Modeling High-Angle Wells in Laminated Pay Reservoirs

Introduction Productivity improvement and acceleration projects have gained substantially from the success of horizontal well drilling technology. Successful placement of near-horizontal wells in difficult reservoir configurations has become routine. However, not all reservoir situations are amenable to horizontal drilling. Specifically, laminated reservoirs such as thinly bedded turbidites in the Gulf of Mexico (GOM) have been perceived as poor targets. Potentially large reserves are locked in these reservoirs. These laminated turbidite systems have near-zero vertical permeability at the Bouma sequence1 scale and extremely small kv/kh ratios kv/kh?0 at the full field, reservoir simulation grid-block scale. In general, a low well count helps minimize development costs. Highly deviated wells (80∘≤θw<90∘) cutting the entire sand package may make it possible to obtain both high field production rates and low well counts. Slanted wells have been known to improve productivity of wells with kv /kh?0. However, the slanted well model given by Cinco 2,3 does not predict any improvement in well productivity for such wells. This apparent paradox is reconciled in this paper. Bed thickness, well diameter, and well angle determine the geometric pseudoskin of these thin-bedded sequences. For wells that are nearly horizontal, a simple technique is introduced to calculate the geometric skin without complex modeling. The range of validity of this approximation was determined by comparison with fine-grid simulations. This paper provides a method to simulate a highly deviated well in a thin-bedded reservoir at field scale without the use of fine grids or local grid coarsening. These inflow relationships have been used to construct the well models for simulations of GOM reservoirs. A field example is presented with guidelines to determine the correct well kh as validated by a grid sensitivity study. Implications of Existing Slanted Well Solutions Thin-bedded turbidite reservoirs in the deep water Gulf of Mexico are currently being developed.4 These reservoirs are comprised of beds that are on the order of 0.25 in. thick and are separated by very low permeability shales. There are two ways to apply Cinco's2,3 slanted well solution to account for this heterogeneity to determine the potential productivity improvement for slanted wells. The first method treats the entire reservoir as an anisotropic system with zero vertical permeability, whereas the second method considers the thin beds explicitly. However, neither of these methods predict any productivity improvement. For the first method (in which the reservoir is modeled as having no vertical permeability, kv=0), the explanation for no improvement in productivity predicted from Cinco's slanted well solution is trivial. It follows from the definition of the anisotropic angle of slant, which becomes zero (as for a vertical well), for a zero vertical permeability reservoir. In the second method, Cinco's2,3 model is applied separately to each bed and the bed productivities are summed to determine the total well productivity. The productivity improvement due to well angle can be determined by examining Cinco's solution for vanishing bed thickness. Fig. 1 shows the geometric pseudoskin as a function of bed thickness normalized by the wellbore radius for various angles between zero and 88°. These results were generated using Cinco's slanted well solution. As the bed thickness approaches zero, the geometric pseudoskin also tends to zero indicating that the well performance will be unchanged compared with a vertical well. This is true for all deviation angles. The slanted well model generally considers a line source well with flux distributed evenly. To mimic the more realistic infinite-conductivity boundary condition, the uniform-flux solution is evaluated at a particular point on an equivalent wellbore. The particular point is located on the semiminor axis of the ellipse that is defined by the intersection of a horizontal plane with the cylindrical wellbore (Fig. 2). This point is located one wellbore radius away from the line source at a distance of either two-tenths or eight-tenths of the bed thickness from the lower bed boundary. When bed thickness tends to zero and there is no vertical component of flow, the particular point is the same point used to evaluate a line source solution for a vertical well in a porous medium of constant horizontal permeability. Thus, this solution indicates no productivity improvement when compared to vertical wells completed in thinly bedded reservoirs. We offer an alternative limiting solution. Highly Deviated Well Model for Thin Beds The limiting solution we offer considers the wellbore to be represented by a fracture at the bed-thickness level. The "fracture" length is governed by the well deviation angle. The intersection of a slanted wellbore with a bedding plane is an ellipse as depicted in Fig. 2(a). For high deviation angles (80∘≤θ<90∘), the size of this ellipse may be significant. The semiminor axis is rw and the semimajor axis is rw/cos(?). Fig. 2(b) is a plot of ellipses for various well angles. The axes of each ellipse have been normalized using the length of the semimajor axis to illustrate the aspect ratio of the ellipses. For well angles greater than 80°, an infinite-conductivity vertical fracture model that approximates an ellipse seems more applicable than the line source approximation.