A Practical Regression Model of Pressure/Inventory Hysteresis in Natural Gas Storage Fields
Authors: Tutt C.J. , Dereniewski E. 
Published: December 2007

A Practical Regression Model of Pressure/Inventory Hysteresis in Natural Gas Pressure/Inventory Hysteresis in Natural Gas Storage Fields
To forecast deliverability in natural gas storage fields, effective field pressure must be predicted. The effects of hysteresis on this pressure are pressure must be predicted. The effects of hysteresis on this pressure are difficult to determine without using complex reservoir models. This paper describes a simple equation that often can be used to predict storage-field hysteresis loops. Several techniques for developing the required coefficients are given and examples demonstrate the use of the equation.

Introduction
The deliverability of a storage field is related to flowing pressure (determined largely by compression/ piping constraints) and the driving formation pressure. piping constraints) and the driving formation pressure. If storage formations were perfect tanks and natural gas was ideal, this formation pressure would be directly proportional to gas inventory. Thus, a plot of pressure proportional to gas inventory. Thus, a plot of pressure vs inventory would be a straight line. Unfortunately, several classes of effects alter this relationship so that the plot seldom approaches a straight line in practice. If we are to predict reservoir deliverability practice. If we are to predict reservoir deliverability effectively, we must find some way to account for these effects.
There are three major classifications of effects that cause a pressure/inventory loop to deviate from a straight line. Deviation from the ideal gas law is one class. Transient effects of natural gas flow is another classification. We assume in this paper that because of close well spacing and choice of storage formation, pseudosteady state is reached relatively quickly in a storage field and that a "key" well or combination of wells is chosen that exhibits a pressure representative of the driving field pressure. The extent to which this assumption applies pressure. The extent to which this assumption applies largely determines the accuracy and applicability of our results. For base-load fields, few problems should be encountered. Sometimes peaking fields (where transient effects are more substantial) invalidate this assumption, although our analysis still may be useful.
Often, the most difficult effects to handle are phenomena that change the effective pore volume of the phenomena that change the effective pore volume of the field with time and pressure. Here, we include rock and water compressibility, concurrent oil and water production, and water influx and efflux. We will assume that water movement dominates and that it obeys the equation
........................(1)
where A is a constant.
The Model
Begin with the gas law at reservoir conditions,....................................(2)
Convert to wellhead conditions,........................(3)
and then differentiate with respect to time, t, for R, T, and e constant as.....(4)
Where injection is positive, withdrawal is negative.
JPT
P. 885