Building the Dynamic Reservoir Model

DYNAMIC MODEL

Well/Facilities Model

Near Wellbore Performance Models

Upscaled Reservoir

Model

Preliminary Dynamic

Model

Calibrated Dynamic

Model

Projected Reservoir

Performance

Field Economic

Model

Optimized Reservoir

Development Plan

Integrated Reservoir Study

Dynamic Reservoir Model

• A mathematical model that describes and simulates the time-dependent flow processes active in a hydrocarbon reservoir

• The dynamic model combines

– The static model

– Pressure- and saturation-dependent properties

– Near-well, wellbore, and facilities properties

to calculate production and pressure vs time

Importance

Static Model• Model of reservoir at initial conditions• Insufficient to predict performance or optimize

development

Dynamic Model• Models entire life of reservoir• Can produce reservoir several times under

different operating conditions• Can optimize reservoir depletion plan

Steps in Model Construction• Selection of the model type• Selection of the fluid model and number of

phases• Selection of the grid coordinate system and

number of dimensions• Selection of optimal grid block sizes• Specification of reservoir properties• Simplification of reservoir geometry• Selection of the well model• Specification of well control• Specification of time step size control• Selection of the numerical solution method

Factors Affecting Model Design

• Objectives of the simulation study

• Quality of the answer needed to satisfy the project objectives

• Complexity of the reservoir processes to be modeled including secondary and/or tertiary recovery processes

• Budget constraints

• Time available to complete the study

Factors Affecting Model Design

• Availability and quality of reservoir data

• Availability and quality of historical production data

• Capabilities and ease of use of available simulators

• Capabilities and availability of computer facilities

Data Categories

• Reservoir and well data

• Simulation specific data

– Simulation grid

– Simulation time schedule

– Simulator control data

Reservoir and Well Data

• Reservoir fluid property data

• Reservoir rock property data

• Strata properties

• Well data

• Wellbore and facilities data

Location of VLE 196 Field in Block V, Lake Maracaibo, Venezuela

VLE - 196AREA

BLOCKV

I

IX X

II

VII

III

VII

XIII

XI

VI

XV

MARACAIBO

LAKE MARACAIBO

N

LakeMaracaibo

COLOMBIA

CaribbeanSea

Barranquilla

Maracaibo

V

VLE 400 Fault

VENEZUELA

1078000.

214000. 216000.

VLE 647

VLE 738

VLE 470

LRF 0009

LRF 0006 LRF 0079

LRF 0003

LRF 0078

LRF 0113

LRF 0062

LRF 0016

LRF 0028

LRF 0039

LRF 0033

LRF 0026

LRF 0035

LRF 0114

VLE 1215

LRF 117

Block VI

Block V

S.A. Holditch & Associates, Inc.

Maraven, VLE-196 ReservoirBlock V Lamar, Lake

Maracaibo

Fault Areas Map

Scale 1:20000.

kilometers0.2 0. 0.2 0.4 0.6 0.8 1.

meters200. 0. 200. 400. 600. 800. 1000.Scale 1:20000.

1072000.

1074000.

1076000.

VLE

400 fault

VL

E 400 fau

lt

67 5

412 11

810

3

9

2

1

Base Map for the C4-C5 Reservoir Simulation Study

Introduction

• VLE-196 field discovered in 1958

• Produced over 200 million STB

• Wells produced with sliding sleeves to control water production

• About 50 wells completed in the Misoa sandstones

Objectives

• Characterize the reservoir for modeling

• Identify bypassed and untapped compartments

• Develop a plan to increase production rates and reserves

Reservoir Fluid Property Data

• 5 basic reservoir fluid types

– Dry gas

– Wet gas

– Retrograde gas (gas condensate)

– Volatile oil

– Black oil

The Fluid Model Must

• Be consistent with the project objectives

• Properly account for the number of phases existing at reservoir and surface conditions (This requirement can be relaxed in cases where immovable fluids exist which do not contain appreciable amounts of the movable fluids or components in solution)

