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Pressure Transient Analysis of Hydraulically Fractured Wells in Multilayered Reservoirs

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Pressure Transient Analysis of Hydraulically Fractured Wells in Multilayered Reservoirs.


New equations for bilinear, formation linear and pseudo-radial flow regimes in an infinite commingled fractured multilayered reservoir have been developed.

The equations have been extended to Tiab’s Direct Synthesis Technique that makes it easy to estimate the individual layer properties without type curve matching.

Regardless of the flow regime, the rate normalized pressure derivative with respect to the appropriate time function has been found analytically to be constant, which depicts a horizontal line on the derivative curve.

This precludes the need to calculate the slope as is conventionally done and aids in easy model diagnosis or system identification and estimation of layered parameters.

Dimensionless pressure and pressure derivative functions which were derived by Bennet et al1 for an infinite commingled fractured multilayered reservoir have been extended to Tiab’s Direct Synthesis Technique to evaluate the average fracture and layer properties without type curve matching.


1.1 Background of Study

Interpretation models cannot be used effectively in multilayered reservoir until a model has been identified for each layer. In multilayered reservoirs, the pressure and pressure derivative do not display the characteristics shapes and slopes of the individual layer model response.

This is because, the wellbore pressure is sensitive to the total system and hence pressure data alone cannot be used directly for layer model identification and subsequent estimation of layer properties.

Consequently, using parameters derived from pressure data alone to forecast production may lead to erroneous estimation of production.

Additionally, wellbore storage effect distorts pressure data which masks early flow regimes and inhibits the estimation of the layered properties.

Moreover, in multilayered reservoir, each layer contributes to production at varying rates at different times. In this regard, using the total flow rate at the surface to estimate the individual layer properties is erroneous.

It is necessary therefore to measure the flow rate of each layer downhole and use the layer flow rate with the pressure data for layer parameters estimation.

The pressure data and flow rate of the individual layers can be converted into an equivalent pressure response that would have been obtained if the well were producing at a constant flow rate.

Correspondents have shown that in many cases, zones in layered reservoir are stimulated individually, and the layers are then commingled3.


Bennett C.O., Camacho-V R.G., Reynolds A.C., Raghavan R. “Approximate Solutions for Fractured Wells Producing Layered Reservoirs”, SPEJ Oct. 1985

Bennett C.O., Raghavan R., Reynolds A.C., “Analysis of Finite Conductivity Fractures Intercepting Multilayer Commingled Reservoirs”, June

Camacho-V R.G., Raghavan R., Reynolds A.C., “ Response of Wells Producing Layered Reservoirs: Unequal Fracture Length”, SPE 12844, 1987

Cinco-Ley H., Samaniego F., “Transient Pressure Analysis of Fractured Wells”, SPE 7490, 1981

Britt L.K., and Bennett C.O. “Determination of Fracture Conductivity in Moderate- Permability Reservoirs Using Bilinear Flow Concepts” SPE 14165

Tiab D., Bettam Y., “Practical Interpretation of Pressure Tests of Hydraulically Fractured Wells in a Naturally Fractured Reservoir”, SPE 107013,

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