Decline curves

Once the production potential of the producing wells is insufficient to maintain the plateau rate, the decline periodbegins. For an individual well in depletion drive, this commences as soon as production starts, and a plateau for the field can only be maintained by drilling more wells. Well performance during the decline period can be estimated by decline curve analysis which assumes that the decline can be described by a mathematical formula. Examples of this would be to assume an exponential decline with 10% decline per annum, or a straight line relationship between the cumulative oil production and the logarithm of the water cut. These assumptions become more robust when based on a fit to measured production data. 

DFR = dislodgeable foliar residue, initial or obtained daily from decline curve... 

Dt50 = 2.9 days Dtgo = 11 days r2 = 0.98 Figure 5 Decline curve for the California site using the turf-clipping method. 

Figure 6 Decline curve for the California site using the California roller method.

Dt50 = 9.5 days Dt90 = 1.5 days r2 = 0.88 Figure 8 Decline curve for the Florida site using the California roller method. 

Figure 9 Decline curve for the Pennsylvania site using the turf-clipping method.

An interwell chemical tracer study established fluid flow patterns within the pilot. Decline curve analysis showed that TFSA injection recovered more than 8150 +... 

Incremental oil production for each of the pilot wells was calculated by subtracting the extrapolated production decline curve which was established prior to TFSA injection from the actual production after TFSA injection. Results of this analysis indicate that a total of 8150 + 850 bbl (1295 + 135 m3) of incremental oil were obtained due to injection of TFSA. 

Analysis of the hyperbolic decline curves indicated that 8150 + 850 bbl (1295 + 135 m3) of incremental 18° API oil were recovered during the 18 month pilot project. 

When a recovery well is located within a contaminant plume and the pump is started, the initial concentration of contaminant removed is close to the maximum level during preliminary testing. As the pump continues to operate, cleaner water is drawn from the plume perimeter through the aquifer pores toward the recovery well. Some of the contaminant is released from the soil into the water in proportion to the equilibrium coefficient. For example, if the Kd is 1000, at equilibrium, 1 part is in the water and 1000 parts are retained in the soil. If the water-soil contact time is sufficient, complete equilibrium will be established. After the first pore volume flush (theoretically), the concentration in the water will be 0.9 and that on the soil will be 999. With each succeeding flush, the 1000 1 ratio will remain the same. If the time of water-soil contact is not sufficient to establish equilibrium, the recovered water will contain a lesser concentration. A typical decline curve is shown on Figure 9.2. Note the asymptotic shape of the curve where the decline rate is significantly reduced. 

A simplified analysis of production decline curves was initially intended for evaluation of individual oil well production however, this type of analysis can also provide reasonable estimates when applied to multiple-well LNAPL recovery systems. This analytical method is applicable to most types of decline curves, whether they tend to follow exponential, hyperbolic, or harmonic forms. The following general differential equation is applicable to all forms of decline curves ... 

Summary of Mathematical Solutions for Production Decline Curves... 

Gentry, R. W., 1972, Decline-Curve Analysis Journal of Petroleum Technology, pp. 38—41. 

In Figures 8 and 9 are shown the data for the dependence of the characteristic film buildup time t on Apg and U. In accord with the model, t is found to be independent of U, with only a very weak dependence on Apg indicated. This latter result could in part be a function of experimental inaccuracy. The data reduction for t introduces no assumptions beyond that needed to draw the exponential flux decline curves such as those shown in Figures 2 and 3. However, an error analysis shows that the maximum errors relative to the exponential curve fits occur at the earlier times of the experiment. This is seen in the typical error curve plotted in Figure 10. The error analysis indicates that during the early fouling stage the relatively crude experimental procedure used is not sufficiently accurate or possibly that the assumed flux decline behavior is not exponential at the early times. In any case, it follows that the accuracy of the determination of 6f is greater than that for t. 

R2. Rundle, F. F., Perry, D., Cass, M., and Oddie, T. H., Rise in serum bilirubin with biliary obstruction and its decline curve after operative relief. Surgery 43, 555-562 (1958). 

The concept of IGV in muddy sediments is less well established because it is difficult to petro-graphically discriminate between grains, cements, and porosity. As a result, compaction within mudrocks is described primarily on the basis of porosity decline curves (Giles et al, 1998). The porosity of muddy sediments is very high at deposition (near 80%) it declines exponentially with depth (summarized in Giles et al., 1998) in response to temperature, burial rate, and the degree of overpressuring (Bjprlykke, 1999). 

Note r is tiie correlation coefficient for % ChE inhibition vs. time for the declining curve is the... 

Thompson presents a study of the molecular distributions of petroleum fluids, as revealed by standard PVT data. The method relies on the observation that carbon number profiles may be fitted by two exponential decline curves (C3-C5 and C]o+). Using PVT data principally from western Canada, Thompson proposes that changes to the C3-C5 and Cjo+ slopes can be related to maturation and phase separation. The addition of allochthonous gas can also be recognized. Given the ubiquity of PVT data, these techniques will prove useful additions to the interpretive armoury. 

From the production declining curve for the Western Embayment of the Pavlova Gora field, it was calculated that without application of EOR methods the reservoir would be depleted by 1977 with a total recovery factor of only 11.7% of oil in place. 

An example of a supervised trial model in the Pesticide Agenda is shown in Figure 1, using bifenthrin at the highest recommended dosage on clementines. Application method, dosage, and equipment used are indicated in the information accompanying the decline curve. Five samples of 16 fruits each were collected at 0, 3, 7, 14, and 21 days after application and processed for residue analysis. 

Figure 1. Residue decline curve for bifenthrin in clementines (Metropolitan, summer 2006).

Experimental data of log D plotted against log c usually exhibit no distinct break and can be fitted by a smoothly declining curve. According to the idea dominating at present, the change in the slope of this curve, after correction for the concentration dependence of may be interpreted as reflecting the gradual transition of chain motion from the Rouse-like to the reptative mode. 

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