Interpretation of Well-Block Pressures in Numerical Reservoir Simulation(includes associated paper 6988 )
- D.W. Peaceman (Exxon Production Research Co.)
- Document ID
- Society of Petroleum Engineers
- Society of Petroleum Engineers Journal
- Publication Date
- June 1978
- Document Type
- Journal Paper
- 183 - 194
- 1978. Society of Petroleum Engineers
- 5.5 Reservoir Simulation, 5.5.8 History Matching, 5.1.5 Geologic Modeling, 5.3.2 Multiphase Flow, 5.1.2 Faults and Fracture Characterisation, 4.1.2 Separation and Treating, 5.6.4 Drillstem/Well Testing
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Original manuscript received in Society of Petroleum Engineers office June 16, 1977. Paper accepted for publication Dec. 20, 1977. Revised manuscript received April 3, 1978. Paper (SPE 6893) first presented at the SPE-AIME 52nd Annual Fall Technical Conference and Exhibition, held in Denver, Oct. 9-12, 1977.
Examination of grid pressures obtained in the numerical simulation of single-phase flow into a single well shows that the well-block pressure is essentially equal to the actual flowing pressure at a radius of 0.2 x. Using the equation for steadystate radial flow then allows calculation of the flouring bottom-hole pressure.
The relation between pressures measured in a buildup test and the simulator well-block pressure is derived. In particular, the buildup pressure and the well-block pressure are shown equal at a shut-in time of 67.5 ct x2/k. This is about one-third the shut-in time stated by previous authors, who derived their results from an erroneous assumption concerning the significance of the well-block pressure.
When only a single buildup pressure is observed at a different shut-in time, an adjustment to the observed pressure can be made for matching with the simulator well-block pressure.
When modeling reservoir behavior by numerical methods, inevitably the horizontal dimensions of any grid block containing a well are much larger than the wellbore radius of that well. It long has been recognized that the pressure calculated for a well block will be greatly different from the flowing bottom-hole pressure of the modeled well, but the literature contains few specific guides as to how to make the correction.
In this study, we confine our attention to singlephase flow in two dimensions. Consider the five blocks abstracted from a regular grid system(Fig. 1) with the center block containing a well producing at rate q. Schwabe and Brand proposed the relationship
2 kh Pe - Pwf q = ------- -----------------,..............(1) 1n(r /r ) + s e w
where re is taken equal to x, and pe is an effective pressure at the"drainage radius," re, obtained from 4 Pe = Po + Fi (Pi - Po). i=1
Schwabe and Brand did not define Fi, but seemed to imply that it be taken as zero. Thus, in the absence of a skin effect, Eq. 1 reduces to
2 kh Po - Pwf q = ------- -------------...................(2) 1n( x/r ) w
The most significant treatment of this subject until now was that of van Poollen et al. They stated that the calculated pressure for a well block should be tithe areal average pressure in the portion of the reservoir represented by the block.
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