`GPMAINT`

Recognised by the OPM Flow parserSCHEDULE

The GPMAINT keyword defines the groups under pressure maintenance control, the associated flow rate and pressure targets, and fluid in-place regions associated with pressure maintenance, as well as various pressure maintenance controls. GPMAINT allows for various regions, as defined by the FIPNUM or FIP keywords in the REGIONS section, to have their average reservoir pressure maintained at a specified value.

Notes:

The keyword is followed by any number of records with each record terminated by a “/” and the keyword should be terminated by a “/”.

The GPMAINT keyword utilizes control theory305 John Doyle, Bruce Francis, Allen Tannenbaum, Feedback Control Theory, Macmillan Publishing Co., 1990., 306 Karl J. Åström; Richard M. Murray (2008). Feedback Systems: An Introduction for Scientists and Engineers. Princeton University Press. ISBN 978-0-691-13576-2., 307 Andrei, Neculai (2005)., Modern Control Theory – A Historical Perspective, Research Institute for Informatics, Center for Advanced Modeling and Optimization,8-10, Averescu Avenue, Bucharest 1, Romania.and 308 Sontag, Eduardo (1998). Mathematical Control Theory: Deterministic Finite Dimensional Systems. Second Edition, Springer. ISBN 978-0-387-98489-6.to calculate the required injection and production rates to ensure some stability in the behavior of the average hydrocarbon pore volume reservoir pressure for a given region and the injection rates over time. For example, if the group’s flow control (GRPCNTL) is set to one of the in situ reservoir volume injection rates (GINJ, OINJ or WINJ), say Q, then the group’s flow injection rates for each time step is calculated by:

John Doyle, Bruce Francis, Allen Tannenbaum, Feedback Control Theory, Macmillan Publishing Co., 1990.

Karl J. Åström; Richard M. Murray (2008). Feedback Systems: An Introduction for Scientists and Engineers. Princeton University Press. ISBN 978-0-691-13576-2.

Andrei, Neculai (2005)., Modern Control Theory – A Historical Perspective, Research Institute for Informatics, Center for Advanced Modeling and Optimization,8-10, Averescu Avenue, Bucharest 1, Romania.

Sontag, Eduardo (1998). Mathematical Control Theory: Deterministic Finite Dimensional Systems. Second Edition, Springer. ISBN 978-0-387-98489-6.

[Q~=~Q_i``+`` %alpha `` left( left(P_TARGET``-``P_{i-1} right)``+`` sum from{i=1} to{i-1} {left(P_TARGET``-``P_{i-1} right) times %DELTA t_i} over %beta right )]

(12.26)

Where:

P TARGET= the regions average hydrocarbon pore volume weighted reservoir

pressure target, the TARGET parameter in Table 12.41.

Pi-1= the resulting average hydrocarbon pore volume weighted reservoir

pressure for the region from the preceding completed time step.

Q=the new in situ reservoir volume rate.

Qi= the initial in situ reservoir volume rate at the time the keyword was

activated in the input. Subsequent GPMAINT keywords will reset Qi.

α=the proportionality constant used to control the flow rates, the ALPHA

parameter in Table 12.41.

β= the time interval parameter used to control the flow rates, the BETA

parameter in Table 12.41.

The [sum from{i=1} to{i-1} left(P_TARGET``-``P_{i-1} right) times %DELTA t_i]term in equation term in equation (12.26)is the cumulative sum of the average hydrocarbon pore volume weighted reservoir pressure error for the region, times the time step length, from when the last GPMAINT keyword was entered, up to the preceding completed time step.

The objective of equation (12.26)is to stabilize the injection/production rates for the group for when there are changes to the average hydrocarbon pore volume weighted reservoir pressure target set by the initial and subsequent GPMAINT keywords, or by any group constraints applied afterwards. In addition, if the pressure error is small [left(P_TARGET``-``P_{i-1} right)]then the equation should result in approximately the same rates as the previous time step, if the then the equation should result in approximately the same rates as the previous time step, if the GPMAINT has been previously entered.

However, if the first time the keyword is entered coincides with the start of injection, then Qi in equation (12.26)by definition will be zero, and the injection rate will start from zero and increase as calculated by the equation. The ALPHA and BETA parameters in Table 12.41can be used to control how the rate is built up to meet the desired average hydrocarbon pore volume weighted reservoir pressure target.

