For the optimum operation of natural gas fields, periodic reviews are made to determine deliverabilities of producing wells, to evaluate reservoir formation characteristics, and to predict recoverable or deliverable reserves. Bottom-hole pressure data are often required for these reviews. Historically, these bottom-hole pressures have generally been obtained through direct bottom-hole measurements, which expose the operator to mechanical or equipment problems and a consequent loss of production and expense funds. The technique presented in the present paper attempts to avoid these problems by the use of fluid flow equations to calculate bottom-hole pressures from wellhead measurements of pressure and temperature. This method could be particularly useful in remote areas where the movement of equipment is difficult and expensive. Calculation of bottom-hole pressures has the advantage of greatly reduced operating costs associated with obtaining reservoir pressures, thus permitting more frequent monitoring of reservoir pressures.

The theory of bottom-hole pressure calculation is based on the conservation of mechanical energy for flow in pipes. The derivation yields an integroarithmetic equation relating fluid properties and the well's physical configuration to the bottom-hole pressure and temperature. A numerical integration technique is often used to perform the integration.

The theoretical calculation of bottom-hole pressures in gas wells has been the subject of many investigations, notably those of Cullender and Smith1 and Sukkar and Cornell2. The efforts of the above two references and that of others led to two methods widely used in the literature and typified by the simplifying assumptions made to facilitate the solution of the resulting equations. One method approximates conditions in a gas well by assuming constant temperature and compressibility throughout the entire gas column. Theother method uses the assumption that the temperature in the gas column is constant as some average value but permits compressibility to vary with pressure at the constant temperature.

Although these assumptions may be justified for shallow gas wells, they become unsatisfactory in the case of deeper, high pressure wells. The method proposed in this paper eliminates the need for unnecessary simplifying assumptions by reducing the equationto a polynomial thus facilitating its solution by the Newton-Raphson iteration technique for determining the roots of polynomials. This method results in a faster more accurate technique for calculating bottom-hole pressures while retaining the general nature of the equations. The method could be conveniently used to estimate reservoir pressures in place of conventional bottom-hole pressure measurements.

Statement Of Equations

The detailed, rigorous derivation of the relevant equations for calculating bottom-hole pressures in gas well is presented in the Appendix. A statement of the final equations is as follows:

Equations (Available in full paper).

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