The Dependence of Electrical Resistivity-Saturation Relationships on Multiphase Flow Instability

Table 3

Summary of the tank inclination angle (φ), pumping rate (𝑄), and fluid conductivity (𝜎_𝑤) for each of the 34 experiments. The corresponding characteristic numbers 𝐶_𝑎, 𝐵_𝑜 and 𝐵^∗_𝑜 are also given (pore size estimated as 0.414 × grain size following [23]).

Experiment index	1	2	3	4	5	6	7
Q (mL/min)	189	251	67	119	157	27	67
φ (degree)	90	90	90	90	90	90	90
𝜎𝑤 (μs/cm)	98	93	90.2	93.7	81.4	126	94.7
𝐵𝑜	1.65𝐸−02	1.65𝐸−02	1.65𝐸−02	1.65𝐸−02	1.65𝐸−02	1.65𝐸−02	1.65𝐸−02
𝐶𝑎	1.39𝐸−01	1.85𝐸−01	4.94𝐸−02	8.78𝐸−02	1.16𝐸−01	1.99𝐸−02	4.94𝐸−02
𝐵^∗𝑜	−1.23𝐸−01	−1.69𝐸−01	−3.30𝐸−02	−7.13𝐸−02	−9.94𝐸−02	−3.47𝐸−03	−3.30𝐸−02
Experiment index	8	9	10	11	12	13	14
Q (mL/min)	119	27	189	251	358	67	99
φ (degree)	90	90	90	90	90	90	90
𝜎𝑤 (μs/cm)	82	78.7	79.5	76.7	78.4	80.1	83.1
𝐵𝑜	1.65𝐸−02	1.65𝐸−02	1.65𝐸−02	1.65𝐸−02	1.65𝐸−02	1.65𝐸−02	1.65𝐸−02
𝐶𝑎	8.78𝐸−02	1.99𝐸−02	1.39𝐸−01	1.85𝐸−01	2.64𝐸−01	4.94𝐸−02	7.30𝐸−02
𝐵^∗𝑜	−7.13𝐸−02	−3.47𝐸−03	−1.23𝐸−01	−1.69𝐸−01	−2.48𝐸−01	−3.30𝐸−02	−5.66𝐸−02
Experiment index	15	16	17	18	19	20	21
Q (mL/min)	89	52	146	119	67	27	67
φ (degree)	90	90	90	90	90	90	90
𝜎𝑤 (μs/cm)	74.8	77.6	74.2	79	77.6	78.3	87
𝐵𝑜	1.65𝐸−02	1.65𝐸−02	1.65𝐸−02	1.65𝐸−02	1.65𝐸−02	1.65𝐸−02	1.65𝐸−02
𝐶𝑎	6.57𝐸−02	3.84𝐸−02	1.08𝐸−01	8.78𝐸−02	4.94𝐸−02	1.99𝐸−02	4.94𝐸−02
𝐵^∗𝑜	−4.92𝐸−02	−2.19𝐸−02	−9.13𝐸−02	−7.13𝐸−02	−3.30𝐸−02	−3.47𝐸−03	−3.30𝐸−02
Experiment index	22	23	24	25	26	27	28
Q (mL/min)	189	251	67	67	67	67	67
φ (degree)	90	90	30	30	30	0	45
𝜎𝑤 (μs/cm)	71.8	72.8	78	91.5	90	81.1	80.5
𝐵𝑜	1.65𝐸−02	1.65𝐸−02	8.23𝐸−03	8.23𝐸−03	8.23𝐸−03	0.00𝐸+00	1.16𝐸−02
𝐶𝑎	1.39𝐸−01	1.85𝐸−01	4.94𝐸−02	4.94𝐸−02	4.94𝐸−02	4.94𝐸−02	4.94𝐸−02
𝐵^∗𝑜	−1.23𝐸−01	−1.69𝐸−01	−4.12𝐸−02	−4.12𝐸−02	−4.12𝐸−02	−4.94𝐸−02	−3.78𝐸−02
Experiment index	29	30	31	32	33	34
Q (mL/min)	67	67	67	67	358	358
φ (degree)	15	60	60	60	90	90
𝜎𝑤 (μs/cm)	82.8	84	79.2	84.7	89.1	88.5
𝐵𝑜	4.26𝐸−03	1.42𝐸−02	1.42𝐸−02	1.42𝐸−02	1.65𝐸−02	1.65𝐸−02
𝐶𝑎	4.94𝐸−02	4.94𝐸−02	4.94𝐸−02	4.94𝐸−02	2.64𝐸−01	2.64𝐸−01
𝐵^∗𝑜	−4.52𝐸−02	−3.52𝐸−02	−3.52𝐸−02	−3.52𝐸−02	−2.48𝐸−01	−2.48𝐸−01