PERFORMANCE PREDICTION

WATER DRIVE RESERVOIRS-2

06.02.2015

The two main questions in the event of Water drive Mechanism are:1. Recognition of Natural water Influx?2. Contribution of Aquifer?

During the early exploration-development period of a reservoir not enough information is available about the presence or characteristics of an aquifer that could provide a source of water influx during the depletion period.

Natural water drive may be assumed by analogy with nearby producing reservoirs.The early reservoir performance trends can provide clues.

1

2

A comparatively low, and decreasing, rate of reservoir pressure decline with increasing cumulative withdrawals.

If the reservoir limits have not been delineated by developed dry holes, however, the influx could be from an undeveloped area

If the reservoir pressure is below the oil saturation pressure, a low rate of increase in produced gas-oil ratio.

Early water production from edge wells is indicative of water encroachment.

Calculation of the increasing original oil – in - place from successive reservoir pressure surveys

SUBSEQUET STAGE OF EXPLORATION/DEVELOPMENT

The efficiency of water drive mechanism is based on the extent of water influx and requires quantitative estimation.The rate of water influx from the aquifer into the reservoir equals the withdrawal of fluids (oil, gas and water) from the reservoir.

Contribution of Aquifer

Predicting Water drive Reservoir BehaviorPrediction of water drive reservoir is more difficult than the gas drive reservoirs. It is required to recognise / add the effect presuure and time to the productive force of WATER ENCROACHMENT.

OIL

UNDER SATURATED

SATURATED

We

P T

REMARKS

While time is a vital parameter for performance evaluation.Care must be taken for the water drive reservoirs producing below the bubble point pressure with respect to the contribution of solution gas and possible Gas Cap drive prediction period.

To predict performance of water drive reservoir, it is necessary to know the nature of aquifer and its cotribution . which is attributed to:1, Expansion of the water in the aquifer2. Compressibility of the aquifer rock,Reservoir-aquifer systems are commonly classified on the basis of:1. Degree of pressure maintenance 2, Flow regimes3. Outer boundary conditions 4. Flow geometries

ESSENTIALITY

ELEMENTS OF AQUIFER PERFORMANCE

Aquifer ExtensionAquifer and its characteristicsAquifer KineticsAquifer Flow characterizationAquifer Flow GeometriesAquifer functionsAquifer Water Flow: Calculations

AQUIFER EXTENSION(1) An oil reservoir represents an extremely small

volume of fluid compared with the volume of aquifer with which it is connected.

(2) The withdrawal of hydrocarbons , oil or gas ,can cause the gradual decompression of a large volume of water of the aquifer.

(3) The water inflows tends to offset the pressure drop that should have occurred inside the oil reservoir.

(4) Consequently a gradual expansion of the aquifer occurs in transient conditions over a long time interval.

(5) The subsequent changes in the reservoir depends on the size of the aquifer and its characteristics.

(1) A very sensitive, very continuous and highly permeable aquifer guarantees virtually perfect pressure maintenance . This is termed as Perfect Water Drive

(2) A relatively small non continuous or mediocre aquifer provides limited support and is called as Partial Water Drive

(3) If an Aquifer has limited source of water and requires supplementation of water injection for necessary oil movement it is said to have limited water drive.

AQUIFER CHARACTERISTICS

Active Water driveThe term active water drive refers to the water encroachment mechanism in which the rate of water influx equals the reservoir total production rate. Active water-drive reservoirs are typically characterized by a gradual and slow reservoir pressure decline.During any long period, the production rate and reservoir pressure remain reasonably constant.The reservoir voidage rate must be equal to the water influx rate.

Basic Equations

Where

In terms of cumulative production by introducing the following derivative terms:

Where

EXAMPLE

Calculate the water influx rate ew in a reservoir whose pressure is stabilized at 3000 psi. Other related data is given as under: Initial Reservoir Pressure = 3500 psidNp /dt = 32,000 STB/day Bo = 1.4 bbl/STBGOR = 900 scf/STB , Rs = 700 scf/STBBg = 0.00082 bbl/scf , dWp/dt = 0Bw = 1.0 bbl/STBApplying Equation above :ew = (1.4) (32,000)

+ (900 − 700) (32,000) (0.00082) + 0= 50,048 bbl/day

SOLUTION

AQUIFER KINETICSDetermining the Water Inflow – We in to the reservoir with respect to time. More specifically the cumulative water inflow as a function of time and drop in pressure in the oil + aquifer zone., with the following ASSUMPTIONS:• An oil reservoir represents an extremely small volume

of fluid as compared with the volume of aquifer with which it is connected.

• The withdrawal of hydrocarbons, oil or gas ,can cause the gradual decompression of a large volume of water.

