A Sand-Erosion Model for Volumetric Sand Predictions in a North Sea Reservoir

Summary Volumetric sand-production data from a North Sea reservoir are interpreted with respect to the applied drawdown. Two sand rates are identified: the initial sand rate related to the increase of drawdown, and the final sand rate related to the magnitude of drawdown. A sand-erosion model is also presented and used for predicting the field data, and the results compare reasonably with the field measurements. Introduction Sand production has become a most effective way to increase well productivity. The industry reports increases in the sand-free rate up to 44% after sand production. At the same time, downhole sand control is the most common formation damage in the North Sea sandstone reservoirs. Much attention has thus been focused on how to operate wells that produce sand from time to time and how to produce loose sand under controlled conditions. This paper addresses these problems through analysis of field data on volumetric sand production and predictions with a sand-erosion model. The capabilities of the model are demonstrated by estimating the character of sand production in terms of the produced sand in a North Sea reservoir as a function of time and drawdown. Currently a volumetric sand model1 has been developed for heavy-oil reservoirs and predictions of sand amount as a function of the changes in drawdown over time. Field data and numerical simulations on volumetric sand production in a North Sea reservoir are presented. Previous work has mainly concentrated on the prediction of sand-production initiation. The current analysis of the field data and model simulations attempt to establish the relation between volumetric sand rate as a function of time, stresses, and fluid-flow rate. Based on such analyses and model predictions, a well-production strategy can be implemented for maximum productivity with minimum sanding problems. Field-Data Interpretation Volumetric sand-production data were collected from an oil-production well in a North Sea reservoir. Table 1 provides the perforation intervals of the well and other perforation data, such as total perforated length of the well and perforation density and phasing. The well inclination at the perforated interval is 50 with respect to the vertical. Various reservoir data, such as porosity and permeability, in-situ stresses, initial reservoir pressure, and current depletion are given in Table 2. The mechanical properties of the reservoir have been characterized through triaxial compression tests at 2, 5, and 15 MPa confining stress. The triaxial test results from two reservoir intervals are given in Table 3. Volumetric sand-production data from this well have been continuously collected. Fig. 1 shows the sand rate, cumulative sand, and the applied drawdown over a 120-hour production period. In this period, the sand-production rate shows three peaks associated with drawdown increases. After each peak and under near-constant drawdown, the sand rate decreases gradually to a near-constant residual value. The residual constant sand-rate value appears to increase with increasing drawdown. A total of approximately 117 kg of sand was produced. For the same 120-hour period, Fig. 2 shows the productivity of the well expressed as the total fluid rate over drawdown, and the oil fraction of the fluid-flow rate. Both the productivity and the oil fraction are constant during this period at approximately 39 std m3/Mpa·h and 0.68, respectively. For the field-data interpretation, the total period is divided into three time intervals associated with a peak and a subsequent decrease of the sand rate. For these time intervals, Table 4 lists the time duration, the increase in drawdown resulting in a peak in sand rate, and the initial and final drawdowns. The sand rates and drawdowns for the three time intervals are plotted in Fig. 3. The sand rate qsand in each time interval is approximated with the following parabolic function of the time t, which is also plotted in Fig. 3.Equation 1 where qisand is the initial sand production and a and b are calibration constants. The final residual sand rate qfsand may then be expressed asEquation 2 The initial and final sand rates and parameters a and b are listed in Table 5 for the three time intervals. The initial drawdown correlates with the drawdown increase and the final sand rate with the final drawdown, such that they increase with larger drawdown increase or final drawdown, respectively, as shown in Fig. 4. This means that if the drawdown is increased, a peak in the sand rate should be expected. The magnitude of the peak is larger for a larger drawdown increase. After the peak, the sand rate decreases and appears to approach a constant value, which depends now on the magnitude of the drawdown itself and not the increase in drawdown. Integration of Eq. 1 gives the cumulative sand production msand as a function of time; i.e.,Equation 3 The field data for the cumulative sand production in the three intervals are plotted in Fig. 5.