SPE1CASE2_Radial_SinglePhase.DATA

-- This reservoir simulation deck is made available under the Open Database
-- License: http://opendatacommons.org/licenses/odbl/1.0/. Any rights in
-- individual contents of the database are licensed under the Database Contents
-- License: http://opendatacommons.org/licenses/dbcl/1.0/

-- Copyright (C) 2020 Equinor

-- This simulation is somewhat based on the data given in 
-- 'Comparison of Solutions to a Three-Dimensional
-- Black-Oil Reservoir Simulation Problem' by Aziz S. Odeh,
-- Journal of Petroleum Technology, January 1981

-- NOTE: THIS IS A MODIFIED SINGLE-PHASE (OIL) VERSION OF SPE1CASE2 WITH RADIAL GRID 
-- KEYWORDS RADIAl, COORDSYS, COMP, INRAD, DRV, DTHETAV, PERMR, PERMTHT ARE ADDED 
-- THIS MODEL HAS ONE OIL PRODUCCER WELL IN THE CENTER OF THE GRID.


---------------------------------------------------------------------------
------------------------ SPE1 - CASE 2 ------------------------------------
---------------------------------------------------------------------------

RUNSPEC
-- -------------------------------------------------------------------------

TITLE
   SPE1 - CASE 2
   
-- r theta z
DIMENS
   10 10 3 /
   
RADIAL
   
-- The number of equilibration regions is inferred from the EQLDIMS
-- keyword.
EQLDIMS
/

-- The number of PVTW tables is inferred from the TABDIMS keyword;
-- when no data is included in the keyword the default values are used.
TABDIMS
/


OIL
GAS
WATER


FIELD

START
   16 'JUN' 1988 /

WELLDIMS
-- Item 1: maximum number of wells in the model
-- 	   - there are one wells in the problem; oil producer
-- Item 2: maximum number of grid blocks connected to any one well
-- 	   - must be the same as nz, we have a full-penetrated vertical well
-- Item 3: maximum number of groups in the model
-- 	   - we are dealing with only one 'group'
-- Item 4: maximum number of wells in any one group
-- 	   - there must be one well in a group as there are one well in total
   1 3 1 1 /

UNIFIN
UNIFOUT

GRID

COORDSYS
1 3 COMP /

-- The INIT keyword is used to request an .INIT file. The .INIT file
-- is written before the simulation actually starts, and contains grid
-- properties and saturation tables as inferred from the input
-- deck. There are no other keywords which can be used to configure
-- exactly what is written to the .INIT file.
INIT

--  SPECIFY INNER RADIUS OF 1ST GRID BLOCK IN THE RADIAL DIRECTION
INRAD
0.25/


-- -------------------------------------------------------------------------
NOECHO

--  SPECIFY GRID BLOCK DIMENSIONS IN THE R DIRECTION
DRV 
   1.75     2.32     5.01    10.84    23.39
   50.55   109.21   235.92   509.68  1101.08  /
DTHETAV
-- There are in total 300 cells with 36 degrees in theta-direction	
	10*36 /
DZ
-- The layers are 20, 30 and 50 ft thick, in each layer there are 100 cells
	100*20 100*30 100*50 /

TOPS
-- The depth of the top of each grid block
	100*8325 /

PORO
-- Constant porosity of 0.3 throughout all 300 grid cells
   	300*0.3 /

PERMR
-- The layers have perm. 500mD, 50mD and 200mD, respectively.
	100*500 100*50 100*200 /

PERMTHT
-- Equal to PERMR
	100*500 100*50 100*200 /

PERMZ
-- Cannot find perm. in z-direction in Odeh's paper
-- For the time being, we will assume PERMZ equal to PERMX and PERMY:
	100*500 100*50 100*200 /
ECHO

PROPS
-- -------------------------------------------------------------------------

PVTW
-- Item 1: pressure reference (psia)
-- Item 2: water FVF (rb per bbl or rb per stb)
-- Item 3: water compressibility (psi^{-1})
-- Item 4: water viscosity (cp)
-- Item 5: water 'viscosibility' (psi^{-1})

-- Using values from Norne:
-- In METRIC units:
-- 	277.0 1.038 4.67E-5 0.318 0.0 /
-- In FIELD units:
    	4017.55 1.038 3.22E-6 0.318 0.0 /

ROCK
-- Item 1: reference pressure (psia)
-- Item 2: rock compressibility (psi^{-1})