• Accurately predict phase changes which occur during the simulation

The Fluid Model Must

• Accurately predict the volumetric properties, including compressibility and density, of the reservoir and surface fluids

• Accurately predict the viscosity of reservoir fluids and any other critical parameters such as specific heats in cases of nonisothermal simulations

• When an equation of state is used to predict phase behavior, the equation must be "tuned" to match all available special laboratory data measured on valid reservoir fluid samples

Reservoir Fluid Property Data

• Fluid PVT data

– Black oil

• Bo(p), Rso(p), o(p), o(p)

• Bg(p), g(p), g(p)

– Volatile oil

• Bo(p), Rso(p), o(p), o(p)

• Bg(p), Rsg(p), g(p), g(p)

PVT Properties

• Undersaturated oil at initial conditions

• Compositional gradient present initially

• Extrapolated PVT data from 5 laboratory analyses

• Resulting black-oil PVT properties used in model

Reservoir Fluid Property Data

• Equilibration data

– Original pressure at datum

– Fluid contact elevations

Reservoir Rock Property Data

• This section contains rock properties usually derived from core analysis

• Small number of samples, so not enough data to generate maps, or distributions, of these properties

• Usually assume these properties are constant throughout a particular zone, or stratum

Reservoir Rock Property Data

• Capillary pressure

• Relative permeability

• Hysteresis in capillary pressure and relative permeability

• Pressure-dependent porosity and permeability functions

• Non-darcy flow (gas)

• Dual-porosity data

Relative Permeability and Capillary Pressure Data

• Initially developed 4 sets of data, for 4 different porosity ranges

• Initially, did not adequately model water production in thin, high-permeability layers

• Pseudo relative permeabilities were developed to match observed water production

Capillary Pressure (J Function) as a Function of Water Saturation

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

0 10 20 30 40 50 60 70 80 90 100

Sw

J(S

w)=

Pc*

(K/P

hi)

^0.

5

Strata Properties

• This section contains rock properties usually derived from well log data or seismic data

• Larger number of samples, so often enough data to generate maps, or distributions, of these properties

• Often input separate maps of these properties for each zone, or stratum

Strata Properties

• Structural properties

– Elevation (structure map)

– Gross interval thickness

– Reservoir limits

– Discontinuities (faults)

Strata Properties

• Formation properties

– Net-to-gross ratio (or net sand thickness)

– Porosity

– Formation permeability

– Pore volume and transmissibility modifications

Reservoir Characterization Previously Documented

• Martin, et al., 1997

• Geophysical, geological and petrophysical analyses

• Geological model consisting of 19 layers

• Correlated seismic attributes to petrophysical parameters to improve reservoir mapping

18

81

21

18

18

81

21

1

2

18

81 12

21

12

12

21

21 21

12

12

21

21

21

21

21

12

12

21

21

12

1221

12

12

12

12

12

18

81

21

18

18

81

81

21

12

12 1818

81

18

18

21 21

12

12

21

2112

12

81

8181

18

18

81

81

18

18

18

81

81

18

18

8181

15

51

51

51

15

18

18

18

81

81

81

18

1 0 9F

1 1 6F

9 4B

1 3 5F

1 2 8F

1 2 0F / R

1 4 5B / R

1 1 5F

1 2 7F / B

1 0 4B / C

1 3 8F / C

1 6 2B

1 0 8F / R

1 6 2B / F

4 3C

1 5 3C / F

8 0F

1 6 9B / F

1 6 6B

1 2 7F

1 5 4B

1 0 2F

1 4 4C / F

1 1 7F / R

1 5 3B

1 2 8F1 6 1

F1 2 1

F / R1 0 2

F / R

1 2 7F

9 9F

1 7 6F / R

1 2 6F / R

1 6 6F

1 5 0F / R

L R F 0 2 3

V L E 1 1 0 2

V L E 3 9 4V L E 1 0 3 4

V L E 1 0 1 6 V L E 4 2 2V L E 1 1 2 8

V L E 9 8 7

V L E 9 9 5V L E 1 0 0 6V L E 1 0 4 6

V L E 6 6 3V L E 1 1 3 9V L E 1 0 0 7

V L E 9 8 5V L E 5 1 0

V L E 9 7 3

V L E 6 3 1

V L E 6 7 5

V L E 1 0 6 3

V L E 6 4 7

V L E 1 0 1 9V L E 4 4 9

V L E 5 1 6

V L E 1 0 0 4

V L E 2 9 7

V L E 1 0 0 5

V L E 1 1 3 5 V L E 6 7 4V L E 1 1 5 5

V L E 1 1 0 1

V L E 6 3 5V L E 6 5 5

V L E 5 0 6 V L E 5 7 1

V L E 1 1 3 0

V L E 6 7 7

V L E 4 7 1 V L E 4 0 0V L E 0 9 6

V L E 1 9 6 V L E 6 5 1

V L E 1 0 0V L E 1 1 4 0

V L E 9 9 2V L E 5 0 4

V L E 4 6 0

V L E 1 1 4 8

V L E 6 1 9

V L E 9 6 8

V L E 0 9 4 V L E 4 5 3

V L E 7 3 8 V L E 4 3 2

V L E 5 1 1V L E 6 7 1

V L E 9 9 9

V L E 4 7 0 V L E 7 1 5 V L E 0 9 1 V L E 4 6 5

L R F 0 0 1 7

L R F 0 1 1 3

L R F 0 0 3 0

V L E 1 1 2 7

BLOCK VI LRF WELLS

BLOCK V VLE WELLS

>21

1512

1815

2118

0 3000

0 1000m

ft

N

Percent

VL

E 4

00 F

ault

Misoa Formation, C-5 Sand, Layer 7, Average Porosity

Well Data

• Completion data

• Production and injection data

• Pressure data

• Operational control and constraint information

Well Data

• Completion data– Well bottomhole location and orientation– Perforation interval– Wellbore radius– Permeability-thickness product– Skin factor– Hydraulic fracture length– Hydraulic fracture conductivity– Well constant

Well Data

• Production and injection data– Production vs time for all produced

fluids – oil, gas, condensate, water

– Injection vs time for all injected fluids – gas, water

Well Data

• Pressure data

– Static pressure data

– Flowing pressure data

– Pressure transient test data

Well Data

• Operational control and constraint information– How are wells produced?

• Natural flow• Rod pump• Gas lift• Submersible pump

Well Data

• Are there any limits, or constraints, on production?

– Equipment pressure limitations

– Maximum fluid lifting capacity

– Maximum water handling capacity

– Economic limit production rates

– Allowable production limited by regulatory agencies

Well Data

• How are injection wells operated?

• Are there any limits, or constraints, on injection?

– Equipment pressure limitations

– Maximum injection rate capacity

Wellbore and Facilities Data

• Well mechanical configuration data– Lengths and ID’s of tubulars through

which fluids are produced and injected• Configuration of surface gathering and

injection system – Note types and locations– Lengths and ID’s of tubulars through

which fluids flow

Simulation Grid

• Primary grid specification

• Local grid refinement specification

Simulation Grid

• The simulation grid is the definition of how we divide, or discretize, space in order to solve the differential equations numerically

• Although we use reservoir and well properties in designing the simulation grid, the simulation grid is independent of the reservoir and well properties.

Primary Grid and Local Grid Refinement

Common Grid Coordinate Systems Include

• Cartesian

• Cylindrical

• Curvilinear (including stream-tube)

• Corner point

Selection of Optimal Grid Block Sizes

• Optimal grid

– Results in the desired level of accuracy

– Properly represents the reservoir geology, and

– Has the lowest computer memory and time requirements to solve the problem.

Effects of Grid Block Sizes on Simulation Results

• FD solution approaches PDE solution as x approaches 0

• Use small blocks where convergent flow• Use small blocks along displacement

fronts

Common Rules for Constructing a Grid

• Logarithmic spacing in cylindrical grids.

• Adjacent blocks increase in length by no more than factor of 3.

• No more than 10 to 20% of the total pressure drop should be between any two adjacent grid blocks.

• Large changes in elevation or thickness should be distributed over multiple grid blocks.

Common Rules for Constructing a Grid

• Reservoir flow units should, in general, be separated by grid block boundaries.

• Vertical discretization should be fine enough for accurate accounting of gas percolation and migration and/or gravity over-ride or under-ride.

• If in doubt, halve the grid blocks (double the number of blocks) in one or more dimensions.

Effect of Grid Block Sizes on a Linear Buckley-Leverett Displacement Simulation With a Sharp

Displacement Front and Mobility Ratio of 50.

Pore Volumes of Water Injected

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

Wat

er/O

il R

ati

o

0.001

0.01

0.1

1

10

100

1000

DX=180

DX=22.5

1 10 161112131415 22212019181723456789 2726252423

1

10

16

1112131415

222120191817

23456789

2726252423

282930

40

393837363534333231

47

46

45

44434241

48

47

46

45

48

1215

1263

1107

3

1220

0

13000

12800

12700

1

10

16

1112131415

222120191817

2

3456789

2726252423

282930

40

393837363534333231

44434241

1 10 161112131415 22212019181723456789 2726252423

Y

X

1

7

2

109

8

3

4

5

6

OW

C

OW

C

OW

C

Block V

Block VI

Legendexisting production wells

true fault tracesfault traces in simulation model

Structure Map and Reservoir Simulation Grid

Simulation Model Horizontal Permeability Distribution for Simulation Layer 1

hist33k - X-Permeability (md)

12/01/1957 00:00:00 0.0000 days

700

600

500

400

300

200

100

0

675 : 5 1394 : 6 1449 : 6 11101 : 8 1

1063 : 11 1674 : 3 1 510 : 4 1

506 : 8 1677 : 6 1 1222 : 1 1 1006 : 3 11140 : 1 1 1155 : 2 1

671 : 2 1 973 : 4 1516 : 5 1422 : 7 1453 : 3 1465 : 4 1

1004 : 6 1196 : 1 1

571 : 5 1 631 : 4 1619 : 4 1 1254 : 1 1

987 : 1 1

297 : 3 1

Simplification of Reservoir Geometry

• Example situations

• Using symmetry to simplify the grid

• Using pseudofunctions

• Checking validity of assumptions

Using Symmetry to Simplify the Grid

• 1/4th of the drainage area containing a well with a hydraulic fracture can be simulated

• Repeated 5-spot water flood pattern can be modeled using 1/8th of the pattern

• Any time a well is centered in a homogeneous drainage area and forces on either side of the lines of symmetry are identical.

Using Pseudofunction to Model 3D Systems With 2D Model

• Pseudo-relative-permeability and pseudo-capillary-pressure functions can be used to simplify simulations of displacement process in layered reservoirs with no crossflow

• Dynamic pseudo-functions can be generated from cross-sectional simulations.

Checking Validity of Assumptions Made in Simplifications

• Any time a simplification is made, it should be validated by run(s) without simplification.

Representing Wells in Simulation

• Well representation should

– Account for near well conditions

– Allow the necessary degree of well control

Well Constant Equations

Pwell

Pcell

cellwellr pp

kbWCq

Well Constant Equations

• The general formula presented by Peaceman for the well constant of a well located in the center of a rectangular grid block is given by

wao rrln

kh00708.0WC

Well Constant Equations

• The apparent wellbore radius, rwa, includes the effect of the skin factor due to damage, stimulation, partial penetration, and wellbore inclination. The equation for rwa is

rwa = rw e-s

Spacing of Wells in the Simulation Grid

• Spacing dependent on objectives, accuracy and flow mechanism

• Rule of thumb is 3 to 5 blocks between wells

• In simulation of waterflood, may need 10 or more

• Interference tests need finer grid spacings

Spacing of Wells in the Simulation Grid

• In early stages of study, perform a grid sensitivity study and select the most coarse grid

• As study progresses, refine grid appropriately

Well Rate and Pressure Specifications and Constraints• The well constraints used in simulations

should represent actual field operating conditions as closely as possible.

• Most simulators will allow specification of production targets and constraints enabling the rate and minimum flowing pressure to be specified.

• The simulator will automatically switch from rate-controlled production to pressure-controlled production.

Timestep Schedule

• The timestep schedule is the definition of how we divide, or discretize, time in order to solve the differential equations numerically

• Although we use reservoir and well properties in designing the timestep schedule, the timestep schedule is independent of the reservoir and well properties.

Scheduling Changes in Production Rates and Other Dynamic Data

• Schedule of times to honor changes in production and injection rates

Rate

Time

Scheduling of Individual Timesteps

Rate

Time

Effects of Time Step Size on Simulation Results

• Several factors must be considered when selecting time step sizes for a simulation. These factors include:

– Data requirements,

– Numerical stability and

– Time-truncation errors.

Common Rules for Time Step Size Control

• Recommended procedure:

– Start with small time step sizes after significant rate changes

– Use large time step size multipliers to build time step sizes quickly

– Use p, S and t limits to restrict time step sizes to reasonable levels

Simulator Control Data

• Numerical solution parameters

• Output control data

• Run control

Output Control Data

• Moderate to large simulations require judicious specification of desired output. Output files sizes can quickly become unmanageable.

• Type of output desired• Frequency of node output• Frequency of map output

Run Control

Rate

Time

C

A

B

Model InitializationS

ub

sea

Ele

vati

on

Pressure

Pi

OWC

Datum

GOCPcgo = 0

Pcgo = Pg - Po

Pw = f(w)

Pcow = Po - Pw

Pcow = 0

Pg = f(g)

Po = f(o)

Model Initialization

Pcow

Sw0 1

Pcgo

Sg0 1

Peow

Pcgo

PcowGOC

OWC

Pc

Su

bse

a el

evat

ion

GOC

OWC

01 Sg

Sw0 1

Complete 3D View of the Simulation Model (Mid-Point Elevations of Simulation

Gridblock, ft Sub-Sea)hist33k - Midpt Elevations (ft ss)

12/01/1957 00:00:00 0.0000 days

-11500

-11600

-11700

-11800

-11900

-12000

-12100

-12200

-12300

-12400

-12500

465 : 3 3465 : 4 1

671 : 2 1

453 : 2 3453 : 3 1

619 : 2 5619 : 3 3619 : 4 1

96s : 1 13

677 : 8 15

1140 : 1 1

677 : 9 13

196 : 8 11

677 : 7 9

1130 : 3 3

196 : 3 5196 : 1 1

677 : 6 1

506s : 1 9

506 : 5 15506 : 6 13506 : 7 11

506s : 4 3

506 : 1 9

1101 : 1 9506 : 4 3506 : 8 1

1101 : 8 1

674 : 4 9

1222 : 1 1

571 : 1 9

674s : 1 9

571 : 3 5

449 : 2 5674 : 3 1

571 : 5 1 1155 : 3 9

516 : 1 9

449 : 6 1

1063 : 4 17516 : 3 5

1155 : 2 1

516 : 5 1

1063 : 1 9

675s : 1 17

1063 : 9 5

675s : 2 15

516s : 2 5

1063 : 11 1

1004 : 4 5 510 : 7 15510 : 8 13

1004 : 6 1

995 : 1 171215 : 1 9

510 : 9 11510 : 5 9

297 : 3 1394 : 2 9

510 : 1 5

510 : 4 1

1127 : 4 9394 : 5 3394 : 6 1

631 : 2 5

973 : 2 5

631 : 4 1

1006 : 3 1973 : 4 1

1102 : 1 51102 : 2 5422 : 1 91254 : 1 1

422 : 7 1

987 : 1 1

Simulation Model Initial Water Saturation Distribution for Layer 1

hist33k - Water Saturation

12/01/1957 00:00:00 0.0000 days

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

675 : 5 1394 : 6 1449 : 6 11101 : 8 1

1063 : 11 1674 : 3 1 510 : 4 1

506 : 8 1677 : 6 1 1222 : 1 1 1006 : 3 11140 : 1 1 1155 : 2 1

671 : 2 1 973 : 4 1516 : 5 1422 : 7 1453 : 3 1465 : 4 1

1004 : 6 1196 : 1 1

571 : 5 1 631 : 4 1619 : 4 1 1254 : 1 1

987 : 1 1

297 : 3 1

Reviewing Simulation Output to Ensure Valid Results

• We recommend using the following procedure to systematically review simulation output to ensure that results are valid.

• The full review will normally be required following major changes in the model. Some items should routinely be reviewed.

Review Warning Messages

• Review output for warning or error messages printed out by the simulator

– Fluid property, relative permeability, and capillary pressure table trend checking

– Grid blocks with zero permeability or porosity

– Wells located in inactive grid blocks– Other simulator specific warning/

error messages

Review Input Data Printout

• Review output to ensure that the simulator is correctly reading the input data.

– Rock properties

– Fluid properties

– Multiphase properties

Review Initialization

• Review reservoir initialization/equilibration as calculated by the model

– Compare original fluids in place in the model to values estimated using volumetrics

– Pressure

– Saturation

– Position of gas-oil, oil-water, gas-water contacts

Review Numerical Performance Statistics

• Material balance error

• Outer iterations

• Inner iterations

• Cutbacks

• Maximum pressure and saturation changes

• Is the model oscillating?

Review Production Statistics

• Ensure that wells are being operated in the desired manner

• Check – That each well is in the desired location– That correct algebraic sign is used for

production and injection– For wells changing from constant rate to

constant pressure

Review Production Statistics

• Check – For wells which have been shut in due to

excessive gas or water production, GOR or WOR

– Total production from multiply completed wells

– For wells drilled or completed by an automatic well management scheme

DYNAMIC MODEL

Well/Facilities Model

Near Wellbore Performance Models

Upscaled Reservoir

Model

Preliminary Dynamic

Model

Calibrated Dynamic

Model

Projected Reservoir

Performance

Field Economic

Model

Optimized Reservoir

Development Plan

Integrated Reservoir Study

References

1. Mattax, C. C., and Dalton, R. L.: Reservoir Simulation, SPE Monograph Series No. 13, 1990.

2. Aziz, K., and Settari, A.: Petroleum Reservoir Simulation, Applied Science, 1979.

3. Odeh, A. S.: "Reservoir Simulation...What is it?" JPT (Nov. 1969) 1383-1388.

4. Coats, K. H.: "Use and Misuse of Reservoir Simulation Models," JPT (Nov. 1969) 1391-1398.

References

5. Coats, K. H.: "Reservoir Simulation: State of the Art," JPT, (Aug. 1982) 1633-1642.

6. Satter, A., Frizzell, D. F., and Varnon, J. E.: "The Role of Mini-Simulation in Reservoir Management," paper presented at the Indonesian Petroleum Association Nineteenth Annual Convention, Oct. 1991

7. Kyte, J. R., and Berry, D. W.: "New Pseudo Functions to Control Numerical Dispersion," SPEJ (Aug. 1975) 269-76.