Records: One or more records, each terminated by /
Items per record: 7

Parameters

No.	Name	Description	Type	Dimension	Field	Metric	Lab	Default
1	`GROUP` manual: `GRPNAME`	A character string of up to eight characters in length that defines the group name for which the group’s associated FIPNUM region will have a targeted average reservoir pressure maintained. The group named FIELD is the top most group and can also be used to set pressure target for the whole field. Note that the group hierarchy should be defined by the GRUPTREE keyword when there is more than one level of groups, otherwise all the groups will sit directly under the FIELD group in the group tree hierarchy.	STRING					None
2	`FLOW_TARGET` manual: `GRPCNTL`	A defined character string of length four, that sets the production or injection control for the group, used to maintain the average pressure for the FIPNUM region. GRPCNTL should be set to one of the following character strings: NONE: the group will no longer maintain the average reservoir pressure for the FIPNUM region by adjusting production and injection rates. GINJ: GRPNAME’s gas in situ reservoir volume injection rate (RESV) will be adjusted in order to maintain FIPNUM’s average reservoir pressure. GINS: GRPNAME’s gas surface rate (GRAT) will be used to maintain FIPNUM’s average reservoir pressure. OINJ: GRPNAME’s oil in situ reservoir volume injection rate (RESV) will be adjusted in order to maintain FIPNUM’s average reservoir pressure. OINS: GRPNAME’s oil surface rate (ORAT) will be used to maintain FIPNUM’s average reservoir pressure. PROD: GRPNAME’s total in situ reservoir volume production rate (RESV) will be adjusted in order to maintain FIPNUM’s average reservoir pressure. Note that group cannot be under prioritization group control, as per the GCONPRI keyword in the SCHEDULE section, with this option. WINJ: GRPNAME’s water in situ reservoir volume injection rate (RESV) will be adjusted in order to maintain FIPNUM’s average reservoir pressure WINS: GRPNAME’s water surface rate (WRAT) will be used to maintain FIPNUM’s average reservoir pressure.	STRING					None
3	`REGION`		INT
4	`FIP_FAMILY` manual: `FIPNAME`	A character string of up to five characters in length, defining the fluid in-place’s name, as defined by the FIP keyword in the REGIONS section. For example, if the FIP keyword has been used to define a FIP group or family, named FIPBLK-A, then FIPNAME would be set to BLK-A. The default value of 1* means that FIPNUM on this keyword applies to the standard FIPNUM array and not to the FIP defined group regions.	STRING					1*
5	`PRESSURE_TARGET`		DOUBLE	Pressure	psia	barsa	atma
6	`PROP_CONSTANT` manual: `ALPHA`	A real positive value that defines the proportionality constant used to control the flow rates in order to maintain/reach the TARGET average hydrocarbon pore volume pressure for the region. See equation (12.26). Larger values of ALPHA accelerate the time for the region’s pressure to satisfy the required target pressure (TARGET). However, ALPHA values that are too large may cause the region’s pressure to oscillate. Thus, the value of ALPHA should be a value that gives the expected steady state flow rate (TARGET) of the group divided by a reasonable transient pressure error.	DOUBLE	ReservoirVolume/Time*Pressure	Liquid: stb/d/psi Gas: Mscf/d/psi RESV: rb/d/psi	Liquid: sm3/day/bars Gas: sm3/day/bars RESV: rm3/day/bars	Liquid: scc/hour/atm Gas: scc/hour/atm RESV: rcc/hour/atm	None
7	`TIME_CONSTANT` manual: `BETA`	A real positive value that defines the time interval used to control the flow rates in order to maintain the TARGET average hydrocarbon pore volume pressure for the region. See equation (12.26). Larger values of BETA reduce the tendency for the regional pressure to oscillate, but consequently decrease the rate at which the pressure reaches its target value. This is because the pressure error is measured at the end of the previous time step, resulting in a “delay” in the response. Also, the larger the time steps the greater the propensity for the pressure to oscillate for given ALPHA and BETA. As a guide BETA should be set to a value that is at least as large as the maximum time step size (see the TUNING keyword in the SCHEDULE section and section 2.2Running OPM Flow 2023-04 From The Command Linefor setting the maximum time step size).	DOUBLE	Time	day	day	day	1*

Example

The first example uses the gas surface rate to maintain the fields’ average hydrocarbon pore volume pressure at 225 barsa, with the ALPHA and BETA parameters set to 40.0 and 70.0 respectively.
--
-- GROUP PRESSURE MAINTENANCE TARGETS AND CONTROLS
--
-- GRUP CNTL FIPNUM FIP PRESS ALPHA BETA
-- NAME MODE REGION FIPNAME TARGET CONST CONST
GPMAINT
FIELD GINS 0 1* 225 40.0 70.0 /
/
The second example uses group’s BLK-A gas surface rate to maintain the average hydrocarbon pore volume pressure at 200 barsa for FIPNUM regions one to four, with the ALPHA and BETA parameters set to 40.0 and 70.0 respectively.
--
-- GROUP PRESSURE MAINTENANCE TARGETS AND CONTROLS
--
-- GRUP CNTL FIPNUM FIP PRESS ALPHA BETA
-- NAME MODE REGION FIPNAME TARGET CONST CONST
GPMAINT
BLK-A GINS 1 1* 200 40.0 70.0 /
BLK-A GINS 2 1* 200 40.0 70.0 /
BLK-A GINS 3 1* 200 40.0 70.0 /
BLK-A GINS 4 1* 200 40.0 70.0 /
BLK-B WINJ 1 FLT-B 215 30.0 65.0 /
BLK-B WINJ 2 FLT-B 215 30.0 65.0 /
BLK-B WINJ 3 FLT-B 215 30.0 65.0 /
BLK-B WINJ 4 FLT-B 215 30.0 65.0 /
/
For group BLK-B, water in situ reservoir volume injection rate (RESV) is used to maintain FIP group/family FLT-B’s average reservoir pressure at 215 barsa for FIPFLT-B regions one to four. Here the ALPHA and BETA parameters set to 30.0 and 65.0 respectively.
| 0 |
|---|
| 0 |
|---|
| [Q~=~Q_i``+`` %alpha `` left( left(P_TARGET``-``P_{i-1} right)``+`` sum from{i=1} to{i-1} {left(P_TARGET``-``P_{i-1} right) times %DELTA t_i}  over %beta right )] | (12.26) |
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------|

Manual source: parts/chapters/subsections/12.3/GPMAINT.fodt