-- Using values from table 1 in Odeh:
	14.7 3E-6 /

SWOF
-- Column 1: water saturation
--   	     - this has been set to (almost) equally spaced values from 0.12 to 1
-- Column 2: water relative permeability
--   	     - generated from the Corey-type approx. formula
--	       the coeffisient is set to 10e-5, S_{orw}=0 and S_{wi}=0.12
-- Column 3: oil relative permeability when only oil and water are present
--	     - we will use the same values as in column 3 in SGOF.
-- 	       This is not really correct, but since only the first 
--	       two values are of importance, this does not really matter
-- Column 4: corresponding water-oil capillary pressure (psi) 

0.12	0    		 	1	0
0.18	4.64876033057851E-008	1	0
0.24	0.000000186		0.997	0
0.3	4.18388429752066E-007	0.98	0
0.36	7.43801652892562E-007	0.7	0
0.42	1.16219008264463E-006	0.35	0
0.48	1.67355371900826E-006	0.2	0
0.54	2.27789256198347E-006	0.09	0
0.6	2.97520661157025E-006	0.021	0
0.66	3.7654958677686E-006	0.01	0
0.72	4.64876033057851E-006	0.001	0
0.78	0.000005625		0.0001	0
0.84	6.69421487603306E-006	0	0
0.91	8.05914256198347E-006	0	0
1	0.00001			0	0 /


SGOF
-- Column 1: gas saturation
-- Column 2: gas relative permeability
-- Column 3: oil relative permeability when oil, gas and connate water are present
-- Column 4: oil-gas capillary pressure (psi)
-- 	     - stated to be zero in Odeh's paper

-- Values in column 1-3 are taken from table 3 in Odeh's paper:
0	0	1	0
0.001	0	1	0
0.02	0	0.997	0
0.05	0.005	0.980	0
0.12	0.025	0.700	0
0.2	0.075	0.350	0
0.25	0.125	0.200	0
0.3	0.190	0.090	0
0.4	0.410	0.021	0
0.45	0.60	0.010	0
0.5	0.72	0.001	0
0.6	0.87	0.0001	0
0.7	0.94	0.000	0
0.85	0.98	0.000	0 
0.88	0.984	0.000	0 /
--1.00	1.0	0.000	0 /
-- Warning from Eclipse: first sat. value in SWOF + last sat. value in SGOF
-- 	   		 must not be greater than 1, but Eclipse still runs
-- Flow needs the sum to be excactly 1 so I added a row with gas sat. =  0.88
-- The corresponding krg value was estimated by assuming linear rel. between
-- gas sat. and krw. between gas sat. 0.85 and 1.00 (the last two values given)

DENSITY
-- Density (lb per ft³) at surface cond. of 
-- oil, water and gas, respectively (in that order)

-- Using values from Norne:
-- In METRIC units:
--      859.5 1033.0 0.854 /
-- In FIELD units:
      	53.66 64.49 0.0533 /

PVDG
-- Column 1: gas phase pressure (psia)
-- Column 2: gas formation volume factor (rb per Mscf)
-- 	     - in Odeh's paper the units are said to be given in rb per bbl, 
-- 	       but this is assumed to be a mistake: FVF-values in Odeh's paper 
--	       are given in rb per scf, not rb per bbl. This will be in 
--	       agreement with conventions
-- Column 3: gas viscosity (cP)

-- Using values from lower right table in Odeh's table 2:
14.700	166.666	0.008000
264.70	12.0930	0.009600
514.70	6.27400	0.011200
1014.7	3.19700	0.014000
2014.7	1.61400	0.018900
2514.7	1.29400	0.020800
3014.7	1.08000	0.022800
4014.7	0.81100	0.026800
5014.7	0.64900	0.030900
9014.7	0.38600	0.047000 /

PVDO
-- Column 1: oil phase pressure (psia)
-- Column 3: oil FVF for saturated oil (rb per stb)
-- Column 4: oil viscosity for saturated oil (cP)

