerock unit is horizontal, then the potential energy of the water in that formation is con-

stant and the water is at rest (hydrostatic). If the potentiometric surface is sloping, thenthe water moves (hydrodynamic) in the direction of the greatest downward slope(Hubbert, 1953).

The figure below shows the potentiometric surface for hydrodynamic updip and downdipflow and hydrostatic no flow. The pressure –depth plot shows hypothetical pressure gradi-ents for each condition.

Potentiometricsurface

Basic Hydrodynamics, continued





Fluid pressure equals ρgH. Under hydrostatic conditions, the buoyant force equals

ρw gH w – ρhgH h

where:ρw = water densityρh = hydrocarbon densityH w = water depthH h = hydrocarbon column height

Under hydrodynamic conditions, the potential for a hydrocarbon column ( Φh) is related tothe potential of the water by the equation

Φh = ρhgH h = ρwgH w – (ρw

– ρh)gZ

Dividing through by g ( ρw – ρh)/ ρh to simplify gives (in a uniformly flat gravity field)

Constant values for the left-hand side of the equation are equipotential surfaces forhydrocarbons. Hubbert (1953) called this factor U. From the right side, constant valuesfor ρw /(ρw – ρh)Hw are equipotential surfaces for water. Hubbert called this factor V. Theelevation factor (Z) is the difference between the equipotential surfaces for hydrocarbonsand water.Substituting U and V in the above equation gives

U = V – ZFluid flow is perpendicular to equipotential surfaces.

ρρ ρ ρρ ρh

w hh w

w hwH H Z− = − −

Potential ofwater vs.hydrocarbons

Hydrodynamic Influence on Trapping

In a hydrostatic environment, the free-water level of a trap is horizontal. In a hydrody-namic environment, the free-water level of a trap is tilted because the buoyant force (P b)is interfered with by the hydrodynamic force (P w). The resultant interference is the vectorknown as the confining force (P cf ). U, an equipotential line, is perpendicular to P cf and istilted because of the effect of P w. The diagram below shows these vectors and the equipo-tential lines for a hydrocarbon accumulation in an anticline in a hydrodynamic environ-ment.

Hydrodynamiceffect on traps

Figure 5– 37. Modified from North, 1985; courtesy Allen and Unwin.




Formation fluid pressure data are necessary for mapping prospective hydrodynamictraps. Combining formation fluid pressures with other data, such as density and subseaelevation, produces maps that help outline areas where hydrodynamic gradients may

have created, destroyed, or modified traps.

Introduction

Mapping Hydrodynamic Traps

Follow the steps listed in the table below to map the location of possible hydrodynamictraps.

Step Action

1 Look for permeability barriers or hydrocarbon –free water levels usingpressure –depth plots.

2 Calculate potentiometric values for each well using the formulaHw = Z + (P/grad P). (See “Calculating H w” below.)

3 Make a water isopotential map with respect to oil or gas, using theformula for V,

Note : Use gas density where gas is expected and oil density where oil isexpected.

4 Make a gas or oil isopotential contour map using the formula for Uwhere U = V – Z. The values for Z, the subsea elevation of the targetaquifer, can be determined by simply overlaying a structure contour mapon the water isopotential map and subtracting (see “Example ” below).

5 Locate possible accumulations of hydrocarbons in hydrodynamic traps bylocating the areas of low gas or oil potential. Locations should make sensein context with all other geologic data.

Procedure:Mappinghydrodynamictraps

A critical step in mapping hydrodynamic traps in a target formation is making a waterisopotential map (step 3 above). Before that can be done, however, one must calculate apotentiometric value for each well.

Calculate H w for each well using the formula

where:Z = structural elevation of target formationP = measured fluid pressure in the formationgrad P = static formation water pressure gradient

For grad P , use 0.435 psi/ft for areas where regional water is probably fresh and 0.465psi/ft for areas where regional water is probably highly saline.

Calculating Hw




The map below shows oil in a hydrodynamic trap (shaded area). No oil could be trapped inthe structure, represented by solid contours, without the aid of hydrodynamics. The boldcontours with long dashes represent the isopotential of oil (labeled U o). To make U o con-

tours, follow this procedure.Step Action

1 Subtract the structure of the target formation (Z) from the isopotential ofwater (V o).

2 Plot the remainder at the intersection of the two sets of contours.

3 Draw contours of the values.

Example:Uo contours

Mapping Hydrodynamic Traps, continued

Figure 5– 38. From Dahlberg, 1994; courtesy Springer-Verlag.



