The Influence of Grid Orientation Modeling of NahrUmr Reservoir / Subba Oil Field
Assist. Prof. Dr. Sameera Mohammed. Hamd- Allah RaadShakorQader
Teacher Petroleum Engineering Department
Petroleum Engineering Department /College of Engineering College of Engineering
University of Baghdad University of Baghdad Iraq Iraq
ABSTRACT
Reservoir simulation models are utilized by oil and gas companies with a purpose to develop fields. Expansions and improvements in simulation software have reduced the time to develop a model. Simulating the reservoir aims to realize fluid flow, physical, and chemical procedures happening in a hydrocarbon reservoir adequately well for the reason of improving hydrocarbon recovery under various working stipulations. Grid orientation effects are complicated problem in numerical reservoir simulation. These influences come from the use of numerical utilization mechanism to equations characterizing physically unsteady displacement procedures. These effects occur in a variety simulations of unfavorable and also favorable mobility ratio displacements. Different values of recovery factors were obtained when the orientation of the grids had been changed.
INTRODUCTION
Grid Orientation Effect (GOE) is a serious problem cannot be ignored in numerical reservoir simulation. This effect also is observed even in simple reservoir geometry such as radial displacement. When the computational grids are rotated we obtain different results in oil recovery for parallel and diagonal grids. If the mobility ratio of the displaced fluid is less than the mobility ratio of the displacing fluid (unfavorable) observing this trouble will expand and also watching this obstacle will develop and likewise when the transition zone is short. In this paper to study the influence ofgrid orientation, Subba oil field / NahrUmr reservoir was selected which is one of the most important three major oil fields in Thi-Qar governorate in the south of Iraq. The field is located in the Southeastern of Nasiriya city.
LITERATURE REVIEW
Many papers and methods were proposed to study grid orientation influence. In spite of that there is not any common method for treating this problem, but there were many trials to reduce the effect.
Todd, ODell, , and Hirasakiin 1972 presented the usage of two – point upstream mobility weighting formula instead of single – point upstream approximation to lessen numerical diffusion of flood foregrounds and cell orientation mistakes. They used saturation contour and oil recovery for measuring the reduction of grid orientation result at mobility ratio ranged from 0.5 to 10. The results showed reduction of the error and it was found at unit mobility ratio breakthrough time, oil recovery and saturation contour converge to the correct value when finer grids were used, despite the fact that there was little difference in oil recoveries for parallel and diagonal grids at high mobility ratio which was an indicator of long transition zone.
Coats, George, Chieh, and Marcum in 1974 used gradually finer parallel and diagonal grids ranged from16 * 16 diagonal grid and 22 * 22 parallel grids to examine grid orientation mistakes in steam injection of a 5 spot with a mobility ratio of about 500. They also explained that the effect of grid type on estimated oil recovery was lesser than its effect on breakthrough time. The results confirmed that the estimated oil recovery curves from parallel grids were equivalent in shape and quite lessen than those estimated from diagonal grids but they did not succeed to determine which grid type gave the correct outcome.
Thomas ,Lmnpkin, , and Reheisin 1974 presented a model to examine the influences of grid orientation by simulating variable bubble point issues above the original bubble point . The model was used as an example problem of gas injection above the bubble point and explained adverse mobility ratio with short transition zone which resulted from gas movement into solution at the front.
Holloway, Thomas, and Pierson in 1975 proposed the usage of two – point weighting scheme in calculating mobilities and used a technique contained adjustment calculated the interblock phase transmissibilities for minimizing grid orientation influence on calculated numerical outcome in finite difference reservoir simulation. The results showed that neither two – point mobility weighting nor the transmissibility modification was suitable to remove cell orientation mistakes.
Yanosik and McCrackenwere the first who published the application of a nine – point finite difference approximation in the petroleum reservoir simulation in 1976. The result showed some improvement in reducing the effects of grid orientation over the previous five – point finite difference methods in adverse mobility ratio (less than 20) piston - like displacement problems.
Stephen and Anthony in 1979 developed a weighted nine - point finite difference arrangement for Cartesian square grid networks which provided numerical diffusion for quarter 5 spot discrete on grid orientation. This method was successfully utilized in adverse mobility ratio piston – like displacement and short transition zone issues. The technique succeeded to reduce grid orientation effect better than the previous five-point procedures.
Bertiger and Padmanabhansuggested in 1983 the use of an alternate nine - point principle for reducing the influence of grid orientation in finite difference issues. This method was established on an extra correct integration of fluid inflowing through cell faces.
The numerical outcomes were obtainable which proved that this procedure seriously reduced the influence of mesh orientation in identical and non – identical grids over the earlier studies which didn't provide sufficient outcome within the case of non – uniform grids.
Chen, Durlofsky, Engquist, and Osherin 1993 were utilized higher order finite difference approaches for modeling miscible and immiscible displacement procedures. They searched on a second order total variation diminishing (TVD) scheme and a third order essentially non – oscillatory (ENO) method. These methods accurately resolved displacement fronts and therefore obtained more reliable solutions than do first order methods. Furthermore making use of a higher order system, fewer grid blocks should be used to achieve the identical accuracy as a first order method.
Wolcott, Kazemi, and Dean in 1996 had been presented new advanced method which used a nine – point construction of the pressure and saturation equations with a third order total variation diminishing (TVD) arrangement. This procedure reduced cell network errors (even when using coarse grids) and numerical diffusion both for miscible and immiscible drives.
Chong, Syihab, Putra, and Schechter in 2004 offered a technique to decrease cell orientation influences on calculated numerical outcomes in finite difference reservoir simulation which included the usage of an exceptional grid - block assignment where four-sided cell blocks were combined with eight - sided cell blocks. The whole area included a structured grid block arrangement identified as the Hybrid Grid Block (HGB). The outcome confirmed that HGB was capable for reducing the cell trend effects for favorable and adverse mobility ratio displacement issues.
GRID ORIENTATION INFLUENCE STUDY
To examine Grid Orientation Effect for Subba oil field / NahrUmr reservoir on simulation results as oil production rate, cumulative oil production, water cut, pressure, and recovery factor we predict water injection plan for twenty years and assume the wells arrangement is a five-spot. Five-spot water flood were conducted using parallel and diagonal Cartesian cell arrangements. The parallel cell arrangement is a cell which is turned parallel to the line joining an injection / production sets while the diagonal cell arrangement is a grid turned at 45o between injection and production sets. The plan includes four cases:
1- Case 1 grid oriented diagonal to the injection / production sets for fine grids as shown in figure 1.
2- Case 2 grid oriented diagonal to the injection/production sets for coarse grids as shown in figure 2.
3- Case 3 grid oriented parallel to the injection / production sets for fine grids as shown in figure 3.
4- Case 4 grid oriented parallel to the injection / production sets for coarse grids as shown in figure 4.
Type of the grids that was used in this study is Cartesian grid has X and Y increments equal (200) m for fine grids and (400) m for coarse grids. statistics of the cells at any angle parallel or diagonal to the injector / producer pair differ by (nI and nJ) cells, total number of 3D cells, (nI and nJ) nodes, total number of 3D nodes, Average X and Y increments, total number of 2D cells, total number of 2D nodes, and total number of defined nodes as shown in tables 1- 4. Simulation results for the field indicated that these results are different in each case as shown in figures 5 – 8. The summarized results at the end of the prediction cases are illustrated in Table5. The static model was built by using Petrel software (version 2009.1) and by Petrel RE we will access to a black oil simulator(Eclipse 100 version 2010) to build a dynamic model.
COMPARISON THE RESULTS OF THE CASES
When comparing the results of the reservoir simulation model for the production wells as water cut and oil production rate, it was found that these results are different from well to another for each case because direction of the flow will change when orientation of the grids has been changed. This means the performance of the cases does not follow a clear trend as shown in figures 9 – 16.
CONCLUSION
1- Statistics of the grids are will change when orientation of the grids has been changed.
2- The results of simulation model for the reservoir under study as water cut, oil production rate, cumulative oil production, and pressure differ from well to another for each case when orientation of the grids has been changed and also for fine grids and coarse grids for the same rotation angle of the grids because when orientation of the grids has been changed direction of the flow will change.
3- Initial oil in place changes when changing orientation of the grids because position of the grids and distribution of the property in the grids (as porosity, water saturation, and net to gross ratio) change which leads to change active cells number.
4- Also volume calculations differ at each angle whereas these calculations are done by trigonometric functions.
5- There is no clear trend or relationship between the simulation results with type of the grids.
6- The Z direction has no influence when changing orientation of the grids which means this effect is areal.
ABBREVIATIONS
GOE = Grid Orientation Effect
TVD = Total Variation Diminishing
ENO =Essentially non – Oscillatory
HGB = Hybrid Grid Block
RE = Reservoir Engineering
ACKNOWLEDGMENT
I would like to express my sincere gratitude to my Supervisor Assist. Prof. Dr. (Sameera Mohammed Hamd-Allah) for the useful comments, remarks and engagement through the learning process of this master thesis.
I am also so grateful to my managers Wisam al-Musawy, Ammar Hassan, and ShukranKhurshid for them supporting and assisting me to provide for post graduated.
Finally, I would like to thank everyone assisted me.
REFERENCES
1- M. R. Todd, P. M. ODell, andG. J.Hirasaki, " Methods for Increased Accuracy in Numerical Reservoir Simulators", Soc. Pet. Eng. J., Trans. AIME, Vol. 253,(December, 1972) 515-530.
2- K. H. Coats, W. D. George, Chu Chieh, andB. E, Marcum, "Three Dimensional Simulation of Steam Flooding", Soc. Pet. Eng. J., Trans. AIME, Vol. 257 (December, 1974) 573-592.
3- L. K. Thomas, W. B. Lumpkin, andG. M. Reheis, 49th Annual Fall Meeting of SPE, Houston, Texas, SPE (October, 1974) 5107.
4- C. C. Holloway, L. K.Thomas and R. G. pierson, "Reduction of Grid Orientation Effects in Reservoir Simulation", SPE (1975) 5522.
5- J.L. Yanosik, and T.A. McCracken, "A Nine-Point Finite-Difference Reservoir Simulator for Realistic Prediction of Unfavorable Mobility Ratio Displacement", SPE (February, 1976) 5734.
6- C. M. KoStephen andD. K. Au Anthony, "AWeighted Nine Point Finite – Difference Scheme for Eliminating the Grid Orientation Effect in Numerical Reservoir Simulation, Dallas, Texas, SPE (1979) 8248.
7- W.I. Bertiger and L. Padmanabhan, " Finite Difference Solutions to Grid Orientation Problems Using IMPES", San Francisco, SPE (November, 1983) 12250.
8- W. H. Chen, L. J. Durlofsky, B. Engquist, and S. Osher, " Minimization of Grid Orientation Effects Through Use of Higher Order Finite Difference Methods", Los Angeles, SPE (1993) 22887.
9- D. S. Wolcott, H. Kazemi, and R. H. Dean, "A Practical Method for Minimizing the Grid Orientation Effect in Reservoir Simulation", Denver, Colorado, U. S. A., SPE (October, 1996) 36723.
10- E. Chong, Z. Syihab, E. Putra, and D. Schechter, " A Unique Grid-Block for Improved Grid Orientation", Perth, Australia, SPE (October, 2004) 88617.
Description / Value(nI*nJ*nK) cells / 61*104*12
(nI*nJ*nK) nodes / 62*105*13
Total number of 3D cells / 76128
Total number of 3D nodes / 84630
Total number of 2D cells / 6344
Total number of 2D nodes / 6510
Total number of defined 2D nodes / 6379
Average X increment (m) / 397.72
Average Y increment (m) / 398.62
Description / Value
(nI*nJ*nK) cells / 121*207*12
(nI*nJ*nK) nodes / 122*208*13
Total number of 3D cells / 300564
Total number of 3D nodes / 329888
Total number of 2D cells / 25047
Total number of 2D nodes / 25376
Total number of defined 2D nodes / 25333
Average X increment (m) / 198.7
Average Y increment (m) / 199.249
Description / Value
(nI*nJ*nK) cells / 232*231*12
(nI*nJ*nK) nodes / 233*232*13
Total number of 3D cells / 643104
Total number of 3D nodes / 702728
Total number of 2D cells / 53592
Total number of 2D nodes / 54056
Total number of defined 2D nodes / 25336
Average X increment (m) / 199.28
Average Y increment (m) / 199.45
Description / Value
(nI*nJ*nK) cells / 116*116*12
(nI*nJ*nK) nodes / 117*117*13
Total number of 3D cells / 161472
Total number of 3D nodes / 177957
Total number of 2D cells / 13456
Total number of 2D nodes / 13689
Total number of defined 2D nodes / 6451
Average X increment (m) / 397.2
Average Y increment (m) / 399
Recovery Factor(%) / Plateau (Year) / Field Oil Production Total (million STB) / Field Pressure (bar) / Field Water Cut (%) / Case Nomber
13.593 / 9 / 292.415 / 196 / 41 / Case1
13.851 / 10 / 296.347 / 192 / 48 / Case2
12.366 / 7 / 279.166 / 200 / 41 / Case3
14.012 / 9 / 281.148 / 196 / 48 / Case4
1