# Inflow performance relationship for solution gas drive wells

Modeling Inflow Performance Relationships for Wells Producing From Two-Layer Solution-Gas Drive Reservoirs Without Cross-Flow. Ibrahim S Nashawi. Inflow Performance Relationships for Solution-Gas Drive Wells. Jo V. VOGEL. MEMBER AIME. Abstract. Its calculating oilwell production, it has commonly been . Abstract. This paper reports that inflow performance of 21 theoretical solution-gas -drive reservoirs was simulated with the Weller method.

They showed that Fetkovich Equation can be a good representation of the deliverability equation especially in the transition zone where the Pwf is slightly lower than the Pb and the shape of Krg is not increasing sharply with increase in gas saturation. The nk values range from 0. Through time IPR curves have used in different applications, Brown [ 21 ] in used IPR combined with tubing intake curves to provide an optimum artificial lift method to produce the well.

InAvery and Evans [ 22 ] utilize IPR curves in examining the well performance under different artificial lift designs. IPR curves were also used during enhanced oil recovery process where Yeu et al.

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After emerging of the multi-lateral technology, Guo et al. These are few of the many applications of IPR in oil industry. Most of the IPR correlations suffer from common limitations that they are not explicitly function of the different reservoir rock and fluid properties that vary from one reservoir to another or its difficulty to be applied.

This will affect the accuracy of the correlations especially if the reservoir properties of the well under study are completely different from the properties used in generating these correlations. In this work, a single well 3D radial reservoir model with solution gas-drive as the main driving mechanism was built and reservoir simulation was used to generate different IPRs by changing the reservoir rock and fluid properties. The most sensitive reservoir rock and fluid properties were selected to generate the new IPR correlation.

This new correlation is based on generating combination of the selected reservoir rock and fluid properties and run the simulation models to generate different IPR curves. Then, the non-parametric regression technique was used to generate the new IPR correlation that is explicitly function of the reservoir rock and fluid properties that highly affect the IPR curve.

The outline of the paper is as follows. Firstly, we presented the assumptions we used in generating the single well reservoir simulation model.

Secondly, we studied the sensitivity of the IPR towards different rock and fluid parameters to choose the highly sensitive parameters to be used in the IPR correlation. Thirdly, we presented the nonlinear and non-parametric regression techniques we used to develop the IPR correlation that is explicitly function of reservoir rock and fluid properties. Finally, we presented the validation of the new correlation based on different synthetic and field cases.

Introduction For slightly compressible fluids, the productivity index is given by: Evinger and Muskat2 observed that when the pressure drops below the bubble-point pressure, the inflow performance curves deviates from that of the simple straight-line relationship as shown in Fig. Based on the literature survey, the most known IPR correlations can be subdivided into empirically derived and analytically derived correlations.

Some of the most known empirical derived correlations are Vogel3Fetkovich4Kilns and Majcher5Wiggins6and Sukarno et al. Some of the most known analytical derived correlations are Wiggins et al.

### Inflow Performance Relationships for Solution-Gas Drive Horizontal Wells - OnePetro

Vogel used twenty-one reservoir data sets to develop the following IPR: Therefore, this will affect the prediction of inflow performance curves in case of solution gas drive reservoirs, because at later stages of production the amount of the free gas that comes out of the oil will be greater than the amount at the early stages of production.

The following relation gives the oil flow rate as introduced by Raghavan So is the oil saturation, and J the modified productivity index for this case, and is defined by: The approach suggested by Fetkovich4 in the pursuit of Eq.

For example, Fetkovich4 proposed the following relationship between the oil mobility function and pr: Fetkovich4 concluded that Eq. Finally, the "Fetkovich form" of the IPR equation is given as the "backpressure" modification form, which is written as: As indicated, the main parameter that has the great effect on the Fetkovich's model is the oil mobility as a function of the average reservoir pressure, which assumed to be a linear relationship as illustrated in Fig.