-- Use values from top left table in Odeh's table 2:
14.700	1.012	1.16
264.70	1.011	1.16
514.70	1.010	1.16
1014.7	1.009	1.16
2014.7	1.008	1.16
2514.7	1.007	1.16
3014.7	1.006	1.16
4014.7	1.005	1.16
5014.7	1.004	1.16
9014.7	1.003	1.16 /	
-- In order to fulfill this requirement, values for oil FVF and viscosity
-- at 9014.7psia and GOR=1.618 for undersaturated oil have been approximated:
-- It has been assumed that there is a linear relation between the GOR
-- and the FVF when keeping the pressure constant at 9014.7psia.
-- From Odeh we know that (at 9014.7psia) the FVF is 2.357 at GOR=2.984
-- for saturated oil and that the FVF is 1.579 at GOR=1.27 for undersaturated oil,
-- so it is possible to use the assumption described above. 
-- An equivalent approximation for the viscosity has been used.
/


SOLUTION
-- -------------------------------------------------------------------------

EQUIL
-- Item 1: datum depth (ft)
-- Item 2: pressure at datum depth (psia)
-- 	   - Odeh's table 1 says that initial reservoir pressure is 
-- 	     4800 psi at 8400ft, which explains choice of item 1 and 2
-- Item 3: depth of water-oil contact (ft)
-- 	   - chosen to be directly under the reservoir
-- Item 4: oil-water capillary pressure at the water oil contact (psi)
-- 	   - given to be 0 in Odeh's paper
-- Item 5: depth of gas-oil contact (ft)
-- 	   - chosen to be directly above the reservoir
-- Item 6: gas-oil capillary pressure at gas-oil contact (psi)
-- 	   - given to be 0 in Odeh's paper

-- Item #: 1 2    3    4 5    6 7 8 9
	8400 4800 9325 0 8325 0 /

SUMMARY
-- -------------------------------------------------------------------------	 

-- 1a) Oil rate vs time
FOPR
-- Field Oil Production Rate

-- 1b) GOR vs time
WGOR
-- Well Gas-Oil Ratio
   'PROD'
/
-- Using FGOR instead of WGOR:PROD results in the same graph
FGOR

-- 2a) Pressures of the cell where the injector and producer are located
BPR
1  1  1 /
1  1  2 /
1  1  3 /
/

-- 2b) Gas saturation at grid points given in Odeh's paper
BGSAT
1  1  1 /
1  1  2 /
1  1  3 /
10 1  1 /
10 1  2 /
10 1  3 /
10 10 1 /
10 10 2 /
10 10 3 /
/

-- In order to compare Eclipse with Flow:
WBHP
  'PROD'
/
WGIR
  'PROD'
/
WGIT
  'PROD'
/
WGPR
  'PROD'
/
WGPT
  'PROD'
/
WOIR
  'PROD'
/
WOIT
  'PROD'
/
WOPR
  'PROD'
/
WOPT
  'PROD'
/
WWIR
  'PROD'
/
WWIT
  'PROD'
/
WWPR
  'PROD'
/
WWPT
  'PROD'
/
SCHEDULE
-- -------------------------------------------------------------------------
RPTSCHED
	'PRES' 'SOIL' 'WELLS' /

RPTRST
	'BASIC=1' /


-- If no resolution (i.e. case 1), the two following lines must be added:
--DRSDT
-- 0 /
-- Since this is Case 2, the two lines above have been commented out.
-- if DRSDT is set to 0, GOR cannot rise and free gas does not 
-- dissolve in undersaturated oil -> constant bubble point pressure

WELSPECS
-- Item #: 1	 2	3	4	5	 6
	'PROD'	'G1'	1	1	8400	'OIL' /
/
-- Coordinates in item 3-4 are retrieved from Odeh's figure 1 and 2
-- Note that the depth at the midpoint of the well grid blocks
-- has been used as reference depth for bottom hole pressure in item 5

COMPDAT
-- Item #: 1	2	3	4	5	6	7	8	9
	'PROD'	1	1	1	3	'OPEN'	1*	1*	0.5 /
/
-- Coordinates in item 2-5 are retreived from Odeh's figure 1 and 2 
-- Item 9 is the well bore internal diameter, 
-- the radius is given to be 0.25ft in Odeh's paper


WCONPROD
-- Item #:1	2      3     4	   5  9
	'PROD' 'OPEN' 'ORAT' 20000 4* 1000 /
/
-- It is stated in Odeh's paper that the maximum oil prod. rate
-- is 20 000stb per day which explains the choice of value in item 4.
-- The items > 4 are defaulted with the exception of item  9,
-- the BHP lower limit, which is given to be 1000psia in Odeh's paper


TSTEP
--Advance the simulater once a month for ONE year:
31 28 31 30 31 30 31 31 30 31 30 31 
 /

END