Abstract
WELCOS is a robust, three-dimensional, three-phase well coning simulator that couples the well rate equation to the reservoir flow equations. This strong coupling allows well rate to be determined simultaneously with reservoir pressures and saturations. The flexibility obtained permits the use of dynamic constraints on well rates, resulting in a highly stable model. The model may be used to obtain the maximum well productivity for a given set of physical limitations and regulatory constraints e.g., minimum surface pressure, maximum allowed GOR, WOR, water rate, gas rate, etc. The model can function either as a production well or an injection well and, in general, may be used to study any single-well behavior.
This paper describes a strongly coupled formulation and discusses its utility in relation to other implicit models. The linearization of the nonlinear finite difference equations and solution of the resulting linear equations are discussed. Example field applications are included to show the utility of user-supplied production constraints in determining well performance.
Introduction
A number of well coning simulators have been reported in the literature. 1–6 This paper describes a three-dimensional, three-phase well coning simulator that has been in extensive use in our company since 1972. A primary consideration in the development of WELCOS was easy usage by inexperienced users working difficult problems. This demands freedom from stability problems and algorithmic parameters requiring user intervention.
This paper emphasizes stability and flexibility of a strongly coupled algorithm. Strong coupling of the production and reservoir flow terms requires simultaneous solution for all unknowns, without auxiliary side calculations or approximations to bring the well rate terms to a desired level of accuracy.
This algorithm is computationally more expensive than a sequential formation7,8 but it has several offsetting advantages. Increased stability permits larger time steps than sequential methods, especially for difficult problems. The coupling of the well constraints yields a very reliable model.
The user can forecast well potential under assigned operating conditions with a single simulation run. Several trial-and-error runs may be required when operating constraints are uncoupled from the flow equations.
The utility of WELCOS is enhanced further by modern concepts of well flow equations.9,10 These include the pseudogas potential function,11 skin factor to account for damage or improvement, non-Darcy flow effect, flow restriction due to restricted entry such as partial penetration, flash surface separation, gas lift calculations, and tubing string pressure losses.
Simplicity and flexibility are key features of the data input and output systems. Data input has free-field formatting with a standard structure for all cards. Each card has a mnemonic field for data identification, a control field for processing instructions, and six data fields. Data need not appear in specific columns within fields. All input cards are read and checked for validity (proper mnemonic card names, valid numbers, etc.) and for inconsistencies (such as monotonic table values, negative numbers, etc.). A data processing run will not be aborted when the first error is detected. Processing will continue until as many errors as possible have been found.
Computation of Unsteady Flows Around Oscillating Blades Using Linear and Nonlinear Harmonic Euler Methods
