Decline Curve Analysis Learning Objectives of Lecture 8: Importance of decline curves Decline curve models Decline curve plots Applications Decline Curve Analysis Preliminaries: MBE analysis yields only G and Gp as a function of p for gas reservoirs. Estimation of production rate specially as function of time is also of great importance Under natural depletion, the rate normally declines with recovery Majority of oil and gas reservoirs show natural production rate decline according to standard trends Unless natural trend is interrupted (water injection, well shut in) the natural decline trend is expected to continue until abandonment Decline Curve Analysis for Reserve Estimation Natural decline trend is dictated by natural drive, rock and fluid properties well completion, and so on. Thus, a major advantage of this decline trend analysis is implicit inclusion of all production and operating conditions that would influence the performance. The standard declines ( observed in field cases and whose mathematical forms are derived empirically) are Exponential decline Harmonic decline Hyperbolic decline Decline Curve Analysis When the average reservoir pressure decreases with time due to oil and gas production, this in turn causes the well and field production rates to decrease yielding a rate time relation similar to that in the following figure. Definition of normalized production rate decline, D: D dq / dt q / t lim t 0 q q Decline Curve Analysis D = continuous production decline rate at time t (1/time) If t = years: Da= annual continuous production decline rate (1/year) If t = months: Dm= monthly continuous production decline rate (1/month) Unit of q is not important Decline curve models The general decline curve models is defined according to their relation with q as follows: q D Di qi n where n is called as the decline exponent The three standard decline models (usually observed in field) are defined as follows. Decline curve models 1. Exponential decline (n=0): D Di cons tan t q D Di qi 2. Harmonic decline (n=1): 3. Hyperbolic decline q D Di qi where Di is the initial decline rate n Decline curve models Producing rate during decline period for each model are (derived in appendix C: exponential rate decline q (t ) q i exp(Di t ) Eq .1 harmonic rate decline hyperbolic rate decline qi q (t ) 1 D i t q (t ) Eq .2 qi 1 nDi t 1/ n Eq .3 Decline curve models Cumulative production as a function of q for each model are determined as: exponential decline harmonic decline hyperbolic decline qi q Gp Di Gp qi ln(q i / q ) Di Eq .4 Eq .5 1 q in 1 Gp n 1 n 1 Eq .6 D i (1 n ) q i q Decline curve models Time at abandonment: If we define the economic limit when the production rate is qa then the exponential, harmonic and hyperbolic declines would have the following abandonment times respectively: 1 qi ta ln Eq .7 Di qa n 1 qi ta 1 Eq .9 nD i q a 1 ta Di qi 1 Eq .8 qa Graphical Features of Models Cartesian plots yields Graphical Features of Models Seilog plots yield Graphical Features of Models Cartesian q vs Gp plots yield Graphical Features of Models Semilog q vs Gp plots yield Graphical Features of Models For hyperbolic decline no immediate straight form is obtained, therefore a linear plot which allows us to determine two parameters namely Di and qi simultaneously is not available. In summary : The production plots allows us two determine the nature of decline and then we can obtain the decline model parameters. Summary Production Plots 1. A plot of log(q) vs t is 2. Linear if decline is exponential Concave upward if decline is hyperbolic (n>0) or harmonic A plot of q vs Np is 3. Linear if decline is exponential Concave upward if decline is hyperbolic(n>0) or harmonic A plot of log(q) vs Np is 4. Linear if decline is harmonic Concave downward if decline is hyperbolic (n<1) or exponential Concave upward if decline is hyperbolic with n>1. A plot of 1/q vs t is Linear if decline is harmonic Concave downward if decline is hyperbolic (n<1) or exponential Concave upward if decline is hyperbolic with n>1. Hyperbolic decline analysis 1. Since no wells have declines where n=0 or 1 exactly it is more appropriate to use a regression technique to determine all three parameters namley Di, qi and n simultaneously. Two approaches are suggested by Towler: An iterative linear regression Nonlinear regression Towler also pointed out that linear regression impose more weight on smaller values of production rates as it involves logs of variables. Furthermore, the two suggested procedures on linear regression do not produce equivalent results. Therefore, he suggests nonlinear regression as a method which produces repeatable results, and weights the production rates equally. The steps of regression on an excel sheet is also provided in Appendix C. Caution for applicability The emprical decline curve equations assume that the well/field analyzed is produced at constant BHP. If the BHP changes, the character of the well's decline changes. They also assume that the well analyzed is producing from an unchanging drainage area (i.e., fixed size) with no-flow boundaries, If the size of the drainage area changes (e.g., from relative changes in reservoir rates), the character of the well's decline changes. If, for example, water is entering the well's drainage area, the character of the well's decline may change suddenly, abruptly, and negatively. Caution for applicability The equation assumes that the well analyzed has constant permeability and skin factor. If permeability decreases as pore pressure decreases, or if skin factor changes because of changing damage or deliberate stimulation, the character of the well's decline changes. It must be applied only to boundary-dominated (stabilized) flow data if we want to predict future performance of even limited duration. Decline Type Curves Prepare a report explaining Carter decline curves Include the solution of exercise 9.5 from the textbook