Inflow Performance Relationships for Solution-Gas-Drive Reservoirs
Authors: Camacho V. R.G. , Raghavan Rajagopal 
Published: December 2007

Summary
In this theoretical study, a numerical model was used to examine the influence of pressure level and skin factor on the inflow performance relationships (IPR's) of wells producing under solution-gas-drive systems. Examination of the synthetic deliverability curves suggests that the exponent of the deliverability curve is a function of time and that the exponent is usually greater than unity. The implication of this observation to field data is discussed. The accuracy of procedures given in the literature to predict oilwell deliverabilities is also examined. It is shown that these methods can used to predict future performance provided that the exponent of the deliverability curve is known and that extrapolations over large time ranges are avoided. If single-point tests are used to predict future performance (such tests assume that the exponent of the deliverability curve is constant), then errors in predictions will be minimized if test conditions correspond closely to actual producing conditions. Under these circumstances, errors in rate predictions will be directly influenced by the magnitude of the error that results from assuming that the exponent of the deliverability curve is known. Although relative permeability and fluid property data are required, the Muskat material-balance equation and the assumption that GOR is independent of distance can be used to predict future production rates. This method avoids problems associated with other methods in the literature and always yields reliable results.
New methods to modify the IPR curve to incorporate changes in skin factor are presented. A new flow-efficiency definition based on the structure of the deliverability equations for solution-gas-drive reservoirs is proposed. This definition avoids problems that result when the currently available methods are applied to heavily stimulated wells.

Introduction
This paper addresses three concerns pertinent to IPR's under solution-gas drive. First, by means of numerical simulations, we examine the IPR when a skin region exists around the wellbore. This phase of our work is intended to address the question of whether the generalized form of the IPR curve is governed by the existence of a skin region. Although the skin region has a dominant effect on the well response, the influence of a skin region has been ignored for all practical purposes. (The seminal work of Vogel, however, briefly addresses the influence of a skin region.)
Second, we address the prediction of future IPR's from test data. Many methods have been proposed in the literature to predict future performance. The methods of Standing and Fetkovich are based on empirical observations of solution-gas-drive reservoir performance. All methods presented in the literature assume that the mobility function, kro(uoBo), is a linear function of pressure, p, where k, is the relative permeability to oil. uo, is the viscosity of oil, and B, is the FVF of oil. Although the methods of Standing and Fetkovich can be justified on the basis of this assumption, this requirement (mobility function is a linear function of pressure) is not a necessary condition for the methods given in Refs. 2 and 3 (or for that matter, in the other references cited above) to be valid. We examine the validity of the procedures suggested by Standing and Fetkovich by means of simulations for a wide range of producing conditions. We show that the success of these methods rests primarily on the fact that the deliverability equations suggested by Vogel and Fetkovich incorporate features that reflect the nonlinear aspects of flow in the reservoir and, more importantly, are calibrated by measurements. Their procedures attempt to predict only the endpoint-the final answer. We demonstrate this point by comparing mobility-function profiles predicted by methods given in the literature.
The third part of this paper examines procedures to modify the IPR curve to incorporate the influence of the skin factor, s. Brown shows that Standing's method to modify the IPR curve can result in inconsistent predictions if s is negative. Whitson says that Standing's method leads to nonphysical results if s less than 0. Whitson's observations suggest that Standing's procedure should be incorrect if s is greater than 0. Here, we show that inconsistent or nonphysical predictions are a result of the definition of flow efficiency used by Standing. Standing defined flow efficiency on the basis of liquid flow and not on the quadratic form suggested by Vogel's equation. In this work, we redefine flow efficiency, Ef, on the basis of the quadratic forms of the deliverability equations suggested by Vogel and Fetkovich and show that the inconsistencies mentioned by Brown can be eliminated. Unfortunately, the curves developed by Standing need to be corrected for all values of s. Incidentally, the definition we present is consistent with the definition of Ef used for gas wells. A new chart to modify the IPR curve based on the appropriate deliverability equation (Vogel or Fetkovich) is presented.

Numerical Model
We consider a homogeneous, closed, circular reservoir with the well located at the center. The well is capable of producing either at constant oil rate or at constant wellbore pressure. Gravity effects are considered to be negligible. The reservoir initially is assumed to be at the bubblepoint. An annular region concentric with the wellbore, with a permeability different from formation permeability, is used to incorporate the influence of a skin region.
Several sets of relative permeability and fluid properties were used in this study. Figs. 1 and 2 show the fluid properties for two of the data sets we considered, and Fig. 3 presents the relative permeability data used in this study. Table 1 presents other information regarding reservoir properties used in this work. The results given in this work, however, can be applied over a wider range of conditions.
A finite-difference model was used to obtain the results presented here. The procedures we followed to ensure that the results are accurate are similar to those presented in Refs. 10 and 11 and will not be considered here.
Non-Darcy flow effects are not considered. The influence of nonDarcy flow for wells producing by solution-gas drive represents a formidable analytical problem. Many fundamental considerations are involved, which are beyond the scope of this work.

Background
From numerical simulations, Vogel showed that the deliverability curve for a well producing under solution-gas drive is given by
..........................................(1)
Here qo/rna, is the maximum possible flow rate (rate corresponding to pwf=0), and q, is the flow rate corresponding to average pressure. p, and wellbore flowing pressure, pwf. In 1973, on the basis of field experiments, Fetkovich suggested that the deliverability curve for solution-gas drive systems is given by the following relation. ..........................................(2)
Here J o(t) is the productivity index for a well producing under solution-gas drive. Field tests presented in Ref.. 3 indicate that the exponent n should be in the range 0.5: - 1.
JPT
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