Predicting Horizontal Well Productivity

Abstract

A series of numerical experiments have been performed to compare horizontal well performance using coarse and fine grid reservoir models. The objective of this work has been to determine the effect of using a standard well model with coarse (i.e., field-scale) grid systems to approximate performance computed with high resolution grid systems in which a well model was not employed. For the systems studied, the theoretical transmissibility connection factor (i.e., well model) calculated using the Peaceman formulation must be reduced to provide reasonable rate forecasts. In homogeneous systems, the calculated value for the well model may need to be reduced by about 1/2. In heterogeneous systems, the magnitude of the required multiplicative factor (λ) was shown to vary over a wide range (0.3 < λ < 0.8), depending upon the single value of the effective vertical permeability which was assumed for the calculation of the connection factor. Owing to this uncertainty and that associated with grid dependency, the use of field-scale grid systems for horizontal well rate projections does not, on its own, seem feasible in the absence of an opportunity to tune the model against observed field response. Introduction The problem of predicting well productivity in the absence of analog field performance is an important one. Although it can be addressed through the use of either analytical or numerical approximations of real systems, there are well known shortcomings to each method of analysis. There are few real situations which meet the limiting assumptions required by the analytical approach and many numerical analyses are limited by both the well model and spatial truncation error. In many engineering studies it is the productivity of a horizontal well which must be predicted and then compared to known performance of conventional producing wells. The objective of the work described here was to determine whether or not a conventional well model developed for horizontal well applications and typical field-scale grid systems can be used to numerically approximate accurate horizontal well performance. To satisfy this objective it was first necessary to establish accurate performance for a series of different reservoir and well placement conditions; this was done by developing an explicit wellbore modelling approach and validating its results with those derived from analytical solutions. Explicit Modelling Technique By an explicit modelling approach we mean that a finite-difference grid system is used to explicitly represent the horizontal wellbore itself and the surrounding reservoir volume. In this approach the wellbore is represented by a series of very small gridblocks scaled to represent the length and diameter of the horizontal well. The permeability of the wellbore gridblocks is set at a very high level (7.5E + 09 md) to establish a negligible wellborepressure gradient (< 0.02 kPa/m) and, as described later, the well model is effectively inactivated in the single completion grid block at the heel of the well by using a very high transmissibility connection factor.

Productivity and Injectivity of Hoeizontal Wells

“…In reality, the ux pattern along the well is non-uniform, which is also the case for the problem considered by Dietrich and Kuo [5]. Recently, Penmatcha at al.…”

“…Dietrich and Kuo [5] have compared horizontal well performance simulated by a uniform coarse grid with a non-uniform ne grid system using the Peaceman model. They concluded that the well productivity is overpredicted using a coarse grid and the conventional well model proposed by Peaceman.…”

“…For example, it is necessary for 3-D simulations of stratied reservoirs or for well coning calculations [5]. Dietrich and Kuo [5] used the approach of grid renement and deactivating the wellbore to realize explicit well modeling.…”

“…For example, it is necessary for 3-D simulations of stratied reservoirs or for well coning calculations [5]. Dietrich and Kuo [5] used the approach of grid renement and deactivating the wellbore to realize explicit well modeling. In this approach, the wellbore is represented by a series of very small gridblocks scaled to represent the length and diameter of the horizontal well, the permeability o f the wellbore is set at a high level and the transmissibility connection factor for the wellbore at the heel is also made very large, so that the well model itself can be removed from the problem and the eect of the well index is trivial.…”

“…The conguration of the non-uniform ne grid is exactly the same as that used in reference [5]. Figure 3 is a typical plot used in well testing.…”