A PSEUDOFUNCTIONLESS DENSITY DIFFUSIVITY EQUATION APPROACH TO NATURAL GAS RESERVOIR ENGINEERING ANALYSIS

Open Access
Author:
Ye, Peng
Graduate Program:
Petroleum and Natural Gas Engineering
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
October 11, 2011
Committee Members:
  • Andre Louis Boehman, Thesis Advisor
  • Luis F Ayala H, Thesis Advisor
Keywords:
  • decline curve
  • density
  • Natural gas
  • reservoir engineering
Abstract:
The traditional approach employed in the analytical analysis of unsteady state responses for natural gas reservoirs is firmly based on recasting the reservoir diffusivity equation in terms of new pseudo variables or pseudofunctions—namely, pseudopressure and pseudotime—able to render the equation amenable to analytical treatment. Since the pseudofunction-based approach succeeds in linearizing the equation and hence generating such required analytical solutions, the recognized inconvenience of these variables in terms of their units and usual introduction of iteration procedure — is understood to be their necessary trade-off that comes with the study of natural gas reservoirs. In this study, we propose a rigorous yet pseudofunctionless density diffusivity equation approach for the analytical solution of the gas diffusivity equation which is more readily linked to the fundamental principle of mass conservation. To demonstrate its validity, we discuss analytical arguments and perform numerical simulations to corroborate performance for the most widely used inner boundary conditions: constant pressure and constant rate production. By honoring the proper material balance equations and implementing the concept of depletion-driven dimensionless parameters, the proposed pseudofunctionless density equation is found to be able to fully describe reservoir unsteady behavior while keeping all variables involved in the analysis firmly grounded in physical intuition. This work also presents another important application of the proposed pseudofunctionless density diffusivity equation approach—rate decline curve analysis. Decline curve analysis is the technique most extensively used by engineers in the evaluation of well performance, production forecasting, and prediction of original fluids in place. State-of-the-art natural gas decline curve analysis heavily relies on the use of liquid (oil) type curves combined with the concepts of pseudopressure and pseudotime and/or empirical curve fitting of rate-time production data using Arps hyperbolic decline model. In this study, we present the true decline equation—in its analytical, closed functional form—that rigorously models production from any gas well producing at constant pressure under boundary dominated flow (BDF) without the use of pseudofunctions or empirical concepts from Arps decline models. New-generation analytical decline equations for boundary dominated flow (BDF) are presented for gas wells producing at 1) full production potential under true wide-open decline and 2) partial production potential under less than wide-open decline. The proposed analytical BDF equation for gas reservoirs producing at full production potential invalidates the commonly-held assumption that the hyperbolic decline exponent (“b”) proposed by Arps is subject to empirical determination from gas rate-time data in single-phase volumetric gas reservoirs. In addition, decline behavior of gas reservoirs producing at partial production potential or drawdown is shown to exhibit a hyperbolic decline character during early boundary dominated flow, but exponential decline character at later times. The proposed model enables the generation of rigorous type-curves for the analysis of natural gas reservoirs producing at constant pressure and under BDF for both full and partial production potential. A universal, single-line BDF gas type curve is shown to be straightforwardly derived for any gas well producing at their full potential. The proposed analytical model and resulting pseudofunctionless type curves can be used to rigorously forecast boundary-dominated performance and, more remarkably, predict original gas in place without: 1) iterative procedures, 2) prior knowledge of reservoir storage properties or geological data, 3) pseudo-functional manipulation of rate-time production data obtained in the field. In addition, another method for the estimation of original gas in place using the back-tracking of viscosity-compressibility changes is also provided.