Unsteady State Gas Flow - Use of Drawdown Data in the Prediction of Gas Well Behavior

The solutions on unsteady state gas flow in a radial system have beenreviewed to aid in the interpretation of drawdown data. It has been thepractice to evaluate the time and rate conversion constants directly orindirectly by using reservoir data. This paper presents a method of determiningthese constants from drawdown data. A simplified approach to determine the time of stabilization for the variousboundary conditions is presented. An example problem illustrating the use ofthis theory appears in the Appendix. Unsteady State Flow Equation The solution of any unsteady-state flow problem involves -1, the continuityequation -2, the equation of state of the fluid -3, the equation of fluidmotion and -4, the boundary conditions. For Darcy flow of a gas in thehorizontal radial plane the equation is (Equation i) when the viscosity, compressibility and permeability to gas flow may beassumed constant and the medium is homogeneous. (Since Kg is assumedconstant subscript gwill be omitted from now on.) By substituting in Equation (i) we may also write (Equation ii) Equations (i) &(ii) are non-linear differential equations and norigorous analytical solutions of these equations are available. Equations (i) and (ii) may be normalized (made dimensionless). Equation (i)becomes (Equation iii) where if the pressure P, in the equation for t may be assumed constant atsome average value. (Equation iv) The clear distinction must be noted between Equations (iii) and (iv). Wehave reduced the non-linear differential Equation (ii) to a linear differentialEquation (iii) by defining a t which contains P assumed constant at P. Katzet al.have justified this assumption. If the assumption is justified, which at best can only result in approximate answers, then we may use all ofthe solutions obtained for liquid flow case by simply replacing P byP2. This has been done in many practical applications of the theoryof unsteady-state flow to gas reservoir problems.