Wellbore storage effects have been identified to significantly smear the accuracy of evaluating reservoir productivity through the fluid outflow rate from the annulus during underbalanced drilling. Such effects have continuously introduced considerable errors in characterizing the reservoir during underbalanced drilling. Conceptually, due to the readily volume changing ability of the gas, wellbore storage becomes a determining factor during underbalanced drilling of a gas reservoir. Wellbore storage could either cause decrease (unloading effects) or increase (loading effects) in the annular gas density depending on the choke opening procedures. Correspondingly, annular fluid outflow rate is considerably affected. Since it is practically difficult to deduct the fluid flow rate due to the wellbore storage from the total fluid outflow rate, reducing the influence of wellbore effects on the evaluation of gas reservoir productivity is presented in this study. Volumetric production analysis at the wellbore-sand face is introduced through a mathematical modeling of inflow of gas bubbles into the wellbore. This mathematical modeling utilizes forces such as the viscous force, drilling fluid ejecting forces from the bit nozzles, buoyancy, interfacial tension, and gas reservoir forces for its analyses. Some analytical results that are overshadowed by wellbore storage are presented and supported by extensive experimental studies.


One of the derivable benefits from under-balanced drilling is the ability to evaluate the productivity of a reservoir during drilling operations.1 Other benefits include little to no invasive formation damage, higher penetration rate especially in hard rocks, and lower cost of drilling operations if under-balanced could consistently be maintained.2 However, from the real-time bottom-hole pressure measurements while drilling, it is obvious that continuous maintenance of under-balanced conditions at the bottom-hole is difficult. Pressure surges that occur during some subsidiary operations such as pipe connections and surveys tend to jeopardize the achievement of no invasive formation damage.3

From the recent literature, reservoir evaluation has been approached through the estimation of the reservoir fluids flow rates into the wellbore. Assumption of the reservoir fluid inflow rate being the difference in the drilling fluid surface injection rate and the fluid outflow rate from the annulus has consistently been used.4–10 So far, efforts in modeling reservoir fluid inflow have been concentrated on the oil inflow.4–10 These present approaches to production evaluation and characterization of gas formation recognize the important effects of wellbore phenomena, but have not been able to provide adequate means of reducing the influences. These wellbore phenomena include the gas bubble coalescence and breakage, and bubble expansion and compression that are not possible to practically quantify during bubble annular upward flow. Since the present approaches involve the comparison of the surface fluid injection rate with the annular outflow rate, the influence of these phenomena on the gas formation evaluation is inevitable.

Unfortunately, all of these wellbore phenomena causes additional annular flow rates that cannot be individually and practically measured, and thus, the reservoir fluid inflow rate at the bottom-hole cannot be practically modified for their influences. Not recognizing the impact of such additional annular flow rates could cause misjudgment of the inflow capabilities of the gas reservoir. In order to properly alleviate these effects on gas inflow analyzes, a volumetric production analysis at the wellbore-sand face contact is presented in this study.

The conduction of gas inflow analyzes have been similarly performed as the liquid inflow in the petroleum engineering sectors. Practically, gas inflow into a denser fluid system is bubbly in character while liquid inflow is streaky. It is, therefore, proper to mathematically couple the forces of the viscous, surface tension, inertia, and the buoyancy that are responsible for gas bubble formation or development to the drilling fluid ejecting forces from the bit nozzles and the reservoir forces in modeling gas inflow scenarios.

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