Semianalytical Model for Reservoirs With Forchheimer’s Non-Darcy Flow

Semi-Analytical Model for Reservoirs with Forchheimer's Non-Darcy Flow Fanhua Zeng; Fanhua Zeng U. of Regina Search for other works by this author on: This Site Google Scholar Gang Zhao Gang Zhao U. of Regina Search for other works by this author on: This Site Google Scholar Paper presented at the SPE Gas Technology Symposium, Calgary, Alberta, Canada, May 2006. Paper Number: SPE-100540-MS https://doi.org/10.2118/100540-MS Published: May 15 2006 Cite View This Citation Add to Citation Manager Share Icon Share Twitter LinkedIn Get Permissions Search Site Citation Zeng, Fanhua, and Gang Zhao. "Semi-Analytical Model for Reservoirs with Forchheimer's Non-Darcy Flow." Paper presented at the SPE Gas Technology Symposium, Calgary, Alberta, Canada, May 2006. doi: https://doi.org/10.2118/100540-MS Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAll ProceedingsSociety of Petroleum Engineers (SPE)SPE Unconventional Resources Conference / Gas Technology Symposium Search Advanced Search AbstractThis paper presents a semi-analytical model to investigate the effect of Forchheimer's non-Darcy flow on the transient pressure behavior of vertical well in an infinite homogeneous reservoir. This model uses the Forchheimer number, defined as the product of the reservoir non-Darcy flow coefficient and a reference rate, to quantify the non-Darcy flow in reservoirs accurately. The traditional non-Darcy skin factor, generally applied to model the non-Darcy flow in reservoirs, is employed to describe the non-Darcy flow across completions only. This study shows that the non-Darcy flow effect may influence the local flow rate profile over a reservoir region of several hundred times the wellbore radius. Therefore, it is not satisfactory to merely use the traditional non-Darcy skin factor to model non-Darcy flow in reservoirs.Type curves are documented for both drawdown and buildup tests for the first time using the semi-analytical model proposed. It is observed that, when non-Darcy flow in reservoirs and/or across completions are considered, the dimensionless pressure derivative curves of drawdown tests have a wider-transition region with gentler slopes, while those of buildup tests exhibit a shorter transition region with steeper slopes. In the radial flow period, compared to the cases with only non-Darcy flow across completions, the cases with non-Darcy flow in reservoirs for drawdown and buildup tests possess dimensionless pressure derivatives that are moving downwards to approach 0.5 at decreasing rates more gradually and smoothly. In general, the pressure derivatives of drawdown tests are larger than those of buildup tests before they converge to 0.5.With this model, the skin factor for non-Darcy flow across completions and the dimensionless Forchheimer number for non-Darcy flow in reservoirs can be estimated from a common drawdown or buildup test. Guidelines for interpreting field test data are presented. Several typical cases from the literature are analyzed, and better type curve matches and more reliable results are obtained.IntroductionIn 1901, Forchheimer[1] found that Darcy's law is inadequate to describe the high-velocity gas flow in porous media and added an additional pressure drop that is proportional to the square of the velocity to the pressure drop predicted by Darcy's law to account for the discrepancy. This yielded the Forchheimer's flow equation,Eq. (1)Different results regarding the mechanism of non-Darcy flow and the meaning of ß factor had been presented in the past century. In the 1950s Cornell and Katz[2] attributed the non-Darcy flow to turbulence; thus, they labeled ß as a turbulence factor. Since the 1970s, many researchers[3–6] have agreed that Forchheimer's non-Darcy flow is not due to turbulence but rather to inertial effect. Thus, ß is called an inertial factor.The study of modeling non-Darcy flow began in the 1960s. Using a numerical method, Smith[7] and Swift and Kiel[8] investigated the effects of non-Darcy flow on gas well testing. Their results indicated that non-Darcy flow of gas leads to an additional pressure drop near the wellbore that can be treated as a flow rate dependent skin factor, which is also called a non-Darcy skin factor.[9] Ramey[9] integrated the wellbore storage effect and the non-Darcy skin factor together and proposed,Eq. (2)Ramey further concluded that the non-Darcy flow coefficient, D, should be computed from at least two different drawdown and/or buildup tests under two different constant flow rates. Wattenbarger and Ramey[10] analyzed synthetic well tests and showed that the kh value calculated from a drawdown test could be significantly lowered when non-Darcy flow was present. In their case, the relative error was 36%. They also stated that the buildup test could be interpreted accurately even with extreme non-Darcy flow. Through experimental study, Nguyen[24] showed that the standard Darcy flow analysis when applied for non-Darcy flow through perforations could overpredict the productivity by as much as 100%. Keywords: drillstem/well testing, flow rate, Upstream Oil & Gas, buildup test, flow in porous media, Fluid Dynamics, coefficient, pressure derivative, wellbore storage, Forchheimer Subjects: Reservoir Fluid Dynamics, Formation Evaluation & Management, Flow in porous media, Drillstem/well testing This content is only available via PDF. 2006. Society of Petroleum Engineers You can access this article if you purchase or spend a download.

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