Annotated Bibliography • 5-63

Section G

Annotated Bibliography

Al-Shaieb, Z., J.O. Puckette, A.A. Abdalla, and P.B. Ely, 1995a, Megacompartment com-plex in the Anadarko basin, in P.J. Ortoleva, ed., Basin Compartments and Seals: AAPGMemoir 61, p. 55 –68.

_____, _____, _____, and _____, 1995b, Three levels of compartmentation within the over-pressured interval of the Anadarko basin, in P.J. Ortoleva, ed., Basin Compartments andSeals: AAPG Memoir 61, p. 69 –83.

Bradley, J.S., and D.E. Powley, 1995, Pressure compartments in sedimentary basins, inP.J. Ortoleva, ed., Basin Compartments and Seals: AAPG Memoir 61, p. 3 –26. Reviewsbasin pressure compartment principles and gives examples.

Collins, A.G., 1987, Properties of produced waters, in H.B. Bradley et al., eds., PetroleumEngineering Handbook: Dallas, SPE, p. 24-1 –24-23.

Dahlberg, E.C., 1994, Applied Hydrodynamics in Petroleum Exploration, 2nd ed.: New York, Springer-Verlag, 295 p. Excellent subsurface fluid pressure reference. Covers hydro-dynamic and static fluids.

Dickey, P.A., 1969, Increasing concentration of subsurface brines with depth: ChemicalGeology, vol. 4, p. 361 –370.

Gaarenstroom, L., R.A.J. Tromp, M.C. de Jong, and A.M. Brandenburg, 1993, Over-pressures in the Central North Sea: implications for trap integrity and drilling safety, inJ.R. Parker, ed., Petroleum Geology of Northwest Europe: Proceedings of the GeologicalSociety ’s 4th Conference, London, p. 1305 –1313.

Gearhart-Owens Industries, 1972, GO Log Interpretation Reference Data Handbook:Fort Worth, Gearhart-Owens Industries Inc., 226 p. A complete reference containing usefulconversion tables, symbols, charts, tables, and nomographs. Each chart is thoroughly ex-

plained and documented with references to source material.

Gunter, J.M., and C.V. Moore, 1987, Improved use of wireline testers for reservoir evalua-tion: Journal of Petroleum Technology, p. 635 –644. Good explanation of the use and inter-

pretation of wireline pressure testers.

Horner, D.R., 1951, Pressure build-up in wells: Proceedings of the Third World PetroleumCongress, The Hague, Section II, p. 503 –521.

Hubbert, K., 1953, Entrapment of petroleum under hydrodynamic conditions: AAPGBulletin, vol. 37, no. 8, p. 1954 –2026. The original paper that proposed hydrodynamics asan important trapping mechanism.



Leonard, R.C., 1993, Distribution of sub-surface pressure in the Norwegian CentralGraben and applications for exploration, in J.R. Parker, ed., Petroleum Geology of Northwest Europe: Proceedings of the Geological Society ’s 4th Conference, London, p.

1305 –1313.

North, F.K., 1985, Petroleum Geology: London, Allen & Unwin, 246 p. Contains manyreadable discussions of fluid pressure and its application.

Powley, D.E., 1990, Pressures and hydrogeology in petroleum basins: Earth ScienceReviews, vol. 29, p. 215 –226.

Schowalter, T.T., 1979, Mechanics of secondary hydrocarbon migration and entrapment: AAPG Bulletin, vol. 63, no. 5, p. 723 –760. Covers many fluid behavior principles, includ-ing pressure, with broad application to petroleum exploration.

Webster ’s New Twentieth Century Dictionary, Unabridged, 2nd ed., 1979: New York,Simon and Schuster, 2129 p.

Annotated Bibliography, continued

I (Forrest Fiedler) received valuable help from Dave Powley in various forms. Dave was amentor at Amoco and inspired me to think things through from basic principles. For thisproject, Dave counseled me and supplied numerous source documents and examples. Itried to honor all his suggestions, but any errors or omissions are my fault, not my men-tor ’s.

Acknowledgment

Documents

05-Formation Fluid Pressure and Its Application