IC Fault Model
PUNQ-S3 Test Case
The PUNQ-S3 case has been taken from a reservoir engineering study on a real field performed Elf Exploration Production. It was qualified as a small-size industrial reservoir engineering model. The model contains 19x28x5 grid blocks, of which 1761 blocks are active. The top structure map of the field shows that the field is bounded to the east and south by a fault, and links to the north and west to a fairly strong aquifer. A small gas cap is located in the center of the dome shaped structure. The field initially contains 6 production wells located around the Gas Oil contact. Due to the strong aquifer, no injection wells are present. The geometry of the field has been modeled using corner-point geometry.
The porosity/permeability fields have been regenerated in order to have more control over the underlying geological / geostatistical model. A corresponding geological description has been developed.
A geostatistical model based on Gaussian Random Fields has been used to generate the porosity / permeability fields. Geostatistical parameters, such as means and variograms have been chosen to be as much as possible consistent with the geological model. Through the use of collocated co-simulation, the porosity and permeability fields have been correlated statistically. To generate the fields, the Fortran program sgcosim from Stanford University has been used. It is part of an extension to the GSLIB software library (Deutsch & Journel, 1992). This has resulted in correlated fields for porosity and horizontal + vertical permeability in each of the five layers.
The reservoir engineering model has been completed with the PVT and aquifer data from the original model, and with power law relative permeability functions. There is no capillary pressure in the model. The production scheduling has been inspired by the original model, i.e. a first year of extended well testing, followed by a three year shut-in period, before field production commences. The well testing year consists of four three-monthly production periods, each having its own production rate. During field production, two weeks of each year are used for each well to do a shut-in test to collect shut-in pressure data. The wells operate under production constraint. After falling below a limiting bottom hole pressure, they will switch to BHP-constraint. Using the thus completed reservoir engineering model, a synthetic history is generated using the reservoir simulator ECLIPSE. The total simulation period is 16.5 years. Pressure, water-cut and gas-oil ratio curves have been generated for each of the wells. The total oil recovery after the simulation period is 3.87 106 Sm3.
Gaussian noise was added to the well porosities / permeabilities and to the synthetic production data. The standard deviation on poro / perm values was set to 15 %. For the production data the Gaussian noise was correlated in time to mimic the more systematic character of errors in such data. The noise level on the shut-in pressures was 3 times smaller than on the flowing pressure, respectively 1 bar and 3 bar, to reflect the more accurate shut-in pressures. The noise level on the GOR was set at 10 % before gas breakthrough and 25 % after gas breakthrough, reflecting the difference between the solution and the free gas situation. Similarly for WCT, 2 % before and 5 % after water breakthrough was used.
Each of the partners in the project was given the noisy well porosities / permeabilities and synthetic production history of the first 8 years. Note that this history includes 1 year of well testing, 3 years of field shut-in, and covers 4 years of actual field production. The synthetic production data consisted of the BHP, WCT and GOR for each of the 6 wells. Within the history period, two wells show gas breakthrough and one well shows the onset of water breakthrough. All partners were asked to forecast the total oil production after 16.5 years including uncertainty estimates, using the Bayesian formalism. Note that none of the partners were given the exact porosity / permeability grids. Only the geological description was distributed. Each of the partners used his own workflow to infer these grids. In a second stage, 5 incremental wells were defined. For the truth case, the extra wells resulted in an incremental recovery of 1.46 106 Sm3. The partners were again asked to forecast the incremental recovery including uncertainty.
The PUNQ-S3 case is based on a real field example provided by Elf Exploration Production.
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