Table 1- Constants for Sukarno and Wisnogroho boi b1i b2i b3i ao 1. They started from the basic principle of mass balance with the pseudo-steady state solution to develop the following analytically IPR correlation: The major problem in applying the Wiggins's analytical IPR is its requirement for the mobility derivatives as a function of average reservoir pressure, which is very difficult in practice. Therefore, in Wiggins6 developed the empirical IPR equations that previously presented i.

An example to the oil mobility-pressure profile that is presented by Wiggins, et al. SPE 5 Fig. In this model, a second-degree polynomial IPR is obtained with a variable coefficient vor the oil IPR parameter that may in fact be a strong function of pressure and saturation. The starting point for this development is the pseudo-pressure formulation for the oil phase, which is given as: Future Inflow Performance Relationship In the absence of saturation data as a function of reservoir pressure, three simple methods can be used to predict future inflow performance curves.

First Method Vogel's Method This method was provided by Vogel3 and provides a rough approximation of the future maximum oil flow rate qo, max f at the specified future average reservoir pressure pr f from the following equation: The relationship has the following mathematical form: In addition, they are not explicitly function of reservoir rock and fluid data, which are different from one reservoir to another.

On the other hand, the analytical correlations suffer from their difficulty to be applied due to its requirement to the oil mobility profiles and its derivatives in addition to the assumptions used in their development. Therefore, the relationship between the oil mobility function and the average reservoir pressure should be accurately determined. In addition, the most common equation that represents a basic start point for the development of any IPR equation, in case of solution gas drive reservoirs is Eq.

Most of the perviously empirical derived IPR equations did not take into their consideration the whole effect of the oil mobility function, this in turn largely reduce the accuracy, power, and utility of these equations.

### Inflow Performance Relationships for Solution-Gas Drive Wells - OnePetro

Even though the models that took into their consideration the effect of this function, such as the models of Fetkovich4 and Wiggins6, assumed the relationships between this function and pr, as the linear form and the third polynomial form for Fetkovich and Wiggins, respectively. In fact, these linear and polynomial forms do not accurately describe the general behavior of the oil mobility function with the average reservoir pressure with an accurate manner.

On the other hand, some of analytical derived IPR equations did not considered the effect of this function, except the models of Wiggins, et al.

Another parameter should be considered in the selecting of the IPR method, is the aspect of conducting the flow tests. It is evident that test costs have to be taken into consideration. Finally, the range of applicability will also influence the selecting of the IPR methods to predict the well performance.

Accordingly based on the literature survey in this work, it is necessary to: The reservoir simulation was used to investigate the shape and in turn the relationship between the oil mobility function and the average reservoir pressure.

**Lec 7: Inflow Performance Relationship (IPR)-I**

Then, a new IPR equation was derived based on the resulted oil mobility-pressure profile; this new IPR is mainly a function of the relationship between the oil mobility and the average reservoir pressure. Then, forty-seven field cases published cases were used to develop an empirical relationship between the oil mobility and average reservoir pressure.

SPE 7 Mobility-Reservoir Pressure Relationship Production rate and pressure results from six simulation cases were used to develop the inflow performance curves. Table 2 presents the ranges of reservoir, rock, and fluid parameters used in the six simulation cases.

The saturation and pressure information was also used to develop the mobility function profiles. The general simulation assumptions that were used in building the reservoir model can be summarized as follows: Results of the Simulator Fig.

The other five cases are shown in Appendix A, and the shapes of Fig.

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Therefore, based on the six simulation cases, a reciprocal relationship between the oil mobility function and the average reservoir pressure was assumed and gives an acceptable and good match with the calculated simulator data as shown in Fig. In this work, a new form for the oil mobility function at different values of the average reservoir pressure i. This reciprocal relationship was used as: The productivity index can be numerically calculated from the following developed equation: When the average reservoir pressure-range is less than or equal to psia the following relationship was developed: When the average reservoir pressure-range is greater than or equal to psia the following relationship was developed: Table 3- Constants of Eq.

Table 4 introduces the ranges of data used in the development of these two equations. Calculate qo, max using Eq.

Assume several values for pwf and calculate the corresponding qo using Eq. Generate the future inflow performance-curve by applying Eq. Gas specific gravity 0. Reservoir and well dimension: