Dispersion of cuttings-transport velocity limits the depth resolution of mud logging. This paper presents an approach to modeling the cuttings-lag-depth distribution caused by the dispersion of cuttings-transport velocity in directional drilling. The presented approach has the ability to evaluate quantitatively the uncertainty in the depth resolution of mud logging that is crucial for improving the lateral quality of reservoir characterization, which can be beneficial in shale oil and gas projects.

Introduction

Drill-cuttings analysis in mud logging provides actual information in real time about the formation being drilled. However, cuttings moving up the wellbore annulus generally are dispersed because of the dependence of cuttings-transport velocity on particle size (e.g., small particles are easily transported, and large particles may be transported at a small fraction of the drilling-fluid velocity) and the existence of radial distribution in drilling-fluid velocity. This dispersion of cuttings-transport velocity limits the depth resolution of mud logging. Collecting and analyzing small cuttings is the best technique to minimize the dispersion of cuttings-lag time or lag depth. At the same time, the dispersion of cuttings-transport velocity because of the radial distribution of drilling-fluid velocity is independent of particle size and cannot be eliminated from the collected cuttings.

In this attempt to model the cuttings-lag-depth distribution caused by the dispersion of cuttings-transport velocity in directional drilling, the depth resolution of mud logging in directional and horizontal wells is evaluated on the basis of cuttings-lag experiments and cuttings-lag-depth simulations using a developed model. The approach of cuttings-lag calculation is based on a previously developed complete physical model of transient cuttings-transport behavior in directional drilling. The lag distribution is modeled using the log-normal distribution probability density function. The parameters of the distribution function are determined by lag-time-measurement experiments for various hole-inclination angles using a large-scale cuttings-transport flow-loop apparatus.

Average-Cuttings-Lag-Depth Equation

Lag time is defined as the time required for drilling fluid, gas, or cuttings traveling from the bottomhole to the surface through the wellbore annulus. Lag depth is defined as the formation depth in which the cuttings sampled or collected at the surface originally existed. The drilling depth increases depending on the rate of penetration when the cuttings drilled at the lag depth are transported to the surface. The complete paper provides equations representing the relationship between current bit depth and lag depth and the lag-depth equation for consideration of cuttings-transport-velocity variation.

Cuttings-Lag Experiments

Cuttings-lag experiments were conducted with a cuttings-transport flow-loop apparatus. A modification was made to the original apparatus so that cuttings colored red can be separately fed into the flowline from a newly equipped small-cuttings hopper (Fig. 1). The experimental procedures were as follows:

• A sufficient amount of standard white ceramic balls (white cuttings) and, consequently, 4 L of red colored ceramic balls (red cuttings, corresponding to a formation thickness of approximately 31 cm) are fed into the flowline.
  • White cuttings are injected from a large injection hopper.
  • Red cuttings are injected from a newly equipped small injection hopper.
• White cuttings are fed at a rate corresponding to a penetration rate of 20 m/h.
• After flow in the test section reaches steady state, the cuttings feed is changed from white to red.
• After all 4 L of red cuttings are fed (confirmed by visual observation through transparent pipe installed upstream of the feeder), the cuttings feed is changed back to white.
• Sampling of cuttings begins when red cuttings are observed to return to the shale shaker.
  • Sampling intervals are 15 to 30 seconds, depending on the experimental condition.
• Sampling finishes when almost all red cuttings have returned.

Experimental conditions were determined on the basis of a typical shale-development project in order to simulate actual drilling situations. The rate of penetration was set at 20 m/h, drillpipe rotation was set to 45 rev/min, and pump rates were set to 40, 50, and 60 m³/h. Two types of drilling fluids, water and partially hydrolyzed polyacrylamide (PHPA) mud (0.15% PHPA solution) were used, and annulus inclination angles were set to 0, 30, 60 and 90°. In total, 24 cases were examined.

Representation of Cuttings-Lag Distribution on the Basis of Experimental Results

Modeling the time distribution of the cuttings amount returned at the surface or the distribution of lag depth in a purely physical manner is not easy. In this study, the authors assumed that the distribution of cuttings can be expressed approximately by a distribution function. Although the most typical distribution function may be the normal distribution function, few natural phenomena exactly follow the normal distribution.

From an example result from a PHPA mud case, the time distribution of collected cuttings appears to have a shape with a peak located at an early time, after which cuttings return continues and gradually decreases for a long period. To describe this kind of distribution, the log-normal distribution function is used.

Modeling of Lag-Depth Distribution for the Entire Well Depth

The experimentally obtained distribution function is for flow through a 10-m-long constant-geometry annulus. To obtain cuttings-lag distribution for an entire well depth, distribution functions need to be convoluted. The most convenient method for convolution is to use the Fourier transform. However, here the authors take the characteristic log-normal distribution probability density function into account so that the multiplication of the functions also forms the log-normal probability density function.

Experimental Results

The 68.2 and 95% confidence intervals of the log-normal distribution probability density function reveal that cuttings-lag time is not significantly distributed at hole inclination angles of less than 30°. However, the cuttings-lag time is widely distributed at high hole-inclination angles and low drilling-fluid-flow rates. Interestingly, the degree of cuttings-lag-time distribution is similar to the distribution of cuttings-transport difficulty or minimum fluid-flow rate.

Example Simulation Study

A model was set up on the basis of actual field data to perform further evaluation of lag-depth distribution for an entire well depth. The model well has two kickoff points at depths of approximately 1200 and 3000 m and reaches total depth at 4500 m. The well is a highly inclined well with a maximum hole-­inclination angle of approximately 70° below the second buildup section.

The behavior of lag depth remaining constant after making a connection in which drilling is stopped is simulated. Although the parameters of log-normal distribution probability density function are not yet determined exactly at this moment, the result shows almost a worst case. In this case, lag depth is distributed in a range of approximately 50 m.

Conclusions

The lag-depth distribution is modeled using the log-normal distribution probability density function. Lag-depth-simulation studies are also presented for a realistic model of a directional well on the basis of field data with consideration of variations in rate of penetration.

The significant finding is that cuttings sampled at the surface can be contaminated by cuttings originating from other unintended depths to a non-negligible extent compared with the typical sampling interval of 10 m. The tendency of smearing in the formations and depths from which the sampled cuttings originated would be significant if the high inclination or horizontal hole section were to exceed a certain length, depending on the rate of penetration.

The presented approach has the ability to evaluate quantitatively the uncertainty in the depth resolution of mud logging that is crucial for improving the lateral quality of reservoir characterization.

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