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In oil and gas industry, mud-pulse telemetry has been widely used to obtain directional data, drilling parameters, formation evaluation data and safety data, etc. Generally, the drilling mud in most current models was considered to be a single-phase fluid through which the mud pulses travel, despite the fact that the drilling mud is composed of two or more phases. In this article, a multiphase flow formula was proposed to calculate the mud-pulse velocity as mud solids and free-gas content change, and a mathematical model was put forward to simulate the dynamic-transmission behavior of the mud-pressure pulse or waves. Compared to conventional methods, the present model provides more accurate mud-pulse attenuation, and the dynamic-transmission behavior of drilling-mud pulses along well bores can also be easily examined. The model is valuable in improving the existing mud-pulse systems and developing new drilling-mud pulse systems.

In today’s drilling industry, the reliable two-way communication and data transmissionbetween the surface and bottom of the wellbore is required, where mud-pressure pulse telemetry has been employed as one of the most popular and low-cost methods. Besides, with the increasing complexity and cost of drilling system, oil and gasindustry has become more dependent on Measurement-While-Drilling (MWD) technology to monitor directional data, drilling parameters, formation evaluation sensors, and safety data. At present, the MWD technology mainly includes hardwired telemetry, electromagnetic and acoustic methods, intelligent drillstrings, fiber optics, etc. When MWD technology is applied, the mud stream inside the drill pipes is generally used as communication medium. In fact, as early as in 1929, the concept of using mud pulses traces was put forward as an effective method for transmitting information along the wellbore. After many years’ research, the first mud pulse system was developed in the 1960s and commercialized in the late 1970s [1-3]. Mud-pulse telemetry has obvious advantages in providing cost-effective data transfer and the closed-loop drilling [4-6], and how to maximize the data communication rate and transmission distance for mud-pulse telemetry has become an issue in the oil industry. On the other hand, the formation rock is almost completely destroyed during the drilling process, forming formation fragments of different sizes. Some other solids, such as barite, are alsocontained in the drilling mud to adjust and control

Although the propagation velocity of mud-pulse is affected by many parameters, it mainly depends on the composition of mud in regular drilling operations. The following is the input data for the calculation of the mud-pulse velocity, in which the influences of free gas and solids are taken into account. Drill pipe: OD=127mm, D=108.6mm, λ = 0.3, Kp = 2.1×105MPa. Environment parameter: p=30MPa, T=70°C. Solid phase: ρs = 2.66 × 103kg/m3, Ks = 1.62× 104MPa. Liquid phase: ρl=1 × 103kg/m3, Kl =2.04× 103MPa (water-base mud). Liquid phase: ρl = 870kg/m3, Kl =1.35× 103MPa (oil-base mud). Gas phase: ρg = 0.9kg/m3 (standard state), mThe results are shown in Figs. 4 and 5.Another example of analyzing the transmission behavior of mud-pulses along a wellbore is also given: Drilling mud: ρ = 1.20× 103kg/m3, μ = 5mPa•s, Q = 28l/s. Bit nozzles: two 8 mm and one 13 mm. Mud-pulse velocity: a = 1.2× 103m/s. Well depth: L = 3× 103m. Figure 6 shows the evolution of pressure at both the surface and the bottom of the well in the vicinity of the drill bit. With Eq. (8) and the input data, the variance of pressure with time can be plotted [14, 15].Based on the analysis above, the following conclusions can be obtained. (1) The magnitude of mud-pulse velocity in mud depends quantitatively on the density and compressibility. (2) A considerable delay of the mud-pulse signals, equal to the mud-pulse travel time in the wellbore, occurs between the surface and bottom. (3) The mud-pulse attenuation is very highcompared to the analogy of an nsulated electrical conductor or hardwire. (4) In regular drilling operations, the attenuation mainly increases with well depth, mud viscosity, and signal frequency. The model is valuable in improving the performance of existing mud-pulse systems and developing new drilling-mud pulse systems. To further validate the model, some field experiments are to be conducted in the future.