• This results in the water inflows so as to off set pressure drop that should have occurred inside the reservoir.

1

2

3

Outer Boundary ConditionsThe aquifer can be classified as Infinite Finite (bounded) a. Infinite system indicates that the effect of the

pressure changes at the oil/aquifer boundary can never be felt at the outer boundary. This boundary is for all intents and purposes at a constant pressure equal to initial reservoir pressure.

b. Finite system indicates that the aquifer outer limit is affected by the influx into the oil zone and that the pressure at this outer limit changes with time.Geologically all formations are finite, but may act as infinite

Aquifer Flow characterizationThere are basically three flow regimes that influence the rate of water influx into the reservoir.

a. Steady-state 325b. Semi steady (pseudo steady)-statec. Unsteady-state

Reservoir-aquifer systems can be classified on the basis of flow geometry as:

a. Edge-water driveb. Bottom-water drivec. Linear-water drive

Pressure p withrespect to Time t at any Location i

pressure at different locations in the reservoir is declining linearly as a function of time, i.e., at constant declining rate,

the rate of change of pressure with respect to time at any position in the reservoir is not zero or constant

rate of change of pressure p with respect to time t at any location i is zero

Aquifer Flow Geometries

Edge-water drive, water moves into the flanks of the reservoir as a result of hydrocarbon production and pressure drop at the reservoir-aquifer boundary. The flow is essentially radial with negligible flow in the vertical direction. Bottom-water drive occurs in reservoirs with large areal extent and gentle dip where the oil -water contact completely underlies the reservoir. The flow is essentially radial and, in contrast to the edge-water drive, the bottom-water drive has significant vertical flow.In linear-water drive, the influx is from one flank of the reservoir. The flow is strictly linear with a constant cross-sectional area.

Aquifer functions• An aquifer# function represents cumulative

water influx into the oil reservoir and is defined as the basic property of aquifer that relating the pressure changes and the flow rate as a function of time. (P,Q)=ft

• The contours of O/W boundaries and of the aquifer are treaded as circles with the radial cylindrical flow

• Water influx may be regarded as a function of aquifer compressibility , initial volume of aquifer and pressure changes.We= F(aq.vol.), Pt# Assuming a relatively small aquifer and pressure drop in the reservoir in instantaneously transmitted throughout the reservoir aquifer system.

Aquifer Models

ra = radius of the aquifer, ftre = radius of the reservoir, fth = thickness of the aquifer, ftφ= porosity of the aquiferθ = encroachment angle

PARAMETERS

PROCESSESWe = cumulative water influx, bblcw = aquifer water compressibility, psi−1

cf = aquifer rock compressibility, psi−1

Wi = initial volume of water in the aquifer, bbl f =fractional encroachment angle f = θ/360°

Radial aquifer geometries.

Pot Model

∆V = c V ∆ p

Water influx into a gas or oil reservoir , is based on the basic definition of compressibility given as:

Applying the above equation to the aquifer flow;

Water influx = (aquifer compressibility) (initial volume of water)# (pressure drop)

ORWe = (cw + cf) Wi (pi − p)pi = initial reservoir pressure, psip = current reservoir pressure, psi

# SQ is Wi and need to be calculated

CALCULATING INITIAL VOLUME OF AQUIFER (Assuming radial shape)

Wi = ----------------π (ra2 –r e

2)hΦ )5.615

1

The above relation envisages radial flow in all the directions , as such a concept of fractional encroachment is incorporated with respect to water influx and the required equation becomes:

We = (cw + cf) Wi f (pi − p) f = fractional encroachment angle = θ/360° θ = is defined as encroachment angle

---------------- 2

Example -2Calculate the cumulative water influx that results from a pressure drop of 200 psi at the oil-water contact with an encroachment angle of 80°.The reservoir-aquifer system is characterized by the following properties:

Reservoir AquiferRadius , ft 2600 10,000Porosity, fraction 0.18 0,12Cf,psi-1 4x 10 -4 3x10-3

Cw,psi-1 5x10--6 4x10-6

h , ft 20 25

SolutionStep 1. Calculate the initial volume of water in the aquifer from equation below:.

Step 2. Determine the cumulative water influx by applying equation below :

Incorporating TIME dependency variable

(aquifer to respond to a pressure change in the reservoir.)The rate of water influx ew as determined byDarcy’s equation may be given as:

The above relationship can be more conveniently expressed as:Whereew = rate of water influx, bbl/dayk = permeability of the aquifer, mdh = thickness of the aquifer, ftra = radius of the aquifer, ftre = radius of the reservoirt = time, days

The parameter C is called the water influx constant and is given inbbl/day/psi.

