Due to the recent advances in well design and production techniques, tight/shale gas reservoirs have received considerable attention. At the early phase of development of these reservoirs, fast analytical models are attractive since data are limited and a large number of sensitivity studies is required. This analytical solution is possible if the governing partial differential equation is linear. However, the pressure dependency of gas compressibility and viscosity makes the governing partial differential equation nonlinear. The use of pseudovariables (i.e. pseudopressure and pseudotime) significantly reduces this nonlinearity. Unlike pseudopressure, which is an exact mathematical transformation, pseudotime is an approximate transformation. For conventional gas reservoirs, the average reservoir pressure was utilized to evaluate pseudotime and worked very well during boundary dominated flow.
However, in low permeability systems, when transient flow prevails, use of average reservoir pressure for pseudotime calculation is not valid and its use can create inconsistent results. Anderson and Mattar (2007) proposed that, during transient and transitional flow, the use of average pressure within the region of influence, rather than the average pressure of the whole reservoir, results in responses that are more consistent with those from numerical simulators.
In this study, the idea of using average pressure within the region of influence is utilized to calculate pseudotime during constant rate production from a tight/shale gas reservoirs. In order to achieve this, the liquid type curve was employed to find the volume of investigation, and then the gas material balance equation was incorporated to evaluate the average pressure within the region of influence. The significant advantage of this method is that the volume of investigation is determined based on material balance principles by imposing a unit-slope line at each point in time, rather than depending on the radius of investigation formulation as was used by Anderson and Mattar (2007). In an irregularly shaped drainage area, different methods were investigated for evaluating the distance of investigation in the x- and y-directions. It was found that the distance of investigation in the x- and y- directions could not be represented by the same formula (i.e., where all parameters are in field units).
The method developed in this paper is applicable in modeling different flow regimes during transient, boundary affected and boundary dominated flow periods. This paper outlines the proposed approach and explains its usefulness by comparing the analytical and numerical results for different cases. It is shown that reliable forecasts of production can be obtained.