The best hyperbolic curve is numerically fit to production decline data from selected oil wells. A production decline data from selected oil wells. A non-linear optimization computer program finds the three best values of the general hyperbolic parameters qo, a, and b using least squares regression. parameters qo, a, and b using least squares regression. By using weighted residuals, better history matching is obtained than with previous least squares methods. The future rate-time behavior of a well with only a few months of production is predicted by an analogy with other similar wells.
This production extrapolation method is superior to graphical or type curve procedures since it does not require engineering judgement until the unbiased curve fit has been calculated from observed production data. The program calculates consistent production data. The program calculates consistent results based only on production values. Then, the evaluation engineer can use his judgement and experience to modify the prediction.
The extrapolation of decline curves is a common method of predicting the performance of a producing oil well or a group of similar wells. However, these methods usually involve some manipulation of the data, such as adjusting scales with type curves (Slider). Some introduce bias into the data previous to the extrapolation, such as graphically choosing one or two parameters to represent trends of widely varying data. These and other decline analysis techniques are discussed by Ramsay, Gentry, McCray, and Fetkovich.
By using an efficient curve-fitting computer program, a general hyperbolic curve can be fit to the program, a general hyperbolic curve can be fit to the raw monthly oil production data. A continuation of this hyperbolic curve beyond the period of known production gives an extrapolation based only on the production gives an extrapolation based only on the production values, and not on any interpretation by production values, and not on any interpretation by the evaluation engineer. After this curve and its corresponding confidence limits are drawn for the user he can then use his own judgement to accept or adjust this prediction.
This investigation is based on the premise that most declining oil production follows a line representable by a hyperbolic equation. A drastic change of conditions during the primary production of a well would upset this trend. Such changes include recompletion in a new zone or mechanical problems.
Confidence intervals show the probable range of errors of an extrapolation of the fit from the actual future production. This interval is based on the deviation of the known production from the calculated fit and the regression calculations which derive the hyperbolic curve.
Comparisons of predictions and confidence intervals of wells in the same area show similarities. Wells in the same geographical area and producing from corresponding geological formations will have similar characteristics in their hyperbolic fits. For example some fields consist of wells which decline at a constant rate of 12% per year; others decline steady at first, then level out after the first year. These similarities can be used to make more reliable predictions for newly completed wells. predictions for newly completed wells.
The general hyperbolic equation for oil production rate (q) as a function of the (t) can be production rate (q) as a function of the (t) can be expressed asbt - 1/bq = qo (1+)a (1)
The parameter q is the initial oil production rate at time zero and has the same units as q. The parameter a is the initial decline rate and has the same units as t. The third parameter, b, has no units and controls the degree of curvature of the hyperbolic line.