Schilthuis Model

ew can be determined independently from a different expression , as explained earlier in slide 12&13. The water influx constant C may be calculated from the reservoir historical production data over a number of selected time intervals, provided that the rate of water influx is known.Vital Issue1. The water influx constant (C)can only be obtained

in this manner in which the reservoir pressure stabilizes,

2. Once it has been found, it may be applied to both stabilized and changing reservoir pressures.

Determining the values of ew and C

The data given in is used in this example:Pi = 3500 psi p = 3000 psi Qo = 32,000 STB/dayBo = 1.4 bbl/STB GOR = 900 scf/STB Rs = 700 scf/STBBg = 0.00082 bbl/scf Qw = 0 Bw = 1.0 bbl/STB

Calculate Schilthuis’ water influx constant

Step 1 Solve for the rate of water influx ew as below :ew = (1.4) (32,000) + (900 − 700) (32,000) (0.00082)+ 0 = 50,048 bbl/dayStep 2.Solve for the water influx constant as below:

* If the steady-state approximation adequately describes the aquifer flow regime, the calculated water influx constant C values will be constant over the historical period.

*

steady-state approximation

In terms of the cumulative water influx We, equation may be integrated as below:

or

WhereWe = cumulative water influx, bbl C = water influx constant, bbl/day/psi t = time, days pi = initial reservoir pressure, psi p = pressure at the oil-water contact at time t, psi

The pressure at the oil/water interface drops as a function of time, the pressure curve can be sub divided into successive increments/sectors

Determination of We

When variation exists with Pressure & Time (Both)

Pressure Variations

Water inflows Qe (P,t)• The water in flows entering the oil zone is

given as:

Where

In this geometry o/w contact surface is replaced by virtual vertical surface in accordance with the amount of oil in place

This area at time t can be determined numerically by using the trapezoidal rule, as:

Pressure Variations with TimeCalculating the area under the curve

RemarksWith its values during the production history , the aquifer function can be determined up to the present time , enabling its extrapolation for production forecasts.

Also depending on the regional geological data , optimization method serve to determine the most probable values of the size and permeability of the aquifer.

These analysis are of fundamental importance , because , depending on the predicted activity of the aquifer function, recovery may vary with in a reasonable range(1 to 10%)

Aquifer Water Flow: Calculations

When aquifer characteristics are known,

When water inflows are estimated from material balance

Example 4

The pressure history of a water-drive oil reservoir is given below:

t, days p, psi0 3500 (pi)100 3450200 3410300 3380400 3340

The aquifer is under a steady-state flowing condition with an estimated water influx constant of 130 bbl/day/psi. Calculate the cumulative water influx after 100, 200, 300, and 400 days using the steady-state model.

When aquifer characteristics are known,

Step 1. Calculate the total pressure drop at each time t.

Step 2. Calculate the cumulative water influx after 100 days:

Step 3. Determine We after 200 days.

Step 4.We after 300 days.

Step 5. Calculate We after 400 days.

Hurst’s Modified Steady-State Model (Hurst) Problems as the water is drained from the aquifer, the aquifer drainage radius ra will increase as the time increases. Solutionthe dimensionless radius ratio ra/re may be replaced with a time dependent function, as:ra/re = atAs such the Equation becomes

---------------2

---------------1

The two unknown constants, a and C, that is determined from the reservoir-aquifer pressure and historical data of

water influx. This may be done by straight line method:

The water influx relation can also be written as:

---------------3

In terms of the cumulative water influx------4

--------5

The linear relationship between a and C may given as:

or ------6Equation 6 indicates that a plot of (pi− p)/ew versus ln(t) will be a straight line with a slope of 1/C and intercept of (1/C)ln(a).

Graphical determination of C and a.

1 Determine the slope or 1/C2 Find the value of C3 Consider any point on the state line;4 Determine its parameters5 Use the following equation to calculate the

value of a by using the value of C

6 Use the following equation within any time limits

METHOD

or

ExampleUse the following data to calculate cumulative water influx after 1186.7 days when the boundary pressure would drop to 3379 psi.

SOLUTIONReconstruct the table for essential data and Plot the term (pi − p)/ew versus ln(t) and draw the best straight line through the points to calculate the slope of the line .

1 Determine the slope or 1/C

3 Consider any point on the state line say X4 Determine its parameters5. Solve for a using following equation to calculate the value of a:

2 Find the value of CLet C= 1/0.02 = 50

Let a = 0.0646. Use the following equation to calculate desired value

or

Calculate the cumulative water influx after 1186.25 days using following relation:

When water inflows are estimated from material balance

Use following data to calculate the produced oil

Assumption :

Recovery due to water encroachment

THANKS