Multilateral Pressure-Transient Response
- Turhan Yildiz (Colorado School of Mines)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- March 2003
- Document Type
- Journal Paper
- 5 - 12
- 2003. Society of Petroleum Engineers
- 5.3.2 Multiphase Flow, 5.6.4 Drillstem/Well Testing, 1.6 Drilling Operations, 1.8 Formation Damage, 4.1.2 Separation and Treating, 2.2.2 Perforating, 4.1.5 Processing Equipment
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This study presents a 3D analytical model to analyze the transient flow into multilateral horizontal wells. The model considers arbitrary phasing angle, selective lateral completion, nonuniform formation damage around each lateral, and areal and vertical permeability anisotropy. Using the model, transient pressure, derivative, and rate distribution characteristics of multilateral horizontal wells are investigated. Flow regimes are examined. Asymptotic approximations for each flow regime and pseudoskin equation are provided.
A sensitivity study is carried out to identify the parameters controlling the transient pressure, derivative, and fractional rate responses. The sensitivity study includes the impact of lateral length, orientation, and number, formation anisotropy, and the degree of formation damage around the laterals. If all the laterals are put on production during the test, it is almost impossible to estimate principal permeabilities, their directions, and skin factors around each lateral by examining transient pressure and derivative responses only. When all the branches produce, the transient rate distribution is strongly controlled by the skin owing to formation damage. Therefore, if transient rate distribution data, as well as the pressure, is recorded during the test, nonuniqueness in the interpretation of test data may be minimized. Although it is more expensive and time-consuming, testing each lateral individually may provide more reliable estimates of formation properties and damage.
In recent years, multibranched wells have been proposed to improve hydrocarbon recovery and to accelerate production. Performance of horizontal wells with single and multiple laterals in anisotropic formations have been considered in several previous studies.1-4 It has been concluded that, even for a single horizontal well, areal permeability anisotropy could impact the well productivity significantly. Therefore, it is recommended that horizontal wells should be drilled perpendicular to the maximum permeability direction to maximize the primary recovery. If there exists a moderate areal permeability anisotropy in the reservoir, then, in the absence of frictional wellbore pressure, a single horizontal well drilled normal to maximum permeability direction may outperform a multilateral well with the same total drilled length.
Transient pressure behavior of single horizontal wells has been well documented.5 The complex well architecture of multilaterals differentiates them from the horizontal wells with a single lateral. Fluid streamlines in the reservoir may be significantly distorted by the existence of multiple fluid-flow entries in multibranched wells. This is also true for other complicated well geometries with multiple fluid entries, such as selectively completed vertical wells, selectively completed horizontal wells, perforated wells, inclined wells, and commingled horizontal wells. Refs. 6 through 12 present analytical solutions and analysis for pressure-transient response of the wells with multiple flow entries and complicated well architecture.
Several studies on the modeling and analysis of transient flow into dual-lateral and multilateral wells have also been presented in the literature.13-22 Karakas et al.13 was the first to investigate the transient pressure behavior of dual-lateral horizontal wells. They used a numerical simulator to predict the pressure response and analyze the field data from dual-lateral wells. Raghavan and Ambashta14 presented a semianalytical flow model to simulate the transient flow into multilateral wells. They identified the flow regimes and proposed asymptotic solutions for each flow regime. Ozkan et al.15 investigated the pressure and derivative characteristics of transient flow into dual-lateral wells in areally anisotropic formations. In a later study, Yildiz and Ozkan16 extended the dual-lateral well model to predict the transient flow into perforated vertical wells. The perforated well model of Ref. 16 can be adapted to examine the unsteady-state flow to multilateral wells. Larsen17 proposed an approximate semianalytical solution for the transient flow of fluids into multibranched wells in layered reservoirs. He divided each lateral into smaller segments and approximated each small branch segment as a fracture. Ding18 used the boundary integral method to model the transient flow into multilateral wells and discussed the computational issues. Ouyang and Aziz19 developed a semianalytical solution for flow into arbitrary well configurations and examined the flux distribution along each lateral.
All the theoretical models mentioned above require a prior knowledge of the principal permeability values, directions of areal principal permeabilities, azimuth angle between laterals and principal permeabilities, length and location of each branch, and degree of formation damage around each lateral. However, estimation of all three principal permeabilities, damage skin around each lateral, and directions of areal principal permeabilities from pressure transient data run in a multilateral is not warranted. As a matter of fact, even for a single horizontal well, the prediction of principal permeabilities from a single pressure test is rather difficult. 4 A set of multiple pressure tests of individual branches has been suggested as the remedy.20,21 Zhang and Dusseault20 described a procedure for the estimation of principal permeability magnitudes and orientations. Their procedure requires two sets of well test data from a dual-lateral horizontal well. Recently, Munoz et al.21 extended the procedure proposed by Zhang and Dusseault. The method suggested by Munoz et al.21 relies on the existence of linear flow regime on the transient pressure response of a single horizontal well. The method also requires a minimum of three well tests independently conducted in three different single horizontal wells with different azimuth angles from the principal areal permeability directions.
This study presents a computationally efficient semianalytical model for transient flow into multilaterals. The model is used to examine transient rate characteristics as well as pressure and pressure derivative. Three flow regimes are recognized. A sensitivity analysis is carried out to investigate the influences of wellbore storage, reservoir boundaries, permeability anisotropy, total drilled length, uneven distribution of lateral length, and nonuniform skin distribution on the characteristics of pressure, derivative, and rate distribution. It is shown that, in general, permeability anisotropy, total drilled length, uneven distribution of lateral length, and nonuniform skin have more recognizable features on transient rate response than on pressure or derivative response. Therefore, transient rate response of each lateral should be monitored to minimize nonuniqueness in test analysis.
Mathematical Model and Solution
The complicated geometry of multilateral wells requires a 3D model to simulate the transient flow into each branch. We will employ the solution procedures used in Refs. 15 and 16 to model the transient flow into multiple branches.
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