Single-Phase Gas Reservoirs Part 2

Section 4, part 2 of the online course in Applied Petroleum Reservoir Engineering. Dr. Ron Terry discusses Single-Phase Gas Reservoirs, calculating hydrocarbon in place using two methods: through geological and geophysical data and through the material balance.

More information on the online course is available here.

Single-Phase Gas Reservoirs

Section 4 of the online course in Applied Petroleum Reservoir Engineering. Dr. Ron Terry discusses Single-Phase Gas Reservoirs, calculating hydrocarbon in place using two methods: through geological and geophysical data and through the material balance.

More information on the online course is available here.

Pressure Transient Testing

Reader’s Question:
If a have Oil rate, water rate, gas injection rate, water cut , annular pressure and PTH, can i calculate reservoir pressure and productivity index?
Pressure transient testing is required to calculate the productivity index and the reservoir pressure. In pressure transient testing the flow rate through the wellbore is changed and pressure is monitored. There are two types of pressure transient testing: Drawdown testing and build up testing. I’ll run you through drawdown testing briefly:
The drawdown test consists of flowing a well at a constant rate following a shut-in period. The shut-in period should be sufficiently long for the reservoir pressure to have stabilized. The basis for the drawdown test is found in Eq. (8.40),Drawdown Test

which predicts the pressure at any radius, r, as a function of time for a given reservoir flow system during the transient period. If r = rw, then p (r, t) will be the pressure at the wellbore. For a given reservoir system, pi, q, m, B, k, h, f, ct, and rw are constant, and Eq. (8.40) can be written as

Drawdown Test


pwf = flowing well pressure in psia

b = constant

t = time in hrs

Drawdown Test



Equation (8.56) suggests that a plot of pwf  versus t on semilog graph paper would yield a straight line with slope m through the early time data that correspond with the transient time period. This is providing that the assumptions inherent in the derivation of Eq. (8.40) are met. These assumptions are the following:

1.   Laminar, horizontal flow in a homogeneous reservoir.

2.   Reservoir and fluid properties, k, f, h, ct, m, and B are independent of pressure.

3.   Single-phase liquid flow in the transient time region.

4.   Negligible pressure gradients.

The expression for the slope, Eq. (8.56), can be rearranged to solve for the capacity, kh, of the drainage area of the flowing well. If the thickness is known, then the average permeability can be obtained by Eq. (8.57):

Drawdown Testing

As for Productivity Index:
The ratio of the rate of production, expressed in STB/day for liquid flow, to the pressure drawdown at the midpoint of the producing interval, is called the productivity index, symbol J.

Productivity Index

The PI is a measure of the well potential, or the ability of the well to produce, and is a commonly measured well property. To calculate J from a production test, it is necessary to flow the well a sufficiently long time to reach pseudosteady-state flow. Only during this flow regime will the difference between  and pwf be constant. It was pointed out in Section 3 that once the pseudosteady-state period had been reached, then the pressure changes at every point in the reservoir at the same rate. This is not true for the other periods, and a calculation of productivity index during other periods would not be accurate.

In some wells, the PI remains constant over a wide variation in flow rate such that the flow rate is directly proportional to the bottom-hole pressure drawdown. In other wells, at higher flow rates the linearity fails, and the PI index declines, as shown in Fig. 8.15. The cause of this decline may be (a) turbulence at increased rates of flow, (b) decrease in the permeability to oil due to presence of free gas caused by the drop in pressure at the well bore, (c) increase in oil viscosity with pressure drop below bubble point, and/or (d) reduction in permeability due to formation compressibility.

In depletion reservoirs, the productivity indicies of the wells decline as depletion proceeds, owing to the increase in oil viscosity as gas is released from solution and to the decrease in the permeability of the rock to oil as the oil saturation decreases. Since each of these factors may change from a few to several-fold during depletion, the PI may decline to a small fraction of the initial value. Also, as the permeability to oil decreases, there is a corresponding increase in the permeability to gas, which results in rising gas-oil ratios. The maximum rate at which a well can produce depends on the productivity index at prevailing reservoir conditions and on the available pressure drawdown. If the producing bottom-hole pressure is maintained near zero by keeping the well “pumped off,” then the available drawdown is the prevailing reservoir pressure, and the maximum rate is .

Productivity Index

Fig. 8.15. Decline in productivity index at higher flow rates.


In wells producing water, the PI, which is based on dry oil production, declines as the water cut increases because of the decrease in oil permeability, even though there is no substantial drop in reservoir pressure. In the study of these “water wells,” it is sometimes useful to place the PI on the basis of total flow, including both oil and water, where in some cases the water cut may rise to 99% or more.

These excerpts are straight from my textbook. If this is helpful to you, I would recommend that you pick up a copy. Use the code ENGINEERING at this site for a 35% discount: Pearson InformIT Bookstore

Estimating Reservoir Size Without 3D Seismic

Estimating reservoir size without 3D Seismic involves estimating the bulk volume of the reservoir using well logs, core data, well test data, and 2-dimensional seismic data. A reservoir engineer uses this data to create contour and isopach maps of the reservoir. The 2D seismic provides the footprint of the reservoir while well logs are used to determine formation thickness. The core data is used to determine the porosity of the rock. Well test data can be used in a history match to fine tune the assumptions.

Here’s how it works:
A subsurface contour map shows lines connecting points of equal elevations on the top of a marker bed and therefore shows geologic structure. A net isopach map shows lines connecting points of equal net formation thickness; and the individual lines connecting points of equal thickness are called isopach lines. The contour map is used in preparing the isopach maps when there is an oil-water, gas-water, or gas-oil contact. The contact line is the zero isopach line. The volume is obtained by planimetering the areas between the isopach lines of the entire reservoir or of the individual units under consideration. The principal problems in preparing a map of this type are the proper interpretation of net sand thickness from the well logs and the outlining of the productive area of the field as defined by the fluid contacts, faults, or permeability barriers on the subsurface contour map.

Formation of Petroleum Reservoirs

The formation of petroleum reservoirs occurs over millions of years as oil and gas accumulations develop in underground traps formed by structural or stratigraphic geological features. These accumulations usually occur in the more porous and permeable sedimentary rock, where the petroleum molecules seep into the small inter-granular spaces, or in joints and fractures of the rock. The reservoir is the portion of the formation containing oil and gas that is hydraulically connected.

Conventional reservoirs need a source rock, a migration path, a reservoir rock and a cap rock.

The source rock is a rock that is rich in organic matter. These form as algae or other plant and animal life die and are buried in the sand. Over millions of years, these rock formations are covered by other rock formations and the pressure and temperature of the rock increases. The organic matter converts to oil and gas as it is heated.

As the oil and gas forms in the source rock, it begins to migrate through the inter-granular spaces, the joints and the fractures of the rock. The oil and gas molecules are less dense than the rock and water and naturally migrate slowly upward towards the surface.

The molecules continue migrating until they hit cap rock. Cap rock is typically a layer of impermeable rock that lacks the inter-granular spaces the molecules need to continue traveling. It overlays the reservoir rock and forms a trap. At this point, with no where for the molecules to go, and more molecules continuing to migrate out of the source rock, the molecules begin to accumulate in the rock directly below the cap rock – the reservoir rock.

If there is no cap rock, the molecules travel all the way to the surface, resulting in a natural oil seep.

Formation of Petroleum Reservoirs
Hyne, Norman J.: Geology for Petroleum Exploration, Drilling and Production, New York: McGraw-Hill Book Co., 1984

In recent years, unconventional reservoirs have been developed. These unconventional reservoirs are unique in that the source rock is the reservoir rock. No migration path or cap rock is needed, as the oil and gas are produced directly from the source rock where it was generated.


Terry, Ronald E., J. Brandon. Rogers, and B. C. Craft. Applied Petroleum Reservoir Engineering. Third ed. Massachusetts: Prentice Hall, 2014. Print.

Darcy’s Law

While the material balance can identify initial hydrocarbon in place, estimate production at various pressure, and provide identify the primary production mechanism, it is unable to answer the question of when the hydrocarbon will be produced. Darcy’s law complements the material balance by calculating flow rates. The combination of Darcy’s law and the material balance results in a model capable of predicting flow rates over time.

Henry Darcy formulated Darcy’s Law in 1856 as a result of his experimental studies on the flow of water through unconsolidated sand beds. Over time, it has been expanded to include the movements of other media and even two or more immiscible fluids.

There are four major influences on fluid flow. These are: number of phases present, the compressibility of the fluid, the geometry of the flow system, and finally the time characteristics of the flow system.

Let’s take a look at Darcy’s Law and discuss the various terms.

Darcy's Law Equation

u = the apparent velocity, bbls/day-ft2

k = permeability, millidarcies (md)

m = fluid viscosity, cp

p = pressure, psia

s = distance along flow path in ft

y = fluid specific gravity (always relative to water)

a = the angle measured counterclockwise from the downward vertical to the positive s direction

We’ll start with the driving force, the term in brackets.

Darcy's LawThe term dp/ds represents the driving force caused by a fluid pressure gradient. The wellbore pressure will be lower than the reservoir pressure causing a pressure gradient to form along the flow path. This term is simply the difference in those pressures divided by the distance.

The second driving force is the hydraulic or gravitational gradient. This term includes a gravitational constat, the specific gravity of the fluid and the angle of the flow path relative to the force of gravity.

This driving force is adjusted by a constant, permeability and viscosity to calculate the apparent velocity of the fluid. This ‘apparent velocity’ is equal to the product of the flow rate and the formation volume factor divided by the total area of the rock perpendicular to the flow path. (v=q*B/A)

Terry, Ronald E., J. Brandon. Rogers, and B. C. Craft. Applied Petroleum Reservoir Engineering. Third ed. Massachusetts: Prentice Hall, 2014. Print.

Drive Mechanisms

Primary production of hydrocarbons from petroleum reservoirs are due to three forces . These are typically referred to as drive mechanisms. They are depletion drive, segregation drive, and water drive.

Depletion drive (DDI) is the volumetric expansion of the oil. This drive harnesses the energy of the oil that has been compressed due to the high initial reservoir pressure.

Segregation (gas cap) drive (SDI) is the volumetric expansion of the gas. Like depletion drive, it harnessed the energy of the compressed gas. As gas is much more compressible the oil, this drive often has a greater impact. Segregation drive includes both to the expansion of the original gas in place and the evolution of gas from the oil as the pressure declines.

Water drive (WDI) is the bulk inflow of water from outside the boundaries of the reservoir, typically from an adjacent aquifer.

Not all reservoirs experience all three types of drive. Water drive applies only to reservoirs with an attached aquifer of sufficient magnitude. Depletion drive does not apply to single-phase gas reservoirs. Segregation drive applies to all reservoir types.

The relative magnitude of each drive on the overall production can be measured using the material balance equation rearranged in the form of a drive index as shown below. It can be summarized as DDI + SDI + WDI = 1. Using this method, the contribution of each drive to a field can be quantified and used for selecting appropriate strategies to increase production.

Eq 3.11

Calculating Gas in Place Using the Material Balance

The material balance can be simplified depending on what type of reservoir we are interested in analyzing. The single-phase gas reservoir is the most simple. We’ll cover calculating gas in place using the material balance. The material balance equation can be simplified, as all the terms for oil production, liquid expansion and rock expansion can be neglected. See Chapter 3 of Applied Petroleum Reservoir Engineering Third Edition for the derivation. See Material Balance for Nomenclature.

Simplified Gas Reservoir Material BalanceSingle-phase gas reservoirs have two possible drive mechanisms: segregation (gas cap) drive and water drive. Segregation drive will occur in all reservoirs, while water drive will only occur in select reservoirs. We’ll cover segregation drive.

Segregation Drive

Under segregation drive, the equation can be simplified even further, first by neglecting water influx and water production and then by substituting in expressions for the gas formation volume factor.

Depletion Drive Volumetric Reservoir Material Balance EquationStraight-line Depletion Drive Material Balance Equation

As pi, zi and G are constants for a given reservoir, a plot of early production data for p/z versus Gp gives us a straight line. The initial gas in place (G) is the intersection with the x axis. Please note that neglecting to correct the pressure term by the gas compressibility factor results in an incorrect extrapolation. In the same manner, a reservoir experiencing water drive will have a slower decline, as the water influx assists in stabilizing the pressure. Using this method for reservoirs with a water drive will also result in an incorrect extrapolation.

Comparison of theoretical vales of p/z plotted versus cumulative production from a volumetric gas reservoir

Terry, Ronald E., J. Brandon. Rogers, and B. C. Craft. Applied Petroleum Reservoir Engineering. Third ed. Massachusetts: Prentice Hall, 2014. Print.

Material Balance

As fluid is produced from the reservoir it doesn’t leave a void, something has to fill the space. Gas, oil, water and rock can all expand, to varying degrees, to fill up the space but it results in a decrease in the reservoir pressure. In addition, water can migrate into the reservoir area. The material balance equation was derived in order track the production of oil, gas and water; the expansion of existing fluid and rock; and the migration of water into the reservoir. The material balance provides reservoir engineers a great deal of insight in knowing the initial hydrocarbon in place, how much hydrocarbon can be produced at different pressures, the primary mechanism for reservoir production and the potential usefulness of varying enhanced recovery techniques. For a detailed derivation, please refer to Chapter 3 of Applied Petroleum Reservoir Engineering.

The material balance equation can be written as:

Oil Expansion + Gas Expansion + Formation and Water Expansion + Water Influx

=Oil and Gas Production + Water Production

General Material Balance Equationwhere

N   Initial reservoir oil, STB

Boi  Initial oil formation volume factor, bbl/STB

Np  Cumulative produced oil, STB

Bo  oil formation volume factor, bbl/STB

G   Initial reservoir gas, SCF

Bgi  Initial gas formation volume factor, bbl/SCF

Gf  Amount of free gas in the reservoir, SCF

Rsoi Initial solution gas-oil ratio, SCF/STB

Rp  Cumulative produced gas-oil ratio, SCF/STB

Rso Solution gas-oil ratio, SCF/STB

Bg  Gas formation volume factor, bbl/SCF

W   Initial reservoir water, bbl

Wp  Cumulative produced water, STB

Bw  Water formation volume factor, bbl/STB

We  Water influx into reservoir, bbl

cw   Water isothermal compressibility, psi–1

Swi  Initial water saturation

Vf   Initial pore volume, bbl

cf   Formation isothermal compressibility, psi–1

Terry, Ronald E., J. Brandon. Rogers, and B. C. Craft. Applied Petroleum Reservoir Engineering. Third ed. Massachusetts: Prentice Hall, 2014. Print.