multivariate production systems optimization - Stanford University

eservoir model. Kuller and Cummings (1974) developed an economic linear
programming model of production and investment for petroleum reservoirs.
Several investigators have attempted to couple numerical reservoir simulation with
linear programming models. The idea has been to use the reservoir simulator to generate a
linearized unit response matrix that could be used with linear programming models.
Wattenbarger (1970) developed a linear programming model to schedule production from a
gas storage reservoir using this technique. Rosenwald and Green (1974) also used
influence functions in a mixed-integer linear programming model that optimized well
placement. Murray and Edgar (1979) used influence functions in a mixed-integer linear
programming model that optimized well placement and production scheduling. See and
Horne (1983), extending on work performed by Coats (1969) and Crichlow (1977),
demonstrated how to refine the unit response matrix using nonlinear regression techniques.
This work was expanded by Lang and Horne (1983) to consider dynamic programming
techniques.
Asheim (1978) studied petroleum developments in the North Sea by coupling
reservoir simulation and optimization. Ali et al. (1983) used nonlinear programming to
study reservoir development and investment policies in Kuwait. McFarland et al. (1984)
used nonlinear optimization to optimize reservoir production scheduling.
Notice that virtually all of the previous research has attempted to model reservoir
performance by linearizing the reservoir performance and feeding this to some variation of
linear programming. The main focus in every case was to model the reservoir
performance. None of the models endeavored to optimize the well performance.
1.2 Modeling Well Performance with Nonlinear Optimization
A clarification of terminology is necessary. In the current literature, the expressions ‘nodal
analysis’ and ‘production optimization’ are virtually synonymous. This leads to confusion
between nodal analysis and nonlinear optimization. A natural question is what
distinguishes nonlinear optimization applied to hydrocarbon production systems from the
conventional procedure of nodal analysis. The distinction is quite simple: nodal analysis
finds the zero of a function which yields the stabilized flow rate of a well (see Figure 1.1);
nonlinear optimization finds the zero of the gradient of a function which yields the
maximum or minimum value the function can achieve. To restate this important